install.packages("statnet")Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.3'
(as 'lib' is unspecified)Lab 4
Preparing the environment, load data, explore
library(statnet)Loading required package: tergmLoading required package: ergmLoading required package: network
'network' 1.18.2 (2023-12-04), part of the Statnet Project
* 'news(package="network")' for changes since last version
* 'citation("network")' for citation information
* 'https://statnet.org' for help, support, and other information
'ergm' 4.6.0 (2023-12-17), part of the Statnet Project
* 'news(package="ergm")' for changes since last version
* 'citation("ergm")' for citation information
* 'https://statnet.org' for help, support, and other information'ergm' 4 is a major update that introduces some backwards-incompatible
changes. Please type 'news(package="ergm")' for a list of major
changes.Loading required package: networkDynamic
'networkDynamic' 0.11.4 (2023-12-10?), part of the Statnet Project
* 'news(package="networkDynamic")' for changes since last version
* 'citation("networkDynamic")' for citation information
* 'https://statnet.org' for help, support, and other informationRegistered S3 method overwritten by 'tergm':
method from
simulate_formula.network ergm
'tergm' 4.2.0 (2023-05-30), part of the Statnet Project
* 'news(package="tergm")' for changes since last version
* 'citation("tergm")' for citation information
* 'https://statnet.org' for help, support, and other information
Attaching package: 'tergm'The following object is masked from 'package:ergm':
snctrlLoading required package: ergm.count
'ergm.count' 4.1.1 (2022-05-24), part of the Statnet Project
* 'news(package="ergm.count")' for changes since last version
* 'citation("ergm.count")' for citation information
* 'https://statnet.org' for help, support, and other informationLoading required package: snaLoading required package: statnet.common
Attaching package: 'statnet.common'The following object is masked from 'package:ergm':
snctrlThe following objects are masked from 'package:base':
attr, ordersna: Tools for Social Network Analysis
Version 2.7-2 created on 2023-12-05.
copyright (c) 2005, Carter T. Butts, University of California-Irvine
For citation information, type citation("sna").
Type help(package="sna") to get started.Loading required package: tsna
'statnet' 2019.6 (2019-06-13), part of the Statnet Project
* 'news(package="statnet")' for changes since last version
* 'citation("statnet")' for citation information
* 'https://statnet.org' for help, support, and other informationedges <- read.csv("/cloud/project/edgelist_retrieve (1).csv")
edges from to
1 1 6
2 1 9
3 2 6
4 2 9
5 3 5
6 3 6
7 3 9
8 3 17
9 4 5
10 4 6
11 4 9
12 4 16
13 4 17
14 5 6
15 5 9
16 5 16
17 5 17
18 6 5
19 6 9
20 6 16
21 7 16
22 12 8
23 12 16
24 13 6
25 13 9
26 13 17
27 14 4
28 14 6
29 14 9
30 14 16
31 15 3
32 15 6
33 15 9
34 15 16
35 15 17
36 16 5
37 16 6
38 16 9
39 17 5
40 17 9
41 17 16attributes <- read.csv("/cloud/project/att_expertise (1).csv")
attributes id expertise
1 1 0.17647059
2 2 0.17647059
3 3 0.17647059
4 4 0.52941176
5 5 0.52941176
6 6 0.58823529
7 7 0.05882353
8 8 0.29411765
9 9 0.58823529
10 10 0.05882353
11 11 0.17647059
12 12 0.05882353
13 13 0.05882353
14 14 0.35294118
15 15 0.23529412
16 16 0.58823529
17 17 0.41176471retrieve_net <- network(x = edges,
directed = T,
vertex.attr = attributes)plot(retrieve_net)
Estimation
Build Model
set.seed(123)
model.retrieve <- ergm(retrieve_net ~ edges + mutual + nodeicov("expertise") + nodeocov("expertise"))Starting maximum pseudolikelihood estimation (MPLE):Obtaining the responsible dyads.Evaluating the predictor and response matrix.Maximizing the pseudolikelihood.Finished MPLE.Starting Monte Carlo maximum likelihood estimation (MCMLE):Iteration 1 of at most 60:Warning: 'glpk' selected as the solver, but package 'Rglpk' is not available;
falling back to 'lpSolveAPI'. This should be fine unless the sample size and/or
the number of parameters is very big.Optimizing with step length 1.0000.The log-likelihood improved by 0.0137.Convergence test p-value: 0.0002. Converged with 99% confidence.
Finished MCMLE.
Evaluating log-likelihood at the estimate. Fitting the dyad-independent submodel...
Bridging between the dyad-independent submodel and the full model...
Setting up bridge sampling...
Using 16 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 .
Bridging finished.
This model was fit using MCMC. To examine model diagnostics and check
for degeneracy, use the mcmc.diagnostics() function.Interpret Results
summary(model.retrieve)Call:
ergm(formula = retrieve_net ~ edges + mutual + nodeicov("expertise") +
nodeocov("expertise"))
Monte Carlo Maximum Likelihood Results:
Estimate Std. Error MCMC % z value Pr(>|z|)
edges -2.2479 0.4456 0 -5.045 <1e-04 ***
mutual -0.1087 0.6071 0 -0.179 0.8579
nodeicov.expertise 2.0333 0.9063 0 2.244 0.0249 *
nodeocov.expertise 0.8309 0.8934 0 0.930 0.3524
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Null Deviance: 291.1 on 210 degrees of freedom
Residual Deviance: 202.0 on 206 degrees of freedom
AIC: 210 BIC: 223.4 (Smaller is better. MC Std. Err. = 0.0144)Model Diagnostics and Goodness of Fit
#MCMC Convergence
pdf("modeldiagnostics.pdf")
mcmc.diagnostics(model.retrieve)Sample statistics summary:
Iterations = 14336:262144
Thinning interval = 1024
Number of chains = 1
Sample size per chain = 243
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
edges 0.8477 5.613 0.3601 0.2854
mutual 0.1523 2.034 0.1305 0.1305
nodeicov.expertise 0.2225 2.109 0.1353 0.1221
nodeocov.expertise 0.1784 1.911 0.1226 0.1077
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
edges -9.000 -3.000 1.000e+00 5.000 11.950
mutual -3.000 -1.000 0.000e+00 1.000 5.000
nodeicov.expertise -3.353 -1.294 1.176e-01 1.735 4.526
nodeocov.expertise -3.053 -1.147 -2.000e-09 1.529 4.232
Are sample statistics significantly different from observed?
edges mutual nodeicov.expertise nodeocov.expertise
diff. 0.847736626 0.1522634 0.22246430 0.17840717
test stat. 2.970622021 1.1668359 1.82268154 1.65612493
P-val. 0.002971973 0.2432766 0.06835164 0.09769652
(Omni)
diff. NA
test stat. 6.5712426
P-val. 0.1693739
Sample statistics cross-correlations:
edges mutual nodeicov.expertise nodeocov.expertise
edges 1.0000000 0.5723729 0.8466874 0.8014552
mutual 0.5723729 1.0000000 0.5104470 0.5103168
nodeicov.expertise 0.8466874 0.5104470 1.0000000 0.6340906
nodeocov.expertise 0.8014552 0.5103168 0.6340906 1.0000000
Sample statistics auto-correlation:
Chain 1
edges mutual nodeicov.expertise nodeocov.expertise
Lag 0 1.00000000 1.00000000 1.00000000 1.000000000
Lag 1024 -0.11954449 0.06809777 -0.10466554 -0.130413824
Lag 2048 -0.10012999 -0.06374528 -0.06913897 -0.041351693
Lag 3072 0.04567336 0.03210058 0.07169223 0.079082995
Lag 4096 0.07151648 -0.08545746 0.04886728 -0.051960509
Lag 5120 -0.06048858 -0.08493815 -0.09172259 0.001945236
Sample statistics burn-in diagnostic (Geweke):
Chain 1
Fraction in 1st window = 0.1
Fraction in 2nd window = 0.5
edges mutual nodeicov.expertise nodeocov.expertise
-1.0369435 -0.1906664 -1.8878406 0.4235794
Individual P-values (lower = worse):
edges mutual nodeicov.expertise nodeocov.expertise
0.29976217 0.84878693 0.05904736 0.67187262
Joint P-value (lower = worse): 0.5354552
Note: 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).dev.off()png
2 #Goodness of Fit
model.retrieve.gof <- gof(model.retrieve)
print(model.retrieve.gof)
Goodness-of-fit for in-degree
obs min mean max MC p-value
idegree0 7 0 0.89 4 0.00
idegree1 3 0 2.76 6 1.00
idegree2 0 0 4.00 10 0.08
idegree3 0 0 3.23 7 0.06
idegree4 0 0 1.98 6 0.16
idegree5 2 0 1.20 4 0.72
idegree6 0 0 0.57 3 1.00
idegree7 0 0 0.22 2 1.00
idegree8 1 0 0.10 3 0.16
idegree9 1 0 0.05 1 0.10
idegree11 1 0 0.00 0 0.00
Goodness-of-fit for out-degree
obs min mean max MC p-value
odegree0 2 0 0.69 3 0.34
odegree1 1 0 2.53 6 0.48
odegree2 3 0 3.86 7 0.82
odegree3 4 0 3.84 7 1.00
odegree4 3 0 2.41 7 0.82
odegree5 2 0 1.04 5 0.56
odegree6 0 0 0.46 3 1.00
odegree7 0 0 0.15 1 1.00
odegree8 0 0 0.02 1 1.00
Goodness-of-fit for edgewise shared partner
obs min mean max MC p-value
esp.OTP0 10 14 23.51 31 0.00
esp.OTP1 13 2 12.86 24 1.00
esp.OTP2 11 0 3.44 16 0.10
esp.OTP3 5 0 0.72 6 0.06
esp.OTP4 2 0 0.04 1 0.00
esp.OTP5 0 0 0.01 1 1.00
Goodness-of-fit for minimum geodesic distance
obs min mean max MC p-value
1 41 29 40.58 54 0.96
2 19 36 65.99 96 0.00
3 4 19 48.38 71 0.00
4 0 1 20.11 45 0.00
5 0 0 6.25 22 0.32
6 0 0 1.76 11 1.00
7 0 0 0.43 7 1.00
8 0 0 0.06 4 1.00
9 0 0 0.01 1 1.00
Inf 146 0 26.43 116 0.00
Goodness-of-fit for model statistics
obs min mean max MC p-value
edges 41.00000 29.000000 40.58000 54.00000 0.96
mutual 4.00000 0.000000 3.81000 9.00000 1.00
nodeicov.expertise 13.52941 9.235294 13.49529 20.47059 0.98
nodeocov.expertise 11.82353 6.588235 11.73647 17.23529 0.90#Plot Goodness of Fit
par(mfrow = c(2, 2))
plot(model.retrieve.gof)
Interpreting Results
H1: Members tend to reciprocate information retrieval ties.
- The mutual parameter, which represents reciprocated ties, has an estimate of -0.1087 with a standard error of 0.6071. The z-value is -0.179, and the p-value is 0.8579. Since the p-value is greater than 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that members tend to reciprocate information retrieval ties.
H2: Members tend to retrieve information from other members with high expertise.
- The nodeicov.expertise parameter, which represents the tendency to form ties based on the expertise of the receiving member, has an estimate of 2.0333 with a standard error of 0.9063. The z-value is 2.244, and the p-value is 0.0249. Since the p-value is less than 0.05, we reject the null hypothesis. This suggests that members tend to retrieve information from other members with high expertise.
H3: High expertise members tend to have more outgoing ties.
The
nodeocov.expertiseparameter, which represents the tendency for high expertise members to form more outgoing ties, has an estimate of 0.8309 with a standard error of 0.8934. The z-value is 0.930, and the p-value is 0.3524. Since the p-value is greater than 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that high expertise members tend to have more outgoing ties.In summary, the results support Hypothesis 2 but do not provide sufficient evidence to support Hypotheses 1 and 3.