Competition Network Analysis Tutorial - Part 2
Code
Contents
- Part 1: Analyzing Example Network Data Sample
- Part 2: Goodness of Fit, Degeneracy, Estimation Algorithm
(You are here.) - Part 3: Adding and Cleaning New data
- Part 4: Computing Period Networks and Covariate Lists
- Part 5: Analyzing Your Network with Updated Data
Part 2: Goodness of Fit, Degeneracy, Estimation Algorithm
Continue using the R script amj_run_TERGM_tutorial_1.R.
Goodness of Fit (GOF)
Check goodness of fit for the following diagnostic statistics by simulating nsim number of random networks from model m0:
dspdyad-wise shared partnersespedge-wise shared partnersdegreedegree distributiongeodesicshortest path distribution
On the order of 1,000 to 10,000 networks should be sampled for reporting goodness of fit results, but for instruction we briefly simulate 30 per period.
gof0 <- gof(fit0, statistics=c(dsp, esp, deg, geodesic), nsim=30)
##
## Starting GOF assessment on a single computing core....
##
## Initial dimensions of the network and covariates:
## t=2 t=3 t=4 t=5 t=6 t=7 t=8
## nets (row) 180 180 180 180 180 180 180
## nets (col) 180 180 180 180 180 180 180
## memory (row) 180 180 180 180 180 180 180
## memory (col) 180 180 180 180 180 180 180
##
## All networks are conformable.
##
## Dimensions of the network and covariates after adjustment:
## t=2 t=3 t=4 t=5 t=6 t=7 t=8
## nets (row) 180 180 180 180 180 180 180
## nets (col) 180 180 180 180 180 180 180
## memory (row) 180 180 180 180 180 180 180
## memory (col) 180 180 180 180 180 180 180
##
## No 'target' network(s) provided. Using networks on the left-hand side of the model formula as observed networks.
## Simulating 30 networks from the following formula:
## nets[[1]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[1]])
## Simulating 30 networks from the following formula:
## nets[[2]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[2]])
## Simulating 30 networks from the following formula:
## nets[[3]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[3]])
## Simulating 30 networks from the following formula:
## nets[[4]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[4]])
## Simulating 30 networks from the following formula:
## nets[[5]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[5]])
## Simulating 30 networks from the following formula:
## nets[[6]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[6]])
## Simulating 30 networks from the following formula:
## nets[[7]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + edgecov(memory[[7]])
## 7 networks from which simulations are drawn were provided.
## Processing statistic: Dyad-wise shared partners
## Processing statistic: Edge-wise shared partners
## Processing statistic: Degree
## Processing statistic: Geodesic distances
print(gof0)
## Dyad-wise shared partners
## obs: mean median min max sim: mean median min max Pr(>z)
## 0 2.6815e+04 26890 23734 30776 2.7695e+04 27529 23360 31484 0.4762126
## 1 4.1563e+03 4294 972 6534 3.4573e+03 3760 556 6896 0.4697068
## 2 9.1171e+02 698 366 1456 7.8336e+02 661 130 1766 0.5246196
## 3 1.9686e+02 198 72 298 1.7090e+02 141 28 374 0.5320781
## 4 8.2857e+01 90 26 130 6.5771e+01 73 4 156 0.3239972
## 5 3.1143e+01 28 4 58 2.5724e+01 26 0 78 0.5430098
## 6 9.1429e+00 8 0 16 8.3524e+00 8 0 28 0.7849971
## 7 6.2857e+00 6 0 14 4.2381e+00 2 0 16 0.3638171
## 8 2.5714e+00 2 0 6 1.8952e+00 0 0 10 0.5446789
## 9 5.7143e-01 0 0 4 1.0571e+00 0 0 6 0.4332566
## 10 3.1429e+00 2 0 8 2.2381e+00 0 0 10 0.5161993
## 11 8.5714e-01 0 0 2 8.1905e-01 0 0 6 0.9291793
## 12 2.8571e-01 0 0 2 2.5714e-01 0 0 4 0.9246306
## 13 0.0000e+00 0 0 0 1.9048e-02 0 0 2 0.1577941
## 14 8.5714e-01 0 0 2 4.1905e-01 0 0 2 0.3226778
## 15 0.0000e+00 0 0 0 1.5238e-01 0 0 2 4.804e-05
## 16 0.0000e+00 0 0 0 0.0000e+00 0 0 0 1.0000000
## 17 0.0000e+00 0 0 0 2.3810e-01 0 0 2 2.735e-07
## 18 2.8571e-01 0 0 2 4.7619e-02 0 0 2 0.4374178
## 19 2.8571e-01 0 0 2 2.5714e-01 0 0 2 0.9244243
## 20 0.0000e+00 0 0 0 3.1429e-01 0 0 2 2.366e-09
## 21 2.8571e-01 0 0 2 1.7143e-01 0 0 2 0.7050653
## 22 5.7143e-01 0 0 2 8.5714e-02 0 0 2 0.2366290
## 23 2.8571e-01 0 0 2 2.7619e-01 0 0 2 0.9747830
## 24 2.8571e-01 0 0 2 4.6667e-01 0 0 2 0.5560331
## 25 8.5714e-01 0 0 2 2.8571e-01 0 0 4 0.2088791
## 26 0.0000e+00 0 0 0 1.1429e-01 0 0 2 0.0004607
## 27 0.0000e+00 0 0 0 2.8571e-02 0 0 2 0.0832610
## 28 0.0000e+00 0 0 0 0.0000e+00 0 0 0 1.0000000
##
## 0
## 1
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15 ***
## 16
## 17 ***
## 18
## 19
## 20 ***
## 21
## 22
## 23
## 24
## 25
## 26 ***
## 27 .
## 28
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
## Edge-wise shared partners
## obs: mean median min max sim: mean median min max Pr(>z)
## 0 150.85714 166 92 194 150.190476 157 72 206 0.9648816
## 1 167.14286 156 102 234 175.876190 178 64 300 0.7020008
## 2 84.57143 78 42 126 78.219048 72 18 146 0.6350366
## 3 62.85714 74 30 92 55.647619 49 18 120 0.4986991
## 4 32.85714 36 14 54 28.095238 30 2 70 0.4291294
## 5 18.57143 18 2 34 14.647619 13 0 48 0.4844099
## 6 7.14286 8 0 12 6.047619 6 0 24 0.6165301
## 7 4.57143 4 0 10 3.228571 2 0 12 0.4255438
## 8 1.71429 2 0 4 1.247619 0 0 6 0.5221666
## 9 0.57143 0 0 4 1.019048 0 0 6 0.4683639
## 10 3.14286 2 0 8 2.238095 0 0 10 0.5161993
## 11 0.57143 0 0 2 0.438095 0 0 6 0.7341107
## 12 0.00000 0 0 0 0.085714 0 0 4 0.0063706 **
## 13 0.00000 0 0 0 0.000000 0 0 0 1.0000000
## 14 0.00000 0 0 0 0.000000 0 0 0 1.0000000
## 15 0.00000 0 0 0 0.019048 0 0 2 0.1577941
## 16 0.00000 0 0 0 0.000000 0 0 0 1.0000000
## 17 0.00000 0 0 0 0.238095 0 0 2 2.735e-07 ***
## 18 0.28571 0 0 2 0.047619 0 0 2 0.4374178
## 19 0.28571 0 0 2 0.257143 0 0 2 0.9244243
## 20 0.00000 0 0 0 0.314286 0 0 2 2.366e-09 ***
## 21 0.28571 0 0 2 0.171429 0 0 2 0.7050653
## 22 0.57143 0 0 2 0.085714 0 0 2 0.2366290
## 23 0.28571 0 0 2 0.276190 0 0 2 0.9747830
## 24 0.28571 0 0 2 0.466667 0 0 2 0.5560331
## 25 0.85714 0 0 2 0.285714 0 0 4 0.2088791
## 26 0.00000 0 0 0 0.114286 0 0 2 0.0004607 ***
## 27 0.00000 0 0 0 0.028571 0 0 2 0.0832610 .
## 28 0.00000 0 0 0 0.000000 0 0 0 1.0000000
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
## Degree
## obs: mean median min max sim: mean median min max Pr(>z)
## 0 50.71429 46 12 105 55.8238095 53 11 110 0.7432710
## 1 45.00000 45 22 61 32.3761905 32 19 48 0.0810802 .
## 2 21.28571 24 14 26 26.9380952 28 10 44 0.0316864 *
## 3 18.28571 16 11 25 19.0714286 19 5 36 0.7410391
## 4 9.42857 9 7 12 11.1190476 11 1 22 0.0706291 .
## 5 11.42857 12 6 17 10.3476190 10 1 20 0.5105855
## 6 8.57143 10 4 12 7.8333333 7 0 17 0.5384777
## 7 2.00000 2 1 3 4.1047619 4 0 13 0.0001864 ***
## 8 3.71429 4 3 5 3.0380952 3 0 7 0.0572705 .
## 9 1.42857 2 0 2 1.9142857 2 0 6 0.1594537
## 10 1.00000 1 0 2 1.4095238 1 0 5 0.2407204
## 11 1.42857 1 1 2 1.1380952 1 0 6 0.2142620
## 12 0.42857 0 0 1 0.4190476 0 0 2 0.9644844
## 13 0.42857 0 0 1 0.3000000 0 0 2 0.5526279
## 14 0.28571 0 0 1 0.3285714 0 0 2 0.8268817
## 15 0.28571 0 0 1 0.3952381 0 0 2 0.5798620
## 16 0.00000 0 0 0 0.1523810 0 0 1 4.326e-09 ***
## 17 0.00000 0 0 0 0.1142857 0 0 2 1.426e-06 ***
## 18 0.28571 0 0 1 0.1095238 0 0 1 0.3783896
## 19 0.28571 0 0 1 0.0666667 0 0 1 0.2809840
## 20 0.14286 0 0 1 0.1285714 0 0 1 0.9244243
## 21 0.14286 0 0 1 0.1428571 0 0 2 1.0000000
## 22 0.57143 1 0 1 0.2904762 0 0 2 0.2166996
## 23 0.00000 0 0 0 0.1333333 0 0 1 4.698e-08 ***
## 24 0.00000 0 0 0 0.0714286 0 0 1 8.464e-05 ***
## 25 0.14286 0 0 1 0.0714286 0 0 1 0.6369134
## 26 0.14286 0 0 1 0.0952381 0 0 1 0.7521784
## 27 0.00000 0 0 0 0.1095238 0 0 1 8.745e-07 ***
## 28 0.28571 0 0 1 0.2476190 0 0 1 0.8448380
## 29 0.28571 0 0 1 0.1142857 0 0 1 0.3906779
## 30 0.00000 0 0 0 0.0142857 0 0 1 0.0832610 .
## 31 0.00000 0 0 0 0.0476190 0 0 1 0.0014252 **
## 32 0.14286 0 0 1 0.0666667 0 0 1 0.6149535
## 33 0.00000 0 0 0 0.0333333 0 0 1 0.0078449 **
## 34 0.00000 0 0 0 0.0047619 0 0 1 0.3184669
## 35 0.00000 0 0 0 0.0000000 0 0 0 1.0000000
## 36 0.00000 0 0 0 0.0000000 0 0 0 1.0000000
## 37 0.00000 0 0 0 0.0000000 0 0 0 1.0000000
## 38 0.00000 0 0 0 0.0047619 0 0 1 0.3184669
## 39 0.00000 0 0 0 0.1047619 0 0 1 1.559e-06 ***
## 40 0.14286 0 0 1 0.0285714 0 0 1 0.4552264
## 41 0.00000 0 0 0 0.0047619 0 0 1 0.3184669
## 42 0.00000 0 0 0 0.0000000 0 0 0 1.0000000
## 43 0.00000 0 0 0 0.0000000 0 0 0 1.0000000
## 44 0.28571 0 0 1 0.0809524 0 0 1 0.3108619
## 45 0.28571 0 0 1 0.1571429 0 0 1 0.5146501
## 46 0.00000 0 0 0 0.1238095 0 0 1 1.524e-07 ***
## 47 0.14286 0 0 1 0.1047619 0 0 1 0.8004085
## 48 0.00000 0 0 0 0.0428571 0 0 1 0.0025105 **
## 49 0.14286 0 0 1 0.0714286 0 0 1 0.6369134
## 50 0.14286 0 0 1 0.1714286 0 0 1 0.8501175
## 51 0.14286 0 0 1 0.1904762 0 0 1 0.7536980
## 52 0.28571 0 0 2 0.1047619 0 0 2 0.5508579
## 53 0.00000 0 0 0 0.0809524 0 0 1 2.724e-05 ***
## 54 0.00000 0 0 0 0.0095238 0 0 1 0.1577941
## 55 0.00000 0 0 0 0.0857143 0 0 1 1.542e-05 ***
## 56 0.14286 0 0 1 0.0571429 0 0 1 0.5722807
## 57 0.14286 0 0 1 0.0047619 0 0 1 0.3712110
## 58 0.00000 0 0 0 0.0000000 0 0 0 1.0000000
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
## Geodesic distances
## obs: mean median min max sim: mean median min max Pr(>z)
## 1 537.43 548 284 728 5.1929e+02 522 216 808 0.812902
## 2 5018.86 4948 1252 7936 4.1557e+03 4342 608 8254 0.462454
## 3 6750.86 5620 1542 11706 5.8890e+03 5059 980 12830 0.640328
## 4 4814.00 5046 1550 7518 3.9995e+03 3968 1032 7100 0.423672
## 5 471.71 536 116 812 8.7863e+02 974 68 1972 0.011941 *
## 6 82.00 14 0 278 2.5990e+02 255 0 836 0.005932 **
## 7 10.00 0 0 38 8.0190e+01 30 0 472 6.11e-08 ***
## 8 0.00 0 0 0 1.9952e+01 2 0 272 2.33e-10 ***
## 9 0.00 0 0 0 5.2286e+00 0 0 152 2.81e-05 ***
## 10 0.00 0 0 0 1.3619e+00 0 0 88 0.009096 **
## 11 0.00 0 0 0 2.9524e-01 0 0 32 0.074865 .
## 12 0.00 0 0 0 6.6667e-02 0 0 8 0.126931
## 13 0.00 0 0 0 9.5238e-03 0 0 2 0.318467
## 14 0.00 0 0 0 0.0000e+00 0 0 0 1.000000
## Inf 14535.14 15184 4164 26670 1.6411e+04 17087 3828 28052 0.631090
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
Plot GOF statistics for m0
plot(gof0)
Now compare the GOF for m1
gof1 <- gof(fit1, statistics=c(dsp, esp, deg, geodesic), nsim=30)
##
## Starting GOF assessment on a single computing core....
##
## Initial dimensions of the network and covariates:
## t=2 t=3 t=4 t=5 t=6 t=7 t=8
## nets (row) 180 180 180 180 180 180 180
## nets (col) 180 180 180 180 180 180 180
## memory (row) 180 180 180 180 180 180 180
## memory (col) 180 180 180 180 180 180 180
##
## All networks are conformable.
##
## Dimensions of the network and covariates after adjustment:
## t=2 t=3 t=4 t=5 t=6 t=7 t=8
## nets (row) 180 180 180 180 180 180 180
## nets (col) 180 180 180 180 180 180 180
## memory (row) 180 180 180 180 180 180 180
## memory (col) 180 180 180 180 180 180 180
##
## No 'target' network(s) provided. Using networks on the left-hand side of the model formula as observed networks.
## Simulating 30 networks from the following formula:
## nets[[1]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[1]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## Simulating 30 networks from the following formula:
## nets[[2]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[2]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## Simulating 30 networks from the following formula:
## nets[[3]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[3]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## Simulating 30 networks from the following formula:
## nets[[4]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[4]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## Simulating 30 networks from the following formula:
## nets[[5]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[5]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## Simulating 30 networks from the following formula:
## nets[[6]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[6]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## Simulating 30 networks from the following formula:
## nets[[7]] ~ edges + gwesp(0, fixed = T) + gwdegree(0, fixed = T) + nodematch("ipo_status", diff = F) + nodematch("state_code", diff = F) + nodecov("age") + absdiff("age") + nodecov("cent_deg") + edgecov(memory[[7]]) + nodecov("genidx_multilevel") + nodecov("cent_pow_n0_4") + absdiff("cent_pow_n0_4") + cycle(3) + cycle(4)
## 7 networks from which simulations are drawn were provided.
## Processing statistic: Dyad-wise shared partners
## Processing statistic: Edge-wise shared partners
## Processing statistic: Degree
## Processing statistic: Geodesic distances
print(gof1)
## Dyad-wise shared partners
## obs: mean median min max sim: mean median min max Pr(>z)
## 0 2.6815e+04 26890 23734 30776 2.6475e+04 25227 21022 31432 0.7812126
## 1 4.1563e+03 4294 972 6534 4.3773e+03 5625 600 8458 0.8167212
## 2 9.1171e+02 698 366 1456 9.8446e+02 991 130 2014 0.7169791
## 3 1.9686e+02 198 72 298 2.2584e+02 230 32 492 0.4910735
## 4 8.2857e+01 90 26 130 8.6505e+01 84 4 200 0.8287811
## 5 3.1143e+01 28 4 58 3.4676e+01 42 0 82 0.6901652
## 6 9.1429e+00 8 0 16 1.3457e+01 12 0 38 0.1716471
## 7 6.2857e+00 6 0 14 8.0476e+00 8 0 28 0.4362546
## 8 2.5714e+00 2 0 6 3.0857e+00 2 0 16 0.6471140
## 9 5.7143e-01 0 0 4 2.5429e+00 2 0 12 0.0125747
## 10 3.1429e+00 2 0 8 2.1810e+00 2 0 10 0.4900297
## 11 8.5714e-01 0 0 2 1.2381e+00 0 0 10 0.4002964
## 12 2.8571e-01 0 0 2 6.2857e-01 0 0 8 0.2891486
## 13 0.0000e+00 0 0 0 4.1905e-01 0 0 4 4.167e-10
## 14 8.5714e-01 0 0 2 3.5238e-01 0 0 6 0.2613795
## 15 0.0000e+00 0 0 0 3.1429e-01 0 0 4 2.010e-08
## 16 0.0000e+00 0 0 0 2.8571e-01 0 0 4 4.364e-08
## 17 0.0000e+00 0 0 0 2.6667e-01 0 0 4 1.409e-07
## 18 2.8571e-01 0 0 2 2.6667e-01 0 0 2 0.9495807
## 19 2.8571e-01 0 0 2 2.9524e-01 0 0 2 0.9747995
## 20 0.0000e+00 0 0 0 3.2381e-01 0 0 2 1.291e-09
## 21 2.8571e-01 0 0 2 2.7619e-01 0 0 2 0.9747830
## 22 5.7143e-01 0 0 2 1.6190e-01 0 0 2 0.3108619
## 23 2.8571e-01 0 0 2 1.9048e-01 0 0 4 0.7523925
## 24 2.8571e-01 0 0 2 2.5714e-01 0 0 4 0.9246306
## 25 8.5714e-01 0 0 2 4.0000e-01 0 0 4 0.3039967
## 26 0.0000e+00 0 0 0 3.6190e-01 0 0 4 1.364e-08
## 27 0.0000e+00 0 0 0 3.3333e-01 0 0 4 3.519e-08
## 28 0.0000e+00 0 0 0 1.0476e-01 0 0 2 0.0008101
## 29 0.0000e+00 0 0 0 4.7619e-02 0 0 2 0.0249929
## 30 0.0000e+00 0 0 0 3.8095e-02 0 0 2 0.0452374
## 31 0.0000e+00 0 0 0 9.5238e-03 0 0 2 0.3184669
## 32 0.0000e+00 0 0 0 9.5238e-03 0 0 2 0.3184669
## 33 0.0000e+00 0 0 0 0.0000e+00 0 0 0 1.0000000
##
## 0
## 1
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9 *
## 10
## 11
## 12
## 13 ***
## 14
## 15 ***
## 16 ***
## 17 ***
## 18
## 19
## 20 ***
## 21
## 22
## 23
## 24
## 25
## 26 ***
## 27 ***
## 28 ***
## 29 *
## 30 *
## 31
## 32
## 33
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
## Edge-wise shared partners
## obs: mean median min max sim: mean median min max Pr(>z)
## 0 150.85714 166 92 194 1.3926e+02 138 70 194 0.4542258
## 1 167.14286 156 102 234 1.6317e+02 169 60 284 0.8604042
## 2 84.57143 78 42 126 9.1562e+01 97 14 176 0.6043855
## 3 62.85714 74 30 92 5.8486e+01 50 18 120 0.6784580
## 4 32.85714 36 14 54 3.5238e+01 35 0 78 0.6899464
## 5 18.57143 18 2 34 1.9067e+01 20 0 48 0.9283142
## 6 7.14286 8 0 12 9.8095e+00 10 0 28 0.2493395
## 7 4.57143 4 0 10 6.5714e+00 6 0 24 0.2557805
## 8 1.71429 2 0 4 2.2571e+00 2 0 10 0.4681195
## 9 0.57143 0 0 4 2.2000e+00 2 0 10 0.0288333 *
## 10 3.14286 2 0 8 2.0667e+00 1 0 10 0.4420056
## 11 0.57143 0 0 2 1.2381e+00 0 0 10 0.1300864
## 12 0.00000 0 0 0 6.2857e-01 0 0 8 6.361e-11 ***
## 13 0.00000 0 0 0 4.1905e-01 0 0 4 4.167e-10 ***
## 14 0.00000 0 0 0 3.4286e-01 0 0 6 2.860e-07 ***
## 15 0.00000 0 0 0 2.6667e-01 0 0 4 3.660e-07 ***
## 16 0.00000 0 0 0 1.8095e-01 0 0 4 2.445e-05 ***
## 17 0.00000 0 0 0 1.3333e-01 0 0 2 0.0001490 ***
## 18 0.28571 0 0 2 1.1429e-01 0 0 2 0.5722807
## 19 0.28571 0 0 2 1.4286e-01 0 0 2 0.6369134
## 20 0.00000 0 0 0 2.3810e-01 0 0 2 2.735e-07 ***
## 21 0.28571 0 0 2 2.1905e-01 0 0 2 0.8248759
## 22 0.57143 0 0 2 1.4286e-01 0 0 2 0.2906634
## 23 0.28571 0 0 2 1.5238e-01 0 0 4 0.6595427
## 24 0.28571 0 0 2 2.3810e-01 0 0 4 0.8746005
## 25 0.85714 0 0 2 3.9048e-01 0 0 4 0.2948466
## 26 0.00000 0 0 0 3.6190e-01 0 0 4 1.364e-08 ***
## 27 0.00000 0 0 0 3.3333e-01 0 0 4 3.519e-08 ***
## 28 0.00000 0 0 0 1.0476e-01 0 0 2 0.0008101 ***
## 29 0.00000 0 0 0 4.7619e-02 0 0 2 0.0249929 *
## 30 0.00000 0 0 0 3.8095e-02 0 0 2 0.0452374 *
## 31 0.00000 0 0 0 9.5238e-03 0 0 2 0.3184669
## 32 0.00000 0 0 0 9.5238e-03 0 0 2 0.3184669
## 33 0.00000 0 0 0 0.0000e+00 0 0 0 1.0000000
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
## Degree
## obs: mean median min max sim: mean median min max Pr(>z)
## 0 50.71429 46 12 105 55.2714286 48.0 9 118 0.7702925
## 1 45.00000 45 22 61 38.9476190 38.0 22 58 0.3550056
## 2 21.28571 24 14 26 24.7238095 26.0 9 41 0.1469390
## 3 18.28571 16 11 25 16.6809524 17.0 2 34 0.5047365
## 4 9.42857 9 7 12 10.0619048 10.5 1 21 0.4557195
## 5 11.42857 12 6 17 9.5666667 9.0 1 21 0.2719355
## 6 8.57143 10 4 12 7.3523810 7.0 1 16 0.3205023
## 7 2.00000 2 1 3 4.3761905 4.0 0 10 6.348e-05 ***
## 8 3.71429 4 3 5 2.7523810 3.0 0 8 0.0140353 *
## 9 1.42857 2 0 2 1.8952381 2.0 0 4 0.1741906
## 10 1.00000 1 0 2 1.3380952 1.0 0 5 0.3231522
## 11 1.42857 1 1 2 0.9714286 1.0 0 5 0.0665010 .
## 12 0.42857 0 0 1 0.7238095 1.0 0 3 0.2010782
## 13 0.42857 0 0 1 0.5285714 0.0 0 4 0.6467909
## 14 0.28571 0 0 1 0.2809524 0.0 0 2 0.9805549
## 15 0.28571 0 0 1 0.3476190 0.0 0 2 0.7529167
## 16 0.00000 0 0 0 0.3714286 0.0 0 2 < 2.2e-16 ***
## 17 0.00000 0 0 0 0.1809524 0.0 0 1 1.108e-10 ***
## 18 0.28571 0 0 1 0.1428571 0.0 0 2 0.4710908
## 19 0.28571 0 0 1 0.1809524 0.0 0 2 0.5937300
## 20 0.14286 0 0 1 0.1190476 0.0 0 2 0.8744872
## 21 0.14286 0 0 1 0.2000000 0.0 0 2 0.7076634
## 22 0.57143 1 0 1 0.1476190 0.0 0 2 0.0811424 .
## 23 0.00000 0 0 0 0.1857143 0.0 0 2 5.591e-10 ***
## 24 0.00000 0 0 0 0.1285714 0.0 0 1 8.473e-08 ***
## 25 0.14286 0 0 1 0.1047619 0.0 0 1 0.8004085
## 26 0.14286 0 0 1 0.0619048 0.0 0 1 0.5934037
## 27 0.00000 0 0 0 0.1047619 0.0 0 1 1.559e-06 ***
## 28 0.28571 0 0 1 0.1714286 0.0 0 2 0.5613693
## 29 0.28571 0 0 1 0.1285714 0.0 0 1 0.4293359
## 30 0.00000 0 0 0 0.1619048 0.0 0 1 1.291e-09 ***
## 31 0.00000 0 0 0 0.0952381 0.0 0 1 4.921e-06 ***
## 32 0.14286 0 0 1 0.0666667 0.0 0 1 0.6149535
## 33 0.00000 0 0 0 0.0285714 0.0 0 1 0.0139540 *
## 34 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 35 0.00000 0 0 0 0.0142857 0.0 0 1 0.0832610 .
## 36 0.00000 0 0 0 0.0333333 0.0 0 1 0.0078449 **
## 37 0.00000 0 0 0 0.0428571 0.0 0 1 0.0025105 **
## 38 0.00000 0 0 0 0.0190476 0.0 0 1 0.0452374 *
## 39 0.00000 0 0 0 0.0380952 0.0 0 1 0.0044309 **
## 40 0.14286 0 0 1 0.0000000 0.0 0 0 0.3559177
## 41 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 42 0.00000 0 0 0 0.0047619 0.0 0 1 0.3184669
## 43 0.00000 0 0 0 0.0000000 0.0 0 0 1.0000000
## 44 0.28571 0 0 1 0.0047619 0.0 0 1 0.1785568
## 45 0.28571 0 0 1 0.0238095 0.0 0 1 0.2057271
## 46 0.00000 0 0 0 0.0428571 0.0 0 1 0.0025105 **
## 47 0.14286 0 0 1 0.0333333 0.0 0 1 0.4735323
## 48 0.00000 0 0 0 0.0380952 0.0 0 1 0.0044309 **
## 49 0.14286 0 0 1 0.0333333 0.0 0 1 0.4735323
## 50 0.14286 0 0 1 0.0428571 0.0 0 1 0.5116132
## 51 0.14286 0 0 1 0.0809524 0.0 0 1 0.6819897
## 52 0.28571 0 0 2 0.0714286 0.0 0 1 0.4822211
## 53 0.00000 0 0 0 0.1190476 0.0 0 2 2.018e-06 ***
## 54 0.00000 0 0 0 0.1047619 0.0 0 2 4.473e-06 ***
## 55 0.00000 0 0 0 0.1142857 0.0 0 2 7.778e-06 ***
## 56 0.14286 0 0 1 0.0904762 0.0 0 1 0.7284695
## 57 0.14286 0 0 1 0.0619048 0.0 0 2 0.5937159
## 58 0.00000 0 0 0 0.0523810 0.0 0 1 0.0008101 ***
## 59 0.00000 0 0 0 0.0380952 0.0 0 1 0.0044309 **
## 60 0.00000 0 0 0 0.0238095 0.0 0 1 0.0249929 *
## 61 0.00000 0 0 0 0.0761905 0.0 0 1 4.804e-05 ***
## 62 0.00000 0 0 0 0.0714286 0.0 0 2 0.0002294 ***
## 63 0.00000 0 0 0 0.0666667 0.0 0 1 0.0001490 ***
## 64 0.00000 0 0 0 0.0761905 0.0 0 2 0.0001314 ***
## 65 0.00000 0 0 0 0.0380952 0.0 0 1 0.0044309 **
## 66 0.00000 0 0 0 0.0333333 0.0 0 1 0.0078449 **
## 67 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 68 0.00000 0 0 0 0.0047619 0.0 0 1 0.3184669
## 69 0.00000 0 0 0 0.0190476 0.0 0 1 0.0452374 *
## 70 0.00000 0 0 0 0.0000000 0.0 0 0 1.0000000
## 71 0.00000 0 0 0 0.0047619 0.0 0 1 0.3184669
## 72 0.00000 0 0 0 0.0000000 0.0 0 0 1.0000000
## 73 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 74 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 75 0.00000 0 0 0 0.0047619 0.0 0 1 0.3184669
## 76 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 77 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 78 0.00000 0 0 0 0.0095238 0.0 0 1 0.1577941
## 79 0.00000 0 0 0 0.0000000 0.0 0 0 1.0000000
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
## Geodesic distances
## obs: mean median min max sim: mean median min max Pr(>z)
## 1 537.43 548 284 728 5.3544e+02 573 204 808 0.979255
## 2 5018.86 4948 1252 7936 5.3485e+03 6567 658 10568 0.776198
## 3 6750.86 5620 1542 11706 6.4890e+03 6130 952 13492 0.886231
## 4 4814.00 5046 1550 7518 3.2026e+03 3027 944 6400 0.138854
## 5 471.71 536 116 812 5.4467e+02 558 20 1294 0.559407
## 6 82.00 14 0 278 1.1897e+02 77 0 450 0.442898
## 7 10.00 0 0 38 1.9933e+01 2 0 256 0.191117
## 8 0.00 0 0 0 2.4381e+00 0 0 120 0.001334 **
## 9 0.00 0 0 0 2.3810e-01 0 0 8 0.005793 **
## 10 0.00 0 0 0 1.9048e-02 0 0 2 0.157794
## 11 0.00 0 0 0 0.0000e+00 0 0 0 1.000000
## Inf 14535.14 15184 4164 26670 1.5958e+04 15448 3150 28678 0.714688
##
## Note: Small p-values indicate a significant difference
## between simulations and observed network(s).
Plot GOF statistics for m1
plot(gof1)
Degeneracy
Check degeneracy of m0 with another sample of random networks based on model parameters (instead of the diagnostic statistics used for GOF above).
degen0 <- checkdegeneracy(fit0, nsim=30)
print(degen0)
##
## Degeneracy check for network 1:
## obs 2.5% 25% 50% 75% 97.5%
## edges 142.000 109.725 113.250 121.000 124.750 133.475
## gwesp.fixed.0 96.000 58.000 62.000 66.500 69.000 75.275
## gwdegree 75.000 70.450 75.500 78.000 82.000 85.275
## nodematch.ipo_status 142.000 108.725 113.250 121.000 124.000 133.475
## nodematch.state_code 19.000 11.000 13.000 14.000 16.000 17.275
## nodecov.age 2271.000 1842.175 1942.250 1984.500 2098.250 2369.850
## absdiff.age 1109.000 827.325 902.250 958.500 1056.000 1281.150
## edgecov.memory[[i]] 42.000 46.525 56.000 60.500 66.750 70.825
##
## Degeneracy check for network 2:
## obs 2.5% 25% 50% 75% 97.5%
## edges 158.000 164.175 170.250 174.500 179.750 185.275
## gwesp.fixed.0 104.000 99.450 104.750 109.000 112.750 119.000
## gwdegree 85.000 89.175 94.000 95.000 97.000 104.000
## nodematch.ipo_status 158.000 164.175 169.250 174.000 179.000 185.275
## nodematch.state_code 22.000 19.450 21.000 22.000 24.000 26.275
## nodecov.age 2735.000 2659.775 2779.000 2839.500 2933.250 3089.775
## absdiff.age 1277.000 1232.675 1325.250 1399.500 1460.500 1636.525
## edgecov.memory[[i]] 122.000 96.725 101.250 106.500 111.750 117.100
##
## Degeneracy check for network 3:
## obs 2.5% 25% 50% 75% 97.5%
## edges 228.000 175.725 182.250 186.000 191.750 200.825
## gwesp.fixed.0 156.000 103.350 111.000 117.000 121.000 127.375
## gwdegree 114.000 98.725 100.000 104.000 108.000 112.650
## nodematch.ipo_status 228.000 174.725 182.250 186.000 191.750 200.825
## nodematch.state_code 33.000 23.000 24.000 25.000 26.000 29.275
## nodecov.age 3905.000 3091.000 3177.750 3249.000 3358.500 3543.500
## absdiff.age 2049.000 1395.625 1447.750 1519.500 1584.250 1805.150
## edgecov.memory[[i]] 78.000 105.175 114.000 119.000 122.000 128.100
##
## Degeneracy check for network 4:
## obs 2.5% 25% 50% 75% 97.5%
## edges 274.00 249.80 256.25 260.00 266.75 274.55
## gwesp.fixed.0 191.00 171.45 177.50 181.50 185.75 196.28
## gwdegree 134.00 119.72 123.25 125.50 128.50 134.82
## nodematch.ipo_status 271.00 247.07 254.00 258.00 263.75 271.55
## nodematch.state_code 37.00 32.45 34.25 35.00 36.00 39.55
## nodecov.age 4792.00 4541.60 4646.75 4726.50 4849.25 4966.07
## absdiff.age 2428.00 2246.55 2332.50 2389.50 2472.25 2644.32
## edgecov.memory[[i]] 168.00 167.18 175.00 178.00 186.00 191.28
##
## Degeneracy check for network 5:
## obs 2.5% 25% 50% 75% 97.5%
## edges 357.00 293.45 301.25 305.00 308.00 314.550
## gwesp.fixed.0 270.00 207.72 213.00 218.00 222.00 228.000
## gwdegree 163.00 133.72 137.00 139.00 140.75 144.825
## nodematch.ipo_status 351.00 290.18 298.00 301.00 303.75 310.275
## nodematch.state_code 48.00 36.00 38.25 40.50 42.00 45.275
## nodecov.age 6197.00 5465.27 5629.75 5667.00 5806.75 6092.700
## absdiff.age 3187.00 2618.60 2696.50 2790.00 2874.75 3063.750
## edgecov.memory[[i]] 177.00 213.45 217.75 222.00 225.75 233.100
##
## Degeneracy check for network 6:
## obs 2.5% 25% 50% 75% 97.5%
## edges 364.000 378.900 388.250 392.000 399.000 403.55
## gwesp.fixed.0 275.000 288.350 296.250 303.000 306.750 317.55
## gwdegree 168.000 163.000 164.000 165.000 166.000 168.55
## nodematch.ipo_status 358.000 372.625 381.000 386.000 391.000 396.38
## nodematch.state_code 47.000 47.725 50.000 51.500 55.000 56.55
## nodecov.age 6847.000 7117.350 7255.500 7380.000 7460.500 7658.00
## absdiff.age 3201.000 3346.700 3448.500 3513.000 3579.000 3724.95
## edgecov.memory[[i]] 336.000 295.900 301.000 307.000 311.250 320.20
##
## Degeneracy check for network 7:
## obs 2.5% 25% 50% 75% 97.5%
## edges 358.00 370.73 375.00 378.00 383.00 387.27
## gwesp.fixed.0 261.00 275.73 280.25 283.50 288.50 293.27
## gwdegree 166.00 166.00 167.00 168.00 168.00 170.28
## nodematch.ipo_status 352.00 364.00 367.25 371.50 375.75 379.82
## nodematch.state_code 44.00 41.00 43.00 44.00 46.00 49.55
## nodecov.age 7670.00 7349.45 7530.75 7638.50 7756.25 7869.20
## absdiff.age 3272.00 3183.70 3320.25 3381.00 3415.50 3523.85
## edgecov.memory[[i]] 334.00 301.45 307.00 311.00 314.75 319.38
Plot degeneracy check of m0 model parameters
par(mfrow=c(3,3))
plot(degen0)
And check degeneracy for m1
degen1 <- checkdegeneracy(fit1, nsim=30)
print(degen1)
##
## Degeneracy check for network 1:
## obs 2.5% 25% 50% 75%
## edges 142.000 102.900 108.250 111.500 114.750
## gwesp.fixed.0 96.000 54.450 60.250 63.000 64.750
## gwdegree 75.000 65.900 70.250 72.000 74.750
## nodematch.ipo_status 142.000 102.900 108.250 111.000 114.750
## nodematch.state_code 19.000 11.725 12.250 14.000 15.000
## nodecov.age 2271.000 1825.325 1900.250 1965.500 2033.500
## absdiff.age 1109.000 808.775 869.500 929.000 1001.750
## nodecov.cent_deg 2372.000 1558.650 1605.500 1659.000 1705.750
## edgecov.memory[[i]] 42.000 59.000 66.500 69.000 73.750
## nodecov.genidx_multilevel 159.620 110.008 114.144 117.525 121.104
## nodecov.cent_pow_n0_4 88.882 56.392 73.299 79.469 86.708
## absdiff.cent_pow_n0_4 356.320 286.640 298.067 306.808 313.882
## cycle3 63.000 32.725 36.000 37.000 39.000
## cycle4 274.000 82.725 87.000 92.000 96.750
## 97.5%
## edges 123.000
## gwesp.fixed.0 68.550
## gwdegree 81.825
## nodematch.ipo_status 123.000
## nodematch.state_code 17.000
## nodecov.age 2226.700
## absdiff.age 1159.450
## nodecov.cent_deg 1763.725
## edgecov.memory[[i]] 78.550
## nodecov.genidx_multilevel 123.946
## nodecov.cent_pow_n0_4 97.518
## absdiff.cent_pow_n0_4 320.285
## cycle3 40.825
## cycle4 110.850
##
## Degeneracy check for network 2:
## obs 2.5% 25% 50% 75%
## edges 158.000 155.725 160.000 164.000 168.750
## gwesp.fixed.0 104.000 97.000 103.000 106.000 110.000
## gwdegree 85.000 80.450 85.500 89.000 92.500
## nodematch.ipo_status 158.000 155.000 159.250 164.000 168.000
## nodematch.state_code 22.000 19.450 21.000 22.000 23.000
## nodecov.age 2735.000 2535.900 2687.000 2732.000 2851.000
## absdiff.age 1277.000 1152.450 1264.250 1312.000 1397.000
## nodecov.cent_deg 2816.000 2696.225 2734.250 2826.000 2861.000
## edgecov.memory[[i]] 122.000 103.625 108.250 112.000 115.750
## nodecov.genidx_multilevel 194.747 187.465 189.545 195.926 198.959
## nodecov.cent_pow_n0_4 42.578 31.397 42.274 49.193 56.291
## absdiff.cent_pow_n0_4 379.337 368.653 383.171 388.047 395.046
## cycle3 69.000 68.000 70.250 73.500 75.000
## cycle4 304.000 283.625 297.250 305.500 313.500
## 97.5%
## edges 174.375
## gwesp.fixed.0 117.100
## gwdegree 97.825
## nodematch.ipo_status 174.100
## nodematch.state_code 26.275
## nodecov.age 2954.075
## absdiff.age 1464.850
## nodecov.cent_deg 3020.325
## edgecov.memory[[i]] 120.275
## nodecov.genidx_multilevel 206.506
## nodecov.cent_pow_n0_4 64.600
## absdiff.cent_pow_n0_4 408.175
## cycle3 78.650
## cycle4 352.750
##
## Degeneracy check for network 3:
## obs 2.5% 25% 50% 75%
## edges 228.000 183.725 191.000 197.000 201.750
## gwesp.fixed.0 156.000 113.450 120.000 130.500 134.000
## gwdegree 114.000 95.725 101.000 102.500 105.750
## nodematch.ipo_status 228.000 183.725 190.250 196.500 201.750
## nodematch.state_code 33.000 23.725 25.000 26.000 28.000
## nodecov.age 3905.000 3073.300 3209.250 3303.000 3391.500
## absdiff.age 2049.000 1374.125 1474.750 1549.000 1620.250
## nodecov.cent_deg 6212.000 4078.075 4208.500 4424.500 4622.750
## edgecov.memory[[i]] 78.000 95.350 105.250 110.000 115.750
## nodecov.genidx_multilevel 314.776 218.917 224.719 236.135 247.667
## nodecov.cent_pow_n0_4 134.805 82.601 92.178 100.926 106.013
## absdiff.cent_pow_n0_4 391.104 346.240 355.427 367.708 377.220
## cycle3 123.000 74.725 79.000 88.500 99.500
## cycle4 665.000 332.900 362.000 401.000 454.750
## 97.5%
## edges 211.55
## gwesp.fixed.0 146.00
## gwdegree 113.83
## nodematch.ipo_status 211.55
## nodematch.state_code 31.10
## nodecov.age 3561.70
## absdiff.age 1774.55
## nodecov.cent_deg 4866.77
## edgecov.memory[[i]] 121.55
## nodecov.genidx_multilevel 258.72
## nodecov.cent_pow_n0_4 120.80
## absdiff.cent_pow_n0_4 398.05
## cycle3 112.28
## cycle4 528.23
##
## Degeneracy check for network 4:
## obs 2.5% 25% 50% 75%
## edges 274.000 267.725 277.000 281.000 287.000
## gwesp.fixed.0 191.000 201.700 213.750 222.000 230.500
## gwdegree 134.000 121.000 125.250 128.000 129.750
## nodematch.ipo_status 271.000 265.725 275.000 278.500 285.000
## nodematch.state_code 37.000 31.725 35.000 38.000 41.000
## nodecov.age 4792.000 4742.175 4836.500 4942.000 5020.750
## absdiff.age 2428.000 2391.925 2454.750 2521.500 2582.500
## nodecov.cent_deg 7528.000 8157.775 8383.000 8752.500 8814.500
## edgecov.memory[[i]] 168.000 140.900 153.000 157.000 161.750
## nodecov.genidx_multilevel 446.700 477.076 489.607 508.751 512.812
## nodecov.cent_pow_n0_4 195.460 166.019 173.892 183.491 188.665
## absdiff.cent_pow_n0_4 450.615 434.535 446.862 455.521 461.400
## cycle3 156.000 170.975 193.000 197.500 204.750
## cycle4 783.000 941.825 1125.500 1175.000 1291.750
## 97.5%
## edges 294.38
## gwesp.fixed.0 240.28
## gwdegree 133.28
## nodematch.ipo_status 291.38
## nodematch.state_code 43.00
## nodecov.age 5179.75
## absdiff.age 2692.43
## nodecov.cent_deg 9064.67
## edgecov.memory[[i]] 172.28
## nodecov.genidx_multilevel 527.74
## nodecov.cent_pow_n0_4 202.47
## absdiff.cent_pow_n0_4 481.42
## cycle3 223.55
## cycle4 1446.00
##
## Degeneracy check for network 5:
## obs 2.5% 25% 50%
## edges 357.000 311.725 318.250 321.500
## gwesp.fixed.0 270.000 230.450 236.250 241.000
## gwdegree 163.000 137.725 141.000 142.500
## nodematch.ipo_status 351.000 307.725 314.000 317.500
## nodematch.state_code 48.000 39.725 41.250 43.000
## nodecov.age 6197.000 5606.250 5757.250 5837.000
## absdiff.age 3187.000 2708.700 2821.750 2887.000
## nodecov.cent_deg 11774.000 9915.425 10204.500 10328.500
## edgecov.memory[[i]] 177.000 197.525 205.250 210.500
## nodecov.genidx_multilevel 495.843 405.967 417.851 422.795
## nodecov.cent_pow_n0_4 83.339 74.304 89.251 93.840
## absdiff.cent_pow_n0_4 543.128 497.596 509.890 514.917
## cycle3 238.000 198.725 205.500 211.000
## cycle4 1492.000 1125.525 1188.750 1244.000
## 75% 97.5%
## edges 326.000 335.375
## gwesp.fixed.0 246.000 256.275
## gwdegree 144.750 146.000
## nodematch.ipo_status 321.750 332.550
## nodematch.state_code 44.000 46.275
## nodecov.age 5932.750 6103.400
## absdiff.age 2973.750 3040.750
## nodecov.cent_deg 10437.500 10693.575
## edgecov.memory[[i]] 214.000 220.275
## nodecov.genidx_multilevel 428.405 439.206
## nodecov.cent_pow_n0_4 103.869 117.172
## absdiff.cent_pow_n0_4 521.315 537.593
## cycle3 218.000 227.575
## cycle4 1287.000 1374.700
##
## Degeneracy check for network 6:
## obs 2.5% 25% 50%
## edges 364.000 381.350 389.250 396.500
## gwesp.fixed.0 275.000 297.075 313.000 322.500
## gwdegree 168.000 161.725 163.000 165.000
## nodematch.ipo_status 358.000 373.900 381.250 389.500
## nodematch.state_code 47.000 48.450 51.000 52.500
## nodecov.age 6847.000 7010.400 7133.500 7334.000
## absdiff.age 3201.000 3252.075 3349.500 3510.000
## nodecov.cent_deg 12180.000 12728.250 13118.000 13229.000
## edgecov.memory[[i]] 336.000 295.000 300.000 304.000
## nodecov.genidx_multilevel 491.650 515.034 530.976 536.390
## nodecov.cent_pow_n0_4 93.621 76.275 83.629 89.201
## absdiff.cent_pow_n0_4 542.199 553.226 562.489 575.944
## cycle3 232.000 260.075 290.250 296.000
## cycle4 1450.000 1736.300 1986.750 2055.500
## 75% 97.5%
## edges 400.000 403.550
## gwesp.fixed.0 326.000 338.550
## gwdegree 165.000 166.000
## nodematch.ipo_status 392.750 396.825
## nodematch.state_code 55.000 56.275
## nodecov.age 7467.750 7562.600
## absdiff.age 3598.250 3688.550
## nodecov.cent_deg 13394.750 13582.975
## edgecov.memory[[i]] 309.750 316.650
## nodecov.genidx_multilevel 544.364 550.716
## nodecov.cent_pow_n0_4 93.974 103.418
## absdiff.cent_pow_n0_4 579.311 595.088
## cycle3 301.750 307.825
## cycle4 2099.500 2215.625
##
## Degeneracy check for network 7:
## obs 2.5% 25% 50%
## edges 358.000 383.000 389.000 393.000
## gwesp.fixed.0 261.000 285.725 300.250 307.000
## gwdegree 166.000 166.000 167.000 167.500
## nodematch.ipo_status 352.000 376.725 381.250 386.000
## nodematch.state_code 44.000 44.725 48.000 49.000
## nodecov.age 7670.000 7716.000 7870.500 7934.500
## absdiff.age 3272.000 3372.500 3452.500 3500.500
## nodecov.cent_deg 11996.000 12756.825 12906.500 13156.500
## edgecov.memory[[i]] 334.000 284.800 300.500 306.500
## nodecov.genidx_multilevel 571.974 613.911 624.292 632.626
## nodecov.cent_pow_n0_4 97.888 105.524 122.135 132.324
## absdiff.cent_pow_n0_4 492.419 511.541 528.729 540.695
## cycle3 221.000 259.700 271.000 282.500
## cycle4 1421.000 1820.675 1909.750 1985.000
## 75% 97.5%
## edges 399.250 413.20
## gwesp.fixed.0 313.750 326.00
## gwdegree 168.000 169.00
## nodematch.ipo_status 391.500 403.93
## nodematch.state_code 50.750 54.00
## nodecov.age 8053.500 8290.95
## absdiff.age 3578.750 3710.57
## nodecov.cent_deg 13275.500 13688.10
## edgecov.memory[[i]] 310.750 314.10
## nodecov.genidx_multilevel 641.961 661.15
## nodecov.cent_pow_n0_4 143.451 163.15
## absdiff.cent_pow_n0_4 549.927 565.85
## cycle3 290.000 304.27
## cycle4 2100.500 2312.55
And plot degeneracy check for m1
par(mfrow=c(3,3))
plot(degen1)
Compare Estimation Algorithms: PMLE vs MCMCMLE
For instructional purposes, we will only compare the estamation algorithm for the first model m0. You may repeat the same steps as needed to compare other models.
Compute the first model m0 again using MCMCMLE (instead of bootstrapped PMLE) and save to disk as an RDS (serialized) file:
## set pseudorandom number generator seed for reproducibility
set.seed(1111)
## estimate the TERGM with bootstrapped PMLE
fit0m <- mtergm(m0, ctrl=control.ergm(seed = 1111))
##
## Initial dimensions of the network and covariates:
## t=2 t=3 t=4 t=5 t=6 t=7 t=8
## nets (row) 180 180 180 180 180 180 180
## nets (col) 180 180 180 180 180 180 180
## memory (row) 180 180 180 180 180 180 180
## memory (col) 180 180 180 180 180 180 180
##
## All networks are conformable.
##
## Dimensions of the network and covariates after adjustment:
## t=2 t=3 t=4 t=5 t=6 t=7 t=8
## nets (row) 180 180 180 180 180 180 180
## nets (col) 180 180 180 180 180 180 180
## memory (row) 180 180 180 180 180 180 180
## memory (col) 180 180 180 180 180 180 180
## Estimating...
## Starting maximum likelihood estimation via MCMLE:
## Iteration 1 of at most 20:
## Optimizing with step length 0.380849430581003.
## The log-likelihood improved by 2.465.
## Iteration 2 of at most 20:
## Optimizing with step length 0.659003375233084.
## The log-likelihood improved by 2.668.
## Iteration 3 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 1.182.
## Step length converged once. Increasing MCMC sample size.
## Iteration 4 of at most 20:
## Optimizing with step length 1.
## The log-likelihood improved by 1.42.
## Step length converged twice. Stopping.
## 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.
## Done.
## SAVE SERIALIZED DATA
fit0m_file <- file.path(data_dir,sprintf('fit_%s_pd%s_%s.rds', firm_i, nPeriods, 'm0m'))
saveRDS(fit0m, file=fit0m_file)
Compare PMLE and MCMCMLE results
## Cache model fits list
fits <- list(PMLE=fit0, MCMCMLE=fit0m)
## Echo model comparison table to screen
screenreg(fits, digits = 3)
##
## ======================================================
## PMLE MCMCMLE
## ------------------------------------------------------
## edges -0.180 -0.477
## [-1.749; 1.067] (0.382)
## gwesp.fixed.0 0.813 * 0.964 ***
## [ 0.658; 0.908] (0.076)
## gwdegree -1.145 * -0.741 ***
## [-1.910; -0.527] (0.144)
## nodematch.ipo_status 0.132 0.175
## [-0.259; 1.070] (0.358)
## nodematch.state_code -0.593 * -0.624 ***
## [-0.770; -0.387] (0.169)
## nodecov.age -0.139 * -0.128 ***
## [-0.199; -0.065] (0.011)
## absdiff.age 0.157 * 0.145 ***
## [ 0.085; 0.216] (0.012)
## edgecov.memory[[i]] 5.229 *
## [ 4.908; 5.769]
## edgecov.memory 5.047 ***
## (0.144)
## ------------------------------------------------------
## Num. obs. 13787 225540
## ======================================================
## *** p < 0.001, ** p < 0.01, * p < 0.05 (or 0 outside the confidence interval).
## SAVE FORMATTED REGRESSION TABLE
compare_file <- file.path(data_dir,sprintf('%s_tergm_results_pd%s_R%s_%s.html', firm_i, nPeriods, R, 'm0PMLE-m0MCMCMLE'))
htmlreg(fits, digits = 3, file=compare_file)
And compare the PMLE and MCMCMLE confidence intervals directly
## Cache model fits list
fits <- list(PMLE=fit0, MCMCMLE=fit0m)
## Echo model comparison table to screen
screenreg(fits, digits = 3, ci.force = T, ci.force.level = .95)
##
## ========================================================
## PMLE MCMCMLE
## --------------------------------------------------------
## edges -0.180 -0.477
## [-1.749; 1.067] [-1.225; 0.271]
## gwesp.fixed.0 0.813 * 0.964 *
## [ 0.658; 0.908] [ 0.814; 1.113]
## gwdegree -1.145 * -0.741 *
## [-1.910; -0.527] [-1.023; -0.459]
## nodematch.ipo_status 0.132 0.175
## [-0.259; 1.070] [-0.527; 0.878]
## nodematch.state_code -0.593 * -0.624 *
## [-0.770; -0.387] [-0.956; -0.292]
## nodecov.age -0.139 * -0.128 *
## [-0.199; -0.065] [-0.150; -0.107]
## absdiff.age 0.157 * 0.145 *
## [ 0.085; 0.216] [ 0.122; 0.168]
## edgecov.memory[[i]] 5.229 *
## [ 4.908; 5.769]
## edgecov.memory 5.047 *
## [ 4.765; 5.330]
## --------------------------------------------------------
## Num. obs. 13787 225540
## ========================================================
## * 0 outside the confidence interval
## SAVE FORMATTED REGRESSION TABLE
compare_file <- file.path(data_dir,sprintf('%s_tergm_results_pd%s_R%s_%s.html', firm_i, nPeriods, R, 'm0PMLE-m0MCMCMLE_ci'))
htmlreg(fits, digits = 3, file=compare_file, ci.force = T, ci.force.level = .05)
Finally, check the MCMCMLE diagnostics
mcmc.diagnostics(fit0m@ergm)
## Sample statistics summary:
##
## Iterations = 16384:4209664
## Thinning interval = 1024
## 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 3.0723 19.700 0.3078 1.2698
## gwesp.fixed.0 3.5552 19.959 0.3119 1.8134
## gwdegree -0.3508 11.232 0.1755 0.5734
## nodematch.ipo_status 1.2542 19.092 0.2983 1.3942
## nodematch.state_code -3.6062 6.416 0.1002 0.3763
## nodecov.age -35.6899 384.359 6.0056 27.4444
## absdiff.age -134.2041 300.434 4.6943 19.9207
## edgecov.memory 10.8696 19.003 0.2969 1.1498
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges -36.00 -10 3 17 42.0
## gwesp.fixed.0 -39.00 -9 4 17 41.0
## gwdegree -21.62 -8 -1 7 22.0
## nodematch.ipo_status -36.62 -11 1 14 38.0
## nodematch.state_code -16.00 -8 -4 1 10.0
## nodecov.age -784.00 -307 -28 231 685.6
## absdiff.age -702.00 -343 -132 73 453.6
## edgecov.memory -27.00 -2 12 24 47.0
##
##
## Sample statistics cross-correlations:
## edges gwesp.fixed.0 gwdegree
## edges 1.0000000 0.6314057 0.6581411
## gwesp.fixed.0 0.6314057 1.0000000 0.1204709
## gwdegree 0.6581411 0.1204709 1.0000000
## nodematch.ipo_status 0.9886884 0.6256350 0.6462060
## nodematch.state_code 0.3580458 0.2441033 0.2293714
## nodecov.age 0.7275301 0.4828927 0.3857011
## absdiff.age 0.5918817 0.3200693 0.3720640
## edgecov.memory -0.8724774 -0.5287060 -0.5860218
## nodematch.ipo_status nodematch.state_code nodecov.age
## edges 0.9886884 0.3580458 0.7275301
## gwesp.fixed.0 0.6256350 0.2441033 0.4828927
## gwdegree 0.6462060 0.2293714 0.3857011
## nodematch.ipo_status 1.0000000 0.3644899 0.7101860
## nodematch.state_code 0.3644899 1.0000000 0.2704267
## nodecov.age 0.7101860 0.2704267 1.0000000
## absdiff.age 0.5755261 0.2028273 0.9265124
## edgecov.memory -0.8753191 -0.3510019 -0.5997116
## absdiff.age edgecov.memory
## edges 0.5918817 -0.8724774
## gwesp.fixed.0 0.3200693 -0.5287060
## gwdegree 0.3720640 -0.5860218
## nodematch.ipo_status 0.5755261 -0.8753191
## nodematch.state_code 0.2028273 -0.3510019
## nodecov.age 0.9265124 -0.5997116
## absdiff.age 1.0000000 -0.5667370
## edgecov.memory -0.5667370 1.0000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges gwesp.fixed.0 gwdegree nodematch.ipo_status
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 1024 0.8838772 0.9425326 0.8096165 0.8798159
## Lag 2048 0.7864046 0.8876284 0.6656872 0.7803422
## Lag 3072 0.7030145 0.8392670 0.5566241 0.6960648
## Lag 4096 0.6326490 0.7922254 0.4692374 0.6253648
## Lag 5120 0.5733575 0.7489398 0.3961800 0.5646937
## nodematch.state_code nodecov.age absdiff.age edgecov.memory
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 1024 0.8347718 0.8881187 0.8874959 0.8749346
## Lag 2048 0.7022984 0.7968271 0.7951130 0.7698871
## Lag 3072 0.5937905 0.7178424 0.7125952 0.6797544
## Lag 4096 0.4979769 0.6498921 0.6418456 0.6035623
## Lag 5120 0.4202840 0.5955045 0.5839419 0.5391573
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges gwesp.fixed.0 gwdegree
## -2.4150 -1.6614 -1.7590
## nodematch.ipo_status nodematch.state_code nodecov.age
## -1.8425 1.1636 -1.2394
## absdiff.age edgecov.memory
## -1.3510 -0.3909
##
## Individual P-values (lower = worse):
## edges gwesp.fixed.0 gwdegree
## 0.01573314 0.09663062 0.07857317
## nodematch.ipo_status nodematch.state_code nodecov.age
## 0.06539507 0.24456780 0.21520396
## absdiff.age edgecov.memory
## 0.17668597 0.69585895
## Joint P-value (lower = worse): 5.638501e-08 .
## Warning in formals(fun): argument is not a function
##
## 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).
That concludes part 2.