Load packages

library(sna)
library(network)
library(ergm)
library(plotly)

## Warning: package 'plotly' was built under R version 3.6.2

library(data.table)
library(Bergm)

ERGM

With the convention that \(z(Y,X)\) is a vector of statistics calculated for the network \(X\) on node set \(V\), and \(\theta\) is a vector of statistical parameters, we can write any ERGM compactly as

\[ p_{\theta}(y)=\exp\left\{\theta^{\top}z(y,x) -\psi(\theta ) \right\} \]

The inner product will be a weighted sum of features \(\theta^{\top}z(y,x)=\sum_{s=1}^p \theta_s z_s(y,x)\), and \(\psi\) is a normalising constant to ensure that the probability \(p_\theta\) sums to 1 over all possbile networks \(y^{\prime}\).

Leave one out

In Koskinen et al. (2018) and outlier is defined on the level of the node and is called an outlier if the estimate \(\hat{\theta}^{(i)}_{\mathbf{ML}}\) of an ERGM for \(Y\) when \(i\) has been removed is different from the estimate \(\hat{\theta}_{\mathbf{ML}}\) based on the entire datset.

Read in the functions

source('https://raw.githubusercontent.com/johankoskinen/BayesERGM/main/ergm.gcd.R')

Test dataset

This is a network of members of the Revolutionary Organization 17 November group. We use the format as described in Koskinen et al. (2018).

temp <- tempfile()
download.file("https://raw.githubusercontent.com/johankoskinen/BayesERGM/main/data/greekAdjacent.txt",temp)
greekBomb<-  read.table(temp)# this two adjacency matrices stacked on top of each other in a text file
unlink(temp)
greekBomb[4,18] <- 1# an error in the dataset
greekBomb.net <- as.network( greekBomb , directed=FALSE)# translate the matrix to a network object
greekBomb.net

##  Network attributes:
##   vertices = 18 
##   directed = FALSE 
##   hyper = FALSE 
##   loops = FALSE 
##   multiple = FALSE 
##   bipartite = FALSE 
##   total edges= 46 
##     missing edges= 0 
##     non-missing edges= 46 
## 
##  Vertex attribute names: 
##     vertex.names 
## 
## No edge attributes

Plot it

plot( greekBomb.net )

Estimate model

est <- ergm( greekBomb.net ~ edges+
               altkstar(2, fixed=TRUE)+
               gwesp(log(2), fixed=TRUE),
             control=control.ergm(init=c(-1.4070,-1.1974,2.1890),
                                  MCMC.interval=5024))

## Starting Monte Carlo maximum likelihood estimation (MCMLE):

## Iteration 1 of at most 20:

## NOTE: Messages 'Error in mcexit(0L)...' may appear; please disregard them.

## Optimizing with step length 1.

## The log-likelihood improved by 0.007366.

## Step length converged once. Increasing MCMC sample size.

## Iteration 2 of at most 20:

## NOTE: Messages 'Error in mcexit(0L)...' may appear; please disregard them.

## Optimizing with step length 1.

## The log-likelihood improved by 0.001231.

## Step length converged twice. Stopping.

## Finished MCMLE.

## Evaluating log-likelihood at the estimate. Using 20 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .
## This model was fit using MCMC.  To examine model diagnostics and check
## for degeneracy, use the mcmc.diagnostics() function.

Check results

summary(est)

## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   greekBomb.net ~ edges + altkstar(2, fixed = TRUE) + gwesp(log(2), 
##     fixed = TRUE)
## 
## Iterations:  2 out of 20 
## 
## Monte Carlo MLE Results:
##                               Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges                          -1.3960     1.2713      0  -1.098   0.2722    
## altkstar.2                     -1.2110     0.4184      0  -2.894   0.0038 ** 
## gwesp.fixed.0.693147180559945   2.2131     0.4649      0   4.761   <1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 212.1  on 153  degrees of freedom
##  Residual Deviance: 150.9  on 150  degrees of freedom
##  
## AIC: 156.9    BIC: 166    (Smaller is better.)

Do MPNet-type convergence check

We can perform a Phase-3 simulation to recalculate

convergence.test(greekBomb.net ~ edges+
               altkstar(2, fixed=TRUE)+
               gwesp(log(2), fixed=TRUE),
                 ergm.est=est,# parameters are taked from the estimation
                 multiplication.factor=30)# this is the same multiplication factor as in MPNet

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: Use of 'statsonly=' argument has been deprecated. Use 'output='stats''
## instead.

##                                    coef        se convergence t      SACF
## edges                         -1.395982 1.2711596   -0.04003708 0.1836639
## altkstar.2                    -1.211027 0.4183779   -0.03628536 0.1859955
## gwesp.fixed.0.693147180559945  2.213067 0.4648084   -0.03389391 0.1787979

                # nsim= est$control$MCMC.samplesize is the default number of graphs in Phase 3, 
                # burnin= est$control$MCMC.burnin, is the default burnin for graphs in Phase 3,

If we compare the MPNet-like table with the statnet table, as well as the additional convergence statistics and SACF we can conclude

The standard errors only differ in the fourth decimal. Converngence t-statistics are all less than 0.1 in absolute value and the SACF is less than 0.4

Calculate the GCD

In the routines, the function ergm.gcd calculates the generalised Cooks distance \[ ||\hat{\theta}^{(i)}_{\mathbf{ML}}-\hat{\theta}_{\mathbf{ML}}||_{\Sigma} \] where \(\hat{\theta}^{(i)}_{\mathbf{ML}}\) is the MLE of the model where \(Y_{\mathrm{obs}}\) has been replaced with \(Y^{(i)}\), which has elements \((Y_{\mathrm{obs}})_{j,k}\) for \(j,k \in V \backslash \{i\}\), and the rows and columns for \(i\) set to NA.

The actual calculation is based on an approximation that does not require re-estimation of \(\hat{\theta}^{(i)}_{\mathbf{ML}}\). Instead, for each \(i \in V\), the ties \(Y_{ij}\) are simulated from the conditional model, conditional on \(Y_{jk}\), for \(j,k \in V \backslash \{i\}\). The difference \[ E_{\hat{\theta}_{\mathbf{ML}}} \left[ z(Y)|Y_{jk}=y_{jk},j,k \in V \backslash \{i\}\right]-z(Y_{\mathrm{obs}}) \] is then weighted together by an appropriate weight matrix.

GCD <- ergm.gcd(greekBomb.net ~ edges+
                  altkstar(2, fixed=TRUE)+
                  gwesp(log(2), fixed=TRUE),
                ergm.est=est)# the following elements have defaults taken from the estimation object

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Calculating GCD for actor:
## 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18

                #nsim= est$control$MCMC.samplesize,
                #burnin=est$control$MCMC.burnin,
                #thinning =est$control$MCMC.interval )       
# these defaults can be altered to make computations quicker or to increase precision

names(GCD)

## [1] "observed.stats" "expected.stats" "GCDMVP"

gcd.scores <- data.frame(edges=GCD$expected.stats[,1],altkstar.2=GCD$expected.stats[,2],gwesp = GCD$expected.stats[,3],gcd.mvp= GCD$GCDMVP)
fig <- plot_ly(gcd.scores, x = ~edges, y = ~altkstar.2, z = ~gwesp,
               marker = list(color = ~gcd.mvp, colorscale = c('#FFE1A1', '#683531'), showscale = TRUE))
fig <- fig %>% add_markers()
fig <- fig %>% layout(scene = list(xaxis = list(title = 'Edges'),
                                   yaxis = list(title = 'Altstar2'),
                                   zaxis = list(title = 'GWESP')),
                      annotations = list(
                        x = 1.13,
                        y = 1.05,
                        text = 'Generalised Cooks Dist',
                        xref = 'paper',
                        yref = 'paper',
                        showarrow = FALSE
                        ))
fig

## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

GCD$GCDMVP

##         V1         V2         V3         V4         V5         V6         V7 
## 2.83370200 0.81859831 1.07650195 1.08189227 0.17017831 0.24443105 0.08434240 
##         V8         V9        V10        V11        V12        V13        V14 
## 0.10426107 0.59794348 0.14832566 0.15057507 0.06139388 0.15517531 0.82375354 
##        V15        V16        V17        V18 
## 0.51367174 0.35777040 0.06748063 0.39894446

hist(GCD$GCDMVP)

Testing outlier score

While it is clear that one node node has a much higher influence score than others, we also know that we may end up with very high-degree nodes in graphs if the degree-distribution is skewed. So, how likely is it to get as high a score as 3.07?

We test this by a Monte Carlo by simulating \(Y^{(r)} \thicksim ERGM(\hat{\theta}_{\mathbf{ML}})\) and recalculating the GCD for all \(r=1,\ldots,R\).

Warning: this might take a while (also, Pavel broke some functionality so the current version is a bit slow)

MCMC.GCD.test <- test.gcd(greekBomb.net ~ edges+
                            altkstar(2, fixed=TRUE)+
                            gwesp(log(2), fixed=TRUE),
                          ergm.est=est,numreps=50,# number of replicate datasets used, R
                          nsim=1000,# number of samples of i's ties
                          burnin=100,# burnin for the samples of i's ties
                          thinning =1000,# thinning inbetween samples of i's ties
                          burnin.rep = 10000)# this is the burnin for replicate networks - probably should be large

## Calculating observed GCD for actor:

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 
##  Doing replicate number:

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 10

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 20

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 30

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 40

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## 50

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

Investigate results

The object MCMC.GCD.test has two main objects

names(MCMC.GCD.test)

## [1] "GCDobs"  "GCDReps"

Where GCDReps is the node by rep, \(n \times R\) matrix of GCD scores across the \(R\) simulated networks. You can investigate these in many ways but one convenient way is to use

test.gcd.plot(MCMC.GCD.test)

##    Actor     GCDVMP p-val
## 1     V1 2.82665434  0.98
## 2     V2 0.81735082  0.98
## 3     V3 1.06539741  0.98
## 4     V4 1.07041244  0.98
## 5     V5 0.17097431  1.00
## 6     V6 0.24822851  1.00
## 7     V7 0.07228699  1.00
## 8     V8 0.09965990  0.98
## 9     V9 0.57950159  1.00
## 10   V10 0.16170067  1.00
## 11   V11 0.15441298  1.00
## 12   V12 0.06058251  1.00
## 13   V13 0.15627456  1.00
## 14   V14 0.81104295  1.00
## 15   V15 0.51000088  1.00
## 16   V16 0.35000564  1.00
## 17   V17 0.06393147  0.98
## 18   V18 0.40952055  1.00

##    Actor     GCDVMP p-val
## 1     V1 2.82665434  0.98
## 2     V2 0.81735082  0.98
## 3     V3 1.06539741  0.98
## 4     V4 1.07041244  0.98
## 5     V5 0.17097431  1.00
## 6     V6 0.24822851  1.00
## 7     V7 0.07228699  1.00
## 8     V8 0.09965990  0.98
## 9     V9 0.57950159  1.00
## 10   V10 0.16170067  1.00
## 11   V11 0.15441298  1.00
## 12   V12 0.06058251  1.00
## 13   V13 0.15627456  1.00
## 14   V14 0.81104295  1.00
## 15   V15 0.51000088  1.00
## 16   V16 0.35000564  1.00
## 17   V17 0.06393147  0.98
## 18   V18 0.40952055  1.00

The vertical reference line is the maximum score and the horizontal like is the \(\Pr(S^{(n)}<k)\), where \(S^{(1)},\ldots,S^{(n)}\) are the ordered scores.

This is the CDF of the maximum GCD score - is our actor number 1 really extreme?

Lazega

Load the Lazega lawfirm partner data set (Lazega 2001).

temp <- tempfile()
download.file("https://www.stats.ox.ac.uk/~snijders/siena/LazegaLawyers.zip", temp)
LazLawer <- fread(unzip(temp, files = "ELwork36.dat"))
LasAtt <- fread(unzip(temp, files = "ELattr.dat"))
rm(temp)
LazLawer <- as.matrix(LazLawer)
senior <- LasAtt[,1]
sex <- LasAtt[,3]-1
office <- LasAtt[,4]
LazNet <- network(LazLawer, 
        directed = FALSE)
LazNet %v% "practice" <- LasAtt[,7]-1
LazNet %v% "senior" <- senior/36
LazNet %v% "sex" <- sex
LazNet %v% "office" <- office

Have a look

plot( LazNet  , 
               vertex.cex = degree(LazNet,gmode="digraph" )/max(degree(LazNet,gmode="digraph" ))+1,
      vertex.col =  "practice", edge.col='grey')

Estimate model

m3 <- ergm(LazNet  ~ edges 
        + nodecov("practice")
        + nodecov("senior")
         + match("practice")
         + match("sex") 
         + match("office")
        + gwesp(0.7781, fixed = TRUE),control=control.ergm(MCMC.samplesize=5000,MCMC.interval=5000))

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: `set_attrs()` is deprecated as of rlang 0.3.0
## This warning is displayed once per session.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

Inspect results

summary(m3)

## 
## ==========================
## Summary of model fit
## ==========================
## 
## Formula:   LazNet ~ edges + nodecov("practice") + nodecov("senior") + match("practice") + 
##     match("sex") + match("office") + gwesp(0.7781, fixed = TRUE)
## 
## Iterations:  2 out of 20 
## 
## Monte Carlo MLE Results:
##                    Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges               -6.5065     0.5790      0 -11.238  < 1e-04 ***
## nodecov.practice     0.4091     0.1160      0   3.526 0.000422 ***
## nodecov.senior       0.8517     0.2368      0   3.597 0.000322 ***
## nodematch.practice   0.7591     0.1948      0   3.897  < 1e-04 ***
## nodematch.sex        0.7011     0.2544      0   2.756 0.005849 ** 
## nodematch.office     1.1452     0.1945      0   5.887  < 1e-04 ***
## gwesp.fixed.0.7781   0.8982     0.1474      0   6.094  < 1e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 873.4  on 630  degrees of freedom
##  Residual Deviance: 457.6  on 623  degrees of freedom
##  
## AIC: 471.6    BIC: 502.7    (Smaller is better.)

Check convergence

convergence.test(LazNet  ~ edges + 
                   nodecov("practice")+ 
                   nodecov("senior")+ 
                   match("practice")+ 
                   match("sex") + 
                   match("office")+
                   gwesp(0.7781, fixed = TRUE),
                 ergm.est=m3,# parameters are taked from the estimation
                 multiplication.factor=30,# this is the same multiplication factor as in MPNet
                 nsim= 1000)

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

##                          coef        se convergence t       SACF
## edges              -6.5064845 0.5789576    0.03990178 0.06182609
## nodecov.practice    0.4091122 0.1160368    0.01516211 0.04673909
## nodecov.senior      0.8517138 0.2367810    0.04011018 0.05001454
## nodematch.practice  0.7591331 0.1947709    0.04858649 0.05973165
## nodematch.sex       0.7010655 0.2543587    0.05527992 0.08245520
## nodematch.office    1.1452017 0.1945311    0.02208252 0.03178745
## gwesp.fixed.0.7781  0.8982200 0.1473822    0.03015685 0.04965234

Calculate outlier scores

GCD <- ergm.gcd(LazNet  ~ edges + 
                   nodecov("practice")+ 
                   nodecov("senior")+ 
                   match("practice")+ 
                   match("sex") + 
                   match("office")+
                   gwesp(0.7781, fixed = TRUE),
                ergm.est=m3,
                nsim= 1000,
                burnin=3000,
                thinning = 100)       

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Calculating GCD for actor:
## 1

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 2

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 3

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 4

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 5

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 6

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 7

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 8

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 9

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 10

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 11

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 12

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 13

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 14

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 15

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 16

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 17

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 18

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 19

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 20

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 21

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 22

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 23

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 24

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 25

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 26

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 27

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 28

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 29

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 30

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 31

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 32

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 33

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 34

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 35

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## 36

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'nodecov' in package 'ergm': Network size or bipartite group
## size is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

## Warning: In term 'match' in package 'ergm': Network size or bipartite group size
## is not a multiple of the length of vertex attributes.

# these defaults can be altered to make computations quicker or to increase precision

Inspect the scores for Lazega

The scores

GCD$GCDMVP

##         V1         V2         V3         V4         V5         V6         V7 
## 0.05343509 0.13048144 0.08943292 0.10657638 0.27238258 0.10862898 0.27606511 
##         V8         V9        V10        V11        V12        V13        V14 
## 0.14896399 0.27494553 0.68825687 0.08230309 0.24154105 0.15851463 0.05259329 
##        V15        V16        V17        V18        V19        V20        V21 
## 2.02963389 0.27821151 0.34367830 0.24191925 0.04896191 0.01532272 0.15439221 
##        V22        V23        V24        V25        V26        V27        V28 
## 0.28566681 0.24415972 0.21340499 0.19182691 0.45348481 0.21059930 0.77450609 
##        V29        V30        V31        V32        V33        V34        V35 
## 0.65317627 0.10927788 0.84476593 0.47289100 0.23979224 0.28360862 0.32845855 
##        V36 
## 0.45118797

should be the same as in column MDMVP in Table 2 in Koskinen et al. (2018).

gcd.scores <- data.frame(edges=GCD$expected.stats[,1],altkstar.2=GCD$expected.stats[,6],gwesp = GCD$expected.stats[,7],gcd.mvp= GCD$GCDMVP)
fig <- plot_ly(gcd.scores, x = ~edges, y = ~altkstar.2, z = ~gwesp,
               marker = list(color = ~gcd.mvp, colorscale = c('#FFE1A1', '#683531'), showscale = TRUE))
fig <- fig %>% add_markers()
fig <- fig %>% layout(scene = list(xaxis = list(title = 'Edges'),
                                   yaxis = list(title = 'Office hom'),
                                   zaxis = list(title = 'GWESP')),
                      annotations = list(
                        x = 1.13,
                        y = 1.05,
                        text = 'Generalised Cooks Dist',
                        xref = 'paper',
                        yref = 'paper',
                        showarrow = FALSE
                        ))
fig

Actor 15 clearly adds a lot of triangles and edges and does not contribute a lot to office match

Bayesian outliers

Load the florentine data set

data(florentine)

Run estimation

Just run the simulation with one chain

# Posterior parameter estimation:
p.flo <- bergm(flomarriage ~ edges + kstar(2),
               burn.in    = 50,
               aux.iters  = 500,
               main.iters = 1000)

##  > MCMC start

summary(p.flo)

## 
##  Posterior Density Estimate for Model: y ~ edges + kstar(2) 
##  
##                        Mean        SD    Naive SE Time-series SE
## theta1 (edges)  -1.29839753 0.7663665 0.012117318     0.06392302
## theta2 (kstar2) -0.08112078 0.1603257 0.002534972     0.01279014
## 
##                       2.5%       25%         50%         75%     97.5%
## theta1 (edges)  -2.6421648 -1.822519 -1.34665640 -0.79979027 0.2595328
## theta2 (kstar2) -0.4329601 -0.180103 -0.06702454  0.03486567 0.1891226
## 
##  Acceptance rate: 0.47 
##  
## 

Run outlier calculation

GCD <- ergm.gcd(flomarriage ~ edges + kstar(2),
                ergm.est=p.flo,
                nsim= 100,# 
                burnin=100,# this becomes the thinning in the Bayesian version
                thinning = 100)     

## ergm.est is bergm output, Bayesian GCD will be tried

## Warning: 'ergm.getmodel' is deprecated.
## Use 'ergm_model' instead.
## See help("Deprecated")

## Warning: 'ergm.getglobalstats' is deprecated.
## Use 'summary.ergm_model' instead.
## See help("Deprecated")

## Calculating GCD for actor:
## 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16