Study of Interaction Patterns in Primary School Children Network
Utsab Shrestha
May 25,2020
Steps to setup data
Step 1: Load the data in gephi
The files were in GEXF format. I loaded the files in gephi and explored different layouts to visualize the network data.
Step 3: Export the node and edge csv file from Gephi
Since I could not load the GEXF file in R, I had to export the edge and node files as CSV file from gephi and read the table in R and write as a graph file.
Step 3: Convert edge and node data into igraph
Step 4: Summary
Degree Distribution by Grade and Gender
### Heatmap of interactions by Grade 
### Data pre-processing
Degree Distribution Histogram
### Network properties
## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] 10## [1] 9Degree Boxplot by Grade
### Giant Components
## [1] 234## IGRAPH UN-- 234 1148 --
## + attr: name (v/c), Label (v/n), timeset (v/l), X0 (v/c), X1
## | (v/c), Age (v/n), Grade (v/c), Type (e/c), Id (e/n), Label
## | (e/l), timeset (e/l), Weight (e/n), X2 (e/n), X3 (e/n),
## | Calc.Weight (e/n)## [1] 235## IGRAPH UN-- 235 1328 --
## + attr: name (v/c), Label (v/n), timeset (v/l), X0 (v/c), X1
## | (v/c), Age (v/n), Grade (v/c), Type (e/c), Id (e/n), Label
## | (e/l), timeset (e/l), Weight (e/n), X2 (e/n), X3 (e/n),
## | Calc.Weight (e/n)Centrality Measures Corr Plot
### Betweeness and Closeness Distributon 
### ERGM Models
Model 1 for Day 1
simple model no mcmc stored
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3))
##
## Iterations: 6 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -3.29971 0.09937 0 < 1e-04 ***
## mix.X1.F.F 0.30291 0.11672 0 0.00946 **
## mix.X1.F.M -0.08278 0.11159 0 0.45822
## mix.X1.M.M 0.51647 0.11317 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 9448 on 27257 degrees of freedom
##
## AIC: 9456 BIC: 9489 (Smaller is better.)
### Model 2 added Age difference and MCMC burnin
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + absdiff("Age")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -0.85584 0.11355 0 <1e-04 ***
## mix.X1.F.F -0.98609 0.12690 0 <1e-04 ***
## mix.X1.F.M -1.38049 0.12180 0 <1e-04 ***
## mix.X1.M.M -0.74723 0.12358 0 <1e-04 ***
## absdiff.Age -1.13837 0.04038 0 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 8048 on 27256 degrees of freedom
##
## AIC: 8058 BIC: 8099 (Smaller is better.)Model 3
added Degree 1
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + degree(2:4) +
## degree(8:9) + absdiff("Age")
##
## Iterations: 4 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -0.79269 0.12165 0 < 1e-04 ***
## mix.X1.F.F -0.92745 0.12788 0 < 1e-04 ***
## mix.X1.F.M -1.35689 0.12719 0 < 1e-04 ***
## mix.X1.M.M -0.75709 0.12808 0 < 1e-04 ***
## degree2 2.11227 0.43478 0 < 1e-04 ***
## degree3 1.59528 0.35976 0 < 1e-04 ***
## degree4 1.27480 0.30049 0 < 1e-04 ***
## degree8 -0.86100 0.33498 0 0.01017 *
## degree9 -0.88450 0.31153 0 0.00453 **
## absdiff.Age -1.14815 0.04086 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 7984 on 27251 degrees of freedom
##
## AIC: 8004 BIC: 8086 (Smaller is better.)
### Model 4 updated degree(2:4) based on GOF from Model 3 and added gwesp
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + degree(2:4) +
## degree(8:9) + absdiff("Age") + gwesp(cutoff = 7)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -2.57449 0.14157 1 <1e-04 ***
## mix.X1.F.F -0.61957 0.09787 2 <1e-04 ***
## mix.X1.F.M -1.03755 0.10462 2 <1e-04 ***
## mix.X1.M.M -0.56446 0.09720 2 <1e-04 ***
## degree2 0.68043 0.40375 0 0.0919 .
## degree3 0.78350 0.43555 0 0.0721 .
## degree4 0.48634 0.45145 0 0.2814
## degree8 -0.74868 0.62571 0 0.2315
## degree9 -0.81530 0.55616 0 0.1427
## absdiff.Age -0.72378 0.02590 1 <1e-04 ***
## gwesp 0.51594 0.02432 0 <1e-04 ***
## gwesp.decay 1.31566 0.03398 1 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 7579 on 27249 degrees of freedom
##
## AIC: 7603 BIC: 7702 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 50000:5165000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 1993.991 85.432 2.66975 16.54264
## mix.X1.F.F 522.465 33.063 1.03323 4.61356
## mix.X1.F.M 709.263 42.547 1.32959 6.85926
## mix.X1.M.M 603.961 37.210 1.16280 4.44671
## degree2 4.781 2.187 0.06836 0.14928
## degree3 5.129 2.587 0.08083 0.28338
## degree4 4.176 2.386 0.07458 0.32020
## degree8 2.431 1.569 0.04904 0.07042
## degree9 2.754 1.655 0.05172 0.05783
## absdiff.Age 1240.912 76.248 2.38274 6.86244
## gwesp 4463.521 268.355 8.38610 49.36679
## gwesp.decay -2884.815 130.673 4.08354 24.39587
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 1813.6 1942.8 2002 2053 2140.0
## mix.X1.F.F 458.0 499.0 524 546 584.4
## mix.X1.F.M 625.6 680.8 709 740 787.4
## mix.X1.M.M 532.0 580.0 604 631 671.4
## degree2 1.0 3.0 5 6 9.0
## degree3 1.0 3.0 5 7 11.0
## degree4 0.0 2.0 4 6 9.0
## degree8 0.0 1.0 2 3 6.0
## degree9 0.0 2.0 3 4 6.0
## absdiff.Age 1079.2 1190.0 1241 1294 1386.7
## gwesp 3879.0 4300.5 4487 4657 4921.0
## gwesp.decay -3101.4 -2979.3 -2901 -2804 -2610.1
##
##
## Sample statistics cross-correlations:
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2
## edges 1.0000000 0.64854114 0.8473006 0.66909334 -0.34776211
## mix.X1.F.F 0.6485411 1.00000000 0.4125069 0.09486298 -0.24939066
## mix.X1.F.M 0.8473006 0.41250687 1.0000000 0.38999358 -0.30414068
## mix.X1.M.M 0.6690933 0.09486298 0.3899936 1.00000000 -0.21657916
## degree2 -0.3477621 -0.24939066 -0.3041407 -0.21657916 1.00000000
## degree3 -0.4791986 -0.33282169 -0.3939830 -0.30668792 0.11019782
## degree4 -0.5030838 -0.35440506 -0.4080000 -0.31108568 0.16934546
## degree8 -0.2700660 -0.16662641 -0.2320741 -0.18428319 0.06477757
## degree9 -0.1697598 -0.10636084 -0.1633089 -0.11039807 0.04748921
## absdiff.Age 0.8194284 0.49995212 0.6811516 0.58627193 -0.25891210
## gwesp 0.9827517 0.64829234 0.8339447 0.65144855 -0.31941027
## gwesp.decay -0.9627086 -0.61906952 -0.8130220 -0.64600436 0.37562961
## degree3 degree4 degree8 degree9 absdiff.Age
## edges -0.47919863 -0.50308376 -0.27006600 -0.16975981 0.8194284
## mix.X1.F.F -0.33282169 -0.35440506 -0.16662641 -0.10636084 0.4999521
## mix.X1.F.M -0.39398301 -0.40800002 -0.23207413 -0.16330886 0.6811516
## mix.X1.M.M -0.30668792 -0.31108568 -0.18428319 -0.11039807 0.5862719
## degree2 0.11019782 0.16934546 0.06477757 0.04748921 -0.2589121
## degree3 1.00000000 0.22482332 0.07107867 0.02340122 -0.3496623
## degree4 0.22482332 1.00000000 0.07399524 0.05081019 -0.3556496
## degree8 0.07107867 0.07399524 1.00000000 0.05703447 -0.1979823
## degree9 0.02340122 0.05081019 0.05703447 1.00000000 -0.1183437
## absdiff.Age -0.34966228 -0.35564960 -0.19798227 -0.11834366 1.0000000
## gwesp -0.44102066 -0.47915968 -0.28239490 -0.17741969 0.7699191
## gwesp.decay 0.49707056 0.51928048 0.26575648 0.16758550 -0.7969449
## gwesp gwesp.decay
## edges 0.9827517 -0.9627086
## mix.X1.F.F 0.6482923 -0.6190695
## mix.X1.F.M 0.8339447 -0.8130220
## mix.X1.M.M 0.6514485 -0.6460044
## degree2 -0.3194103 0.3756296
## degree3 -0.4410207 0.4970706
## degree4 -0.4791597 0.5192805
## degree8 -0.2823949 0.2657565
## degree9 -0.1774197 0.1675855
## absdiff.Age 0.7699191 -0.7969449
## gwesp 1.0000000 -0.9279204
## gwesp.decay -0.9279204 1.0000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2 degree3
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.9008796 0.8422287 0.8239322 0.8410396 0.3033610 0.3913391
## Lag 10000 0.8208001 0.7345352 0.7122471 0.7410395 0.2166939 0.3048311
## Lag 15000 0.7541697 0.6563672 0.6269672 0.6585687 0.2042927 0.3007758
## Lag 20000 0.6883340 0.5968886 0.5518889 0.5831834 0.1772719 0.2663521
## Lag 25000 0.6426112 0.5315558 0.4944206 0.5321341 0.1223783 0.2651056
## degree4 degree8 degree9 absdiff.Age gwesp
## Lag 0 1.0000000 1.00000000 1.000000000 1.0000000 1.0000000
## Lag 5000 0.3854949 0.07004986 0.050475523 0.7657024 0.8839421
## Lag 10000 0.3547671 0.13405949 0.062588166 0.6057205 0.7897196
## Lag 15000 0.3339432 0.04682326 -0.020676629 0.4896142 0.7199504
## Lag 20000 0.3025383 0.06597519 0.030875139 0.3967045 0.6551354
## Lag 25000 0.3236647 0.09748826 -0.003226675 0.3314613 0.6111442
## gwesp.decay
## Lag 0 1.0000000
## Lag 5000 0.9043520
## Lag 10000 0.8361846
## Lag 15000 0.7747848
## Lag 20000 0.7190098
## Lag 25000 0.6771558
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2 degree3
## 0.3971 0.6746 -0.4449 0.7307 -1.4091 -1.0110
## degree4 degree8 degree9 absdiff.Age gwesp gwesp.decay
## -1.0313 -1.0327 -0.3278 0.4542 0.4160 -0.4288
##
## Individual P-values (lower = worse):
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2 degree3
## 0.6913113 0.4999042 0.6563927 0.4649537 0.1587952 0.3120213
## degree4 degree8 degree9 absdiff.Age gwesp gwesp.decay
## 0.3024063 0.3017263 0.7430849 0.6496927 0.6774031 0.6680948
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
### Model 6 added Degree 9, nodematch for Grade and increased burnin computation This is much better model. MCMC statistics show some autocorrelation but the joint pvalue is better.
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + nodematch("X0") +
## degree(2:4) + degree(9)
##
## Iterations: 4 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -3.68843 0.08760 0 < 1e-04 ***
## mix.X1.F.F -0.42904 0.09784 0 < 1e-04 ***
## mix.X1.F.M -1.04572 0.09695 0 < 1e-04 ***
## mix.X1.M.M -0.26522 0.09314 0 0.00441 **
## nodematch.X0 3.94314 0.07686 0 < 1e-04 ***
## degree2 4.14135 0.33006 0 < 1e-04 ***
## degree3 2.95658 0.33088 0 < 1e-04 ***
## degree4 2.23026 0.29091 0 < 1e-04 ***
## degree9 -0.84032 0.31849 0 0.00833 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 6099 on 27252 degrees of freedom
##
## AIC: 6117 BIC: 6191 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 1e+05:20575000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 4096
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges -13.66382 91.473 1.42927 13.80263
## mix.X1.F.F -5.46997 30.855 0.48210 3.66628
## mix.X1.F.M -6.93506 37.769 0.59014 4.99763
## mix.X1.M.M -2.09766 27.852 0.43518 2.54928
## nodematch.X0 -8.74414 63.205 0.98758 9.28293
## degree2 0.75586 5.859 0.09154 0.84932
## degree3 0.91235 5.705 0.08914 0.81774
## degree4 1.16602 6.407 0.10012 0.81451
## degree9 -0.07227 3.259 0.05092 0.06986
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges -234.6 -66.25 2 50.00 129.6
## mix.X1.F.F -72.0 -25.00 -3 17.00 49.0
## mix.X1.F.M -93.0 -29.00 -2 20.00 55.0
## mix.X1.M.M -66.0 -20.00 0 17.00 46.0
## nodematch.X0 -162.0 -45.00 1 36.25 90.0
## degree2 -7.0 -3.00 0 4.00 15.0
## degree3 -8.0 -3.00 0 4.00 15.0
## degree4 -9.0 -3.25 0 5.00 16.0
## degree9 -6.0 -2.00 0 2.00 7.0
##
##
## Sample statistics cross-correlations:
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## edges 1.00000000 0.85775713 0.92400390 0.77151715 0.97567718
## mix.X1.F.F 0.85775713 1.00000000 0.75043524 0.47152503 0.84151366
## mix.X1.F.M 0.92400390 0.75043524 1.00000000 0.62203424 0.91914532
## mix.X1.M.M 0.77151715 0.47152503 0.62203424 1.00000000 0.75578202
## nodematch.X0 0.97567718 0.84151366 0.91914532 0.75578202 1.00000000
## degree2 -0.83441832 -0.73487368 -0.77051072 -0.60486427 -0.81447905
## degree3 -0.82723780 -0.72330528 -0.76458964 -0.61704506 -0.80854331
## degree4 -0.81875942 -0.71433137 -0.75141628 -0.62239090 -0.79804457
## degree9 0.05053908 0.07348491 0.05065768 -0.00826246 0.04504015
## degree2 degree3 degree4 degree9
## edges -0.8344183 -0.82723780 -0.8187594 0.05053908
## mix.X1.F.F -0.7348737 -0.72330528 -0.7143314 0.07348491
## mix.X1.F.M -0.7705107 -0.76458964 -0.7514163 0.05065768
## mix.X1.M.M -0.6048643 -0.61704506 -0.6223909 -0.00826246
## nodematch.X0 -0.8144790 -0.80854331 -0.7980446 0.04504015
## degree2 1.0000000 0.65407198 0.6260663 -0.13268049
## degree3 0.6540720 1.00000000 0.6033828 -0.09768586
## degree4 0.6260663 0.60338279 1.0000000 -0.09415660
## degree9 -0.1326805 -0.09768586 -0.0941566 1.00000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.9511848 0.9052019 0.8999225 0.8554150 0.9687199
## Lag 10000 0.9250263 0.8631506 0.8516169 0.7932068 0.9416796
## Lag 15000 0.9049214 0.8312281 0.8170676 0.7516522 0.9180119
## Lag 20000 0.8860790 0.8069029 0.7869850 0.7144684 0.8957487
## Lag 25000 0.8699562 0.7834487 0.7614632 0.6752455 0.8737800
## degree2 degree3 degree4 degree9
## Lag 0 1.0000000 1.0000000 1.0000000 1.00000000
## Lag 5000 0.7785616 0.7214853 0.7117399 0.05549559
## Lag 10000 0.7399260 0.7013840 0.6892196 0.07378195
## Lag 15000 0.7213618 0.6884767 0.6714934 0.04825174
## Lag 20000 0.7047914 0.6708178 0.6535243 0.02863306
## Lag 25000 0.6991061 0.6530943 0.6388633 0.03976281
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.5443 0.4658 0.6542 0.9741 0.5935
## degree2 degree3 degree4 degree9
## -0.6367 -0.4703 -0.5762 0.6156
##
## Individual P-values (lower = worse):
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.5862662 0.6413416 0.5129901 0.3300264 0.5528261
## degree2 degree3 degree4 degree9
## 0.5243065 0.6381238 0.5644464 0.5381821
## Joint P-value (lower = worse): 0.9940786 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
Model 1 for Day 2
Simple model to begin with
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodemix("X1") + nodematch("X0")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -6.56876 0.60448 0 < 1e-04 ***
## mix.X1.F.F 2.21000 0.60464 0 0.000258 ***
## mix.X1.F.M 1.81354 0.60285 0 0.002630 **
## mix.X1.M.M 2.56825 0.60450 0 < 1e-04 ***
## mix.X1.F.Unknown 2.61712 0.62282 0 < 1e-04 ***
## mix.X1.M.Unknown 2.62221 0.62233 0 < 1e-04 ***
## mix.X1.Unknown.Unknown NA 0.00000 0 NA
## nodematch.X0 4.08483 0.07257 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 6654 on 27487 degrees of freedom
##
## AIC: 6670 BIC: 6736 (Smaller is better.)Model 2 and 3
added age difference and nodemix for gender
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + absdiff("Age")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -1.12167 0.10696 0 <1e-04 ***
## mix.X1.F.F -0.71536 0.11890 0 <1e-04 ***
## mix.X1.F.M -0.98003 0.11338 0 <1e-04 ***
## mix.X1.M.M -0.47303 0.11663 0 <1e-04 ***
## absdiff.Age -0.96642 0.03418 0 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 9290 on 27490 degrees of freedom
##
## AIC: 9300 BIC: 9341 (Smaller is better.)
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + nodematch("X0") +
## absdiff("Age") + degree(2:5) + degree(8) + degree(12)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -1.26211 0.06646 0 <1e-04 ***
## mix.X1.F.F 0.14024 0.06037 0 0.0202 *
## mix.X1.F.M -0.13757 0.05911 0 0.0199 *
## mix.X1.M.M 0.47062 0.05744 0 <1e-04 ***
## nodematch.X0 2.97452 0.07566 1 <1e-04 ***
## absdiff.Age 0.29011 0.01011 0 <1e-04 ***
## degree2 14.61122 NA NA NA
## degree3 7.65666 NA NA NA
## degree4 4.82784 NA NA NA
## degree5 3.33014 NA NA NA
## degree8 -1.75119 NA NA NA
## degree12 0.11071 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 28109 on 27483 degrees of freedom
##
## AIC: 28133 BIC: 28232 (Smaller is better.)
## Sample statistics summary:
##
## Iterations = 1e+05:5215000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 10288 74.46 2.3269 6.071
## mix.X1.F.F 2177 35.91 1.1222 3.078
## mix.X1.F.M 3845 46.99 1.4683 3.588
## mix.X1.M.M 2501 36.98 1.1556 3.443
## nodematch.X0 1150 14.56 0.4551 1.771
## absdiff.Age 25710 200.94 6.2795 18.388
## degree2 -10 0.00 0.0000 0.000
## degree3 -8 0.00 0.0000 0.000
## degree4 -10 0.00 0.0000 0.000
## degree5 -14 0.00 0.0000 0.000
## degree8 -8 0.00 0.0000 0.000
## degree12 -9 0.00 0.0000 0.000
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 10146 10238 10289 10337 10434
## mix.X1.F.F 2105 2153 2177 2201 2249
## mix.X1.F.M 3752 3814 3844 3879 3938
## mix.X1.M.M 2430 2475 2502 2526 2576
## nodematch.X0 1124 1140 1150 1161 1181
## absdiff.Age 25325 25576 25706 25843 26117
## degree2 -10 -10 -10 -10 -10
## degree3 -8 -8 -8 -8 -8
## degree4 -10 -10 -10 -10 -10
## degree5 -14 -14 -14 -14 -14
## degree8 -8 -8 -8 -8 -8
## degree12 -9 -9 -9 -9 -9
##
##
## Sample statistics cross-correlations:
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## edges 1.0000000 0.54110445 0.63901830 0.49683419 0.12757846
## mix.X1.F.F 0.5411044 1.00000000 0.04170776 0.06302899 0.08773853
## mix.X1.F.M 0.6390183 0.04170776 1.00000000 -0.02088295 0.04121998
## mix.X1.M.M 0.4968342 0.06302899 -0.02088295 1.00000000 0.12425320
## nodematch.X0 0.1275785 0.08773853 0.04121998 0.12425320 1.00000000
## absdiff.Age 0.7620371 0.36743234 0.36642576 0.35916330 -0.11559052
## degree2 NA NA NA NA NA
## degree3 NA NA NA NA NA
## degree4 NA NA NA NA NA
## degree5 NA NA NA NA NA
## degree8 NA NA NA NA NA
## degree12 NA NA NA NA NA
## absdiff.Age degree2 degree3 degree4 degree5 degree8 degree12
## edges 0.7620371 NA NA NA NA NA NA
## mix.X1.F.F 0.3674323 NA NA NA NA NA NA
## mix.X1.F.M 0.3664258 NA NA NA NA NA NA
## mix.X1.M.M 0.3591633 NA NA NA NA NA NA
## nodematch.X0 -0.1155905 NA NA NA NA NA NA
## absdiff.Age 1.0000000 NA NA NA NA NA NA
## degree2 NA 1 NA NA NA NA NA
## degree3 NA NA 1 NA NA NA NA
## degree4 NA NA NA 1 NA NA NA
## degree5 NA NA NA NA 1 NA NA
## degree8 NA NA NA NA NA 1 NA
## degree12 NA NA NA NA NA NA 1
##
## Sample statistics auto-correlation:
## Chain 1
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.7435861 0.7651016 0.7128441 0.7973492 0.8759881
## Lag 10000 0.5630193 0.6035315 0.5284366 0.6337419 0.7704237
## Lag 15000 0.4224339 0.4605978 0.3677002 0.4961827 0.6711204
## Lag 20000 0.3164321 0.3457924 0.2691034 0.4018330 0.5953178
## Lag 25000 0.2353476 0.2733610 0.2001352 0.3189354 0.5164186
## absdiff.Age degree2 degree3 degree4 degree5 degree8 degree12
## Lag 0 1.0000000 NaN NaN NaN NaN NaN NaN
## Lag 5000 0.7909311 NaN NaN NaN NaN NaN NaN
## Lag 10000 0.6268851 NaN NaN NaN NaN NaN NaN
## Lag 15000 0.4979887 NaN NaN NaN NaN NaN NaN
## Lag 20000 0.4193958 NaN NaN NaN NaN NaN NaN
## Lag 25000 0.3498309 NaN NaN NaN NaN NaN NaN
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.8993 0.4526 0.4244 -0.1207 -0.7585
## absdiff.Age degree2 degree3 degree4 degree5
## 2.2353 NaN NaN NaN NaN
## degree8 degree12
## NaN NaN
##
## Individual P-values (lower = worse):
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.36847482 0.65086571 0.67130254 0.90392120 0.44814787
## absdiff.Age degree2 degree3 degree4 degree5
## 0.02540091 NaN NaN NaN NaN
## degree8 degree12
## NaN NaN
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).Model 4
added Nodematch for Grade and Degrees based on GOF and also increased computational power
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0",
## diff = T) + absdiff("Age")
##
## Iterations: 6 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -5.03047 0.10436 0 < 1e-04 ***
## nodematch.X1.F 0.28886 0.08749 0 0.000963 ***
## nodematch.X1.M 0.74920 0.08435 0 < 1e-04 ***
## nodematch.X1.Unknown 0.30588 0.75447 0 0.685168
## nodematch.X0.1A 3.87557 0.16913 0 < 1e-04 ***
## nodematch.X0.1B 4.91508 0.14924 0 < 1e-04 ***
## nodematch.X0.2A 5.08792 0.15856 0 < 1e-04 ***
## nodematch.X0.2B 4.18506 0.14944 0 < 1e-04 ***
## nodematch.X0.3A 4.48412 0.15777 0 < 1e-04 ***
## nodematch.X0.3B 5.27094 0.17080 0 < 1e-04 ***
## nodematch.X0.4A 3.78439 0.18224 0 < 1e-04 ***
## nodematch.X0.4B 3.20159 0.21147 0 < 1e-04 ***
## nodematch.X0.5A 4.79063 0.16781 0 < 1e-04 ***
## nodematch.X0.5B 4.09425 0.16255 0 < 1e-04 ***
## nodematch.X0.Teachers 1.16924 1.27047 0 0.357412
## absdiff.Age 0.16816 0.02633 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 6465 on 27479 degrees of freedom
##
## AIC: 6497 BIC: 6629 (Smaller is better.)
### Model 5 AIC and BIC are still not looking good. P-values are not significant. GOF is not performing well
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0") +
## absdiff("Age")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -5.02913 0.10354 0 <1e-04 ***
## nodematch.X1.F 0.33879 0.08444 0 <1e-04 ***
## nodematch.X1.M 0.69893 0.08213 0 <1e-04 ***
## nodematch.X1.Unknown -1.90835 0.60111 0 0.0015 **
## nodematch.X0 4.42033 0.10093 0 <1e-04 ***
## absdiff.Age 0.17097 0.02618 0 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 6654 on 27489 degrees of freedom
##
## AIC: 6666 BIC: 6715 (Smaller is better.)
### Model 6 MCMC statistics have high correlations, and joint p-value is also 0.
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0") +
## absdiff("Age") + degree(1:5)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -1.44779 0.02836 0 <1e-04 ***
## nodematch.X1.F 0.32826 0.03589 0 <1e-04 ***
## nodematch.X1.M 0.46388 0.03680 0 <1e-04 ***
## nodematch.X1.Unknown -0.01960 0.24919 1 0.937
## nodematch.X0 2.87234 0.05881 1 <1e-04 ***
## absdiff.Age 0.20200 0.00702 0 <1e-04 ***
## degree1 15.87292 NA NA NA
## degree2 17.96196 NA NA NA
## degree3 12.06530 NA NA NA
## degree4 9.02377 NA NA NA
## degree5 4.53998 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 21444 on 27484 degrees of freedom
##
## AIC: 21466 BIC: 21556 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 1e+05:5215000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 8671.02 71.864 2.2458 5.967
## nodematch.X1.F 1989.81 34.564 1.0801 2.809
## nodematch.X1.M 2035.56 34.482 1.0776 2.926
## nodematch.X1.Unknown 53.56 4.058 0.1268 0.412
## nodematch.X0 1082.63 18.173 0.5679 2.341
## absdiff.Age 20157.12 224.372 7.0116 21.714
## degree1 -6.00 0.000 0.0000 0.000
## degree2 -10.00 0.000 0.0000 0.000
## degree3 -8.00 0.000 0.0000 0.000
## degree4 -10.00 0.000 0.0000 0.000
## degree5 -14.00 0.000 0.0000 0.000
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 8524 8626 8670 8718 8813
## nodematch.X1.F 1918 1967 1992 2015 2054
## nodematch.X1.M 1965 2014 2037 2060 2097
## nodematch.X1.Unknown 45 51 54 56 61
## nodematch.X0 1050 1070 1082 1095 1120
## absdiff.Age 19718 20011 20151 20310 20589
## degree1 -6 -6 -6 -6 -6
## degree2 -10 -10 -10 -10 -10
## degree3 -8 -8 -8 -8 -8
## degree4 -10 -10 -10 -10 -10
## degree5 -14 -14 -14 -14 -14
##
##
## Sample statistics cross-correlations:
## edges nodematch.X1.F nodematch.X1.M
## edges 1.0000000 0.506013821 0.50352757
## nodematch.X1.F 0.5060138 1.000000000 0.01715936
## nodematch.X1.M 0.5035276 0.017159359 1.00000000
## nodematch.X1.Unknown 0.0521729 -0.002297513 0.03169561
## nodematch.X0 0.2109071 0.073681715 0.16862869
## absdiff.Age 0.7277478 0.337087535 0.23001722
## degree1 NA NA NA
## degree2 NA NA NA
## degree3 NA NA NA
## degree4 NA NA NA
## degree5 NA NA NA
## nodematch.X1.Unknown nodematch.X0 absdiff.Age degree1
## edges 0.052172899 0.21090710 0.72774784 NA
## nodematch.X1.F -0.002297513 0.07368172 0.33708753 NA
## nodematch.X1.M 0.031695606 0.16862869 0.23001722 NA
## nodematch.X1.Unknown 1.000000000 0.03852014 0.09121932 NA
## nodematch.X0 0.038520143 1.00000000 -0.01723911 NA
## absdiff.Age 0.091219319 -0.01723911 1.00000000 NA
## degree1 NA NA NA 1
## degree2 NA NA NA NA
## degree3 NA NA NA NA
## degree4 NA NA NA NA
## degree5 NA NA NA NA
## degree2 degree3 degree4 degree5
## edges NA NA NA NA
## nodematch.X1.F NA NA NA NA
## nodematch.X1.M NA NA NA NA
## nodematch.X1.Unknown NA NA NA NA
## nodematch.X0 NA NA NA NA
## absdiff.Age NA NA NA NA
## degree1 NA NA NA NA
## degree2 1 NA NA NA
## degree3 NA 1 NA NA
## degree4 NA NA 1 NA
## degree5 NA NA NA 1
##
## Sample statistics auto-correlation:
## Chain 1
## edges nodematch.X1.F nodematch.X1.M nodematch.X1.Unknown
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.7516683 0.7422407 0.7609935 0.8267206
## Lag 10000 0.5801770 0.5547542 0.5915540 0.6732658
## Lag 15000 0.4603087 0.4180819 0.4811029 0.5453079
## Lag 20000 0.3534212 0.3060658 0.3883866 0.4302482
## Lag 25000 0.2528577 0.2418055 0.3192034 0.3312220
## nodematch.X0 absdiff.Age degree1 degree2 degree3 degree4 degree5
## Lag 0 1.0000000 1.0000000 NaN NaN NaN NaN NaN
## Lag 5000 0.8887010 0.8109793 NaN NaN NaN NaN NaN
## Lag 10000 0.7866424 0.6571145 NaN NaN NaN NaN NaN
## Lag 15000 0.7021136 0.5371072 NaN NaN NaN NaN NaN
## Lag 20000 0.6355066 0.4372619 NaN NaN NaN NaN NaN
## Lag 25000 0.5818446 0.3511194 NaN NaN NaN NaN NaN
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges nodematch.X1.F nodematch.X1.M
## 1.5226 0.3117 2.5783
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## 1.1857 0.4955 0.9459
## degree1 degree2 degree3
## NaN NaN NaN
## degree4 degree5
## NaN NaN
##
## Individual P-values (lower = worse):
## edges nodematch.X1.F nodematch.X1.M
## 0.127862755 0.755244733 0.009928507
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## 0.235735400 0.620244055 0.344178144
## degree1 degree2 degree3
## NaN NaN NaN
## degree4 degree5
## NaN NaN
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
### Model 7 Still the model does not perform well with updated degree
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0") +
## absdiff("Age") + degree(1:3) + gwesp(0.25, fixed = T)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges 100.92368 0.76745 0 <1e-04 ***
## nodematch.X1.F -14.39717 0.47522 2 <1e-04 ***
## nodematch.X1.M -9.95276 0.28433 4 <1e-04 ***
## nodematch.X1.Unknown 10.45895 5.90279 1 0.0764 .
## nodematch.X0 0.07386 0.21593 3 0.7323
## absdiff.Age -30.10102 0.16209 3 <1e-04 ***
## degree1 293.97616 2.58069 2 <1e-04 ***
## degree2 190.52786 2.44390 2 <1e-04 ***
## degree3 78.92477 7.25561 0 <1e-04 ***
## gwesp.fixed.0.25 1.37738 0.55530 0 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 749561 on 27485 degrees of freedom
##
## AIC: 749581 BIC: 749663 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 16384:1063936
## Thinning interval = 1024
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 1592.296 251.9596 7.873739 1.950e+02
## nodematch.X1.F -279.420 23.3252 0.728912 1.709e+01
## nodematch.X1.M 1660.910 6.0511 0.189096 1.916e+00
## nodematch.X1.Unknown -2.952 0.2435 0.007609 5.940e-02
## nodematch.X0 -475.146 44.7189 1.397465 3.030e+01
## absdiff.Age 2886.300 342.8155 10.712983 2.699e+02
## degree1 92.493 2.2645 0.070766 1.592e-01
## degree2 47.561 4.2033 0.131354 2.025e+00
## degree3 -4.979 0.1451 0.004533 5.369e-03
## gwesp.fixed.0.25 2018.375 325.7808 10.180649 2.513e+02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 1223 1406 1561 1797 2095.3
## nodematch.X1.F -310 -297 -285 -265 -231.0
## nodematch.X1.M 1649 1656 1662 1666 1671.0
## nodematch.X1.Unknown -3 -3 -3 -3 -2.0
## nodematch.X0 -551 -505 -469 -444 -387.6
## absdiff.Age 2383 2634 2852 3172 3567.4
## degree1 89 91 92 94 97.0
## degree2 40 44 48 51 55.0
## degree3 -5 -5 -5 -5 -5.0
## gwesp.fixed.0.25 1541 1775 1977 2283 2669.9
##
##
## Sample statistics cross-correlations:
## edges nodematch.X1.F nodematch.X1.M
## edges 1.00000000 0.99132684 -0.12526221
## nodematch.X1.F 0.99132684 1.00000000 -0.12641307
## nodematch.X1.M -0.12526221 -0.12641307 1.00000000
## nodematch.X1.Unknown 0.39885819 0.42486353 0.23910165
## nodematch.X0 0.98567530 0.96829408 -0.17575053
## absdiff.Age 0.99919003 0.98935111 -0.10005555
## degree1 -0.10033683 -0.09397505 0.01400860
## degree2 -0.83621179 -0.83215863 0.12988549
## degree3 0.02143553 0.03358081 -0.02118473
## gwesp.fixed.0.25 0.99998252 0.99131560 -0.12570837
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## edges 0.39885819 0.98567530 0.99919003
## nodematch.X1.F 0.42486353 0.96829408 0.98935111
## nodematch.X1.M 0.23910165 -0.17575053 -0.10005555
## nodematch.X1.Unknown 1.00000000 0.40156260 0.39339896
## nodematch.X0 0.40156260 1.00000000 0.98143866
## absdiff.Age 0.39339896 0.98143866 1.00000000
## degree1 -0.05702137 -0.09497544 -0.09039615
## degree2 -0.29938302 -0.83003889 -0.83923287
## degree3 -0.02913327 0.01103371 0.02204290
## gwesp.fixed.0.25 0.39884983 0.98571721 0.99913458
## degree1 degree2 degree3 gwesp.fixed.0.25
## edges -0.10033683 -0.83621179 0.02143553 0.9999825
## nodematch.X1.F -0.09397505 -0.83215863 0.03358081 0.9913156
## nodematch.X1.M 0.01400860 0.12988549 -0.02118473 -0.1257084
## nodematch.X1.Unknown -0.05702137 -0.29938302 -0.02913327 0.3988498
## nodematch.X0 -0.09497544 -0.83003889 0.01103371 0.9857172
## absdiff.Age -0.09039615 -0.83923287 0.02204290 0.9991346
## degree1 1.00000000 -0.44879370 0.04805910 -0.1022904
## degree2 -0.44879370 1.00000000 -0.07427729 -0.8351722
## degree3 0.04805910 -0.07427729 1.00000000 0.0215547
## gwesp.fixed.0.25 -0.10229039 -0.83517222 0.02155470 1.0000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges nodematch.X1.F nodematch.X1.M nodematch.X1.Unknown
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 1024 0.9967397 0.9963635 0.9806860 0.9520802
## Lag 2048 0.9934831 0.9927468 0.9608453 0.9041605
## Lag 3072 0.9902240 0.9891875 0.9416382 0.8562407
## Lag 4096 0.9869741 0.9856516 0.9214165 0.8083209
## Lag 5120 0.9836984 0.9820377 0.9025006 0.7604012
## nodematch.X0 absdiff.Age degree1 degree2 degree3
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.00000000
## Lag 1024 0.9957502 0.9968509 0.6612215 0.8981141 0.25673777
## Lag 2048 0.9915909 0.9936874 0.4575008 0.8353756 -0.02199897
## Lag 3072 0.9874383 0.9904848 0.3161060 0.7912070 -0.02202041
## Lag 4096 0.9832946 0.9872869 0.1794769 0.7482556 -0.02204185
## Lag 5120 0.9790890 0.9840394 0.1266253 0.7300598 0.02438925
## gwesp.fixed.0.25
## Lag 0 1.0000000
## Lag 1024 0.9967200
## Lag 2048 0.9934507
## Lag 3072 0.9901912
## Lag 4096 0.9869426
## Lag 5120 0.9836766
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges nodematch.X1.F nodematch.X1.M
## -4.2059 -3.7005 1.2851
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## -0.8431 -6.4607 -3.9156
## degree1 degree2 degree3
## 2.1624 8.9570 -0.4088
## gwesp.fixed.0.25
## -4.2399
##
## Individual P-values (lower = worse):
## edges nodematch.X1.F nodematch.X1.M
## 2.600980e-05 2.152092e-04 1.987610e-01
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## 3.991559e-01 1.042219e-10 9.019679e-05
## degree1 degree2 degree3
## 3.058421e-02 3.336467e-19 6.826770e-01
## gwesp.fixed.0.25
## 2.236109e-05
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).CUG test
High Assortativity on both Grade and Gender attributes. The Grade has higher assortativity so the assortativity is higher than random generated graphs.
## [1] 0.8271385## [1] 0.9335869
##
## Univariate Conditional Uniform Graph Test
##
## Conditioning Method: edges
## Graph Type:
## Diagonal Used: FALSE
## Replications: 1000
##
## Observed Value: 0.8271385
## Pr(X>=Obs): 0
## Pr(X<=Obs): 1
##
## Univariate Conditional Uniform Graph Test
##
## Conditioning Method: edges
## Graph Type:
## Diagonal Used: FALSE
## Replications: 1000
##
## Observed Value: 0.9335869
## Pr(X>=Obs): 0
## Pr(X<=Obs): 1QAP test
Assortativity test passes for QAP test also. High Assotativity for Grade than Gender. The nodes were not randomly assortative. 
##
## QAP Test Results
##
## Estimated p-values:
## p(f(perm) >= f(d)): 0
## p(f(perm) <= f(d)): 1
##
## Test Diagnostics:
## Test Value (f(d)): 0.8271385
## Replications: 1000
## Distribution Summary:
## Min: -0.07708173
## 1stQ: -0.02363722
## Med: -0.005516279
## Mean: -0.00421788
## 3rdQ: 0.01431553
## Max: 0.1021992
##
## QAP Test Results
##
## Estimated p-values:
## p(f(perm) >= f(d)): 0
## p(f(perm) <= f(d)): 1
##
## Test Diagnostics:
## Test Value (f(d)): 0.9335869
## Replications: 1000
## Distribution Summary:
## Min: -0.09729193
## 1stQ: -0.02399636
## Med: -0.004650142
## Mean: -0.004481402
## 3rdQ: 0.01362934
## Max: 0.1518945Conditional Probability For Grade Match, Male-Male, Female-Female, Male-Female Edges forming
Highest probability for Same grade nodes to form an edge
## Case edges nodemixFF nodemixFM nodemixMM nodematch.XO logodds
## 1 F-M 1 0 1 0 0 -4.7341445
## 2 F-F 1 1 0 0 0 -4.1174639
## 3 M-M 1 0 0 1 0 -3.9536443
## 4 Grade-Match 1 0 0 0 1 0.2547093
## cond_prob
## 1 0.008713375
## 2 0.016024789
## 3 0.018823536
## 4 0.563335289