Edge based analysis with network statistics
The edge based analysis with network statistics can be conducted using the function sem.net.edge.
As an example, we analyze the the attorney cowork and advice networks. In this example, the advice network is predicted by gender and years in practice, and the cowork network is predicted by the advice network, gender, and years in practice all together. In this case, the advice network acts as a mediator, while gender and years in practice exert indirect effect onto the cowork network through the advice network in addition to having direct effects. The model specification is given below.
model <-'
advice ~ gender + years
cowork ~ advice + gender + years
'To use the function sem.net.edge(), we need to specify whether the covariate values to be run with the social network edge values in SEM should be calculated as the ”difference” across two individuals or the ”average” across two individuals. Here, the argument ordered = c("cowork", "advice") is used to tell lavaan that the outcome variables cowork and advice are binary.
set.seed(100)
res <- sem.net.edge(model = model, data = data,
network = network, type = "difference", ordered = c("cowork", "advice")) This model is again estimated in two stages. In the first stage, the non-network variables of gender and years in practice are converted to be pairwise such that years in practice for the pair of individuals $i$ and $j$ would be the difference between years in
practice for individual $i$ and for individual $j$. After obtaining the pairwise non-network statistics, these variables are compiled into the same file as the network edge variables, which are binary, and also pairwise. This data frame is then given to lavaan to be used with the SEM framework. Thus, in this model, SEM used each pair of individuals as the unit of analysis. The output can be access via summary(res$estimates, fit=TRUE) and is shown below.
lavaan 0.6.15 ended normally after 19 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 7
Number of observations 5041
Model Test User Model:
Standard Scaled
Test Statistic 0.000 0.000
Degrees of freedom 0 0
Model Test Baseline Model:
Test statistic 1343.292 1343.292
Degrees of freedom 1 1
P-value 0.000 0.000
Scaling correction factor 1.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.000 1.000
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.000 0.000
P-value H_0: RMSEA <= 0.050 NA NA
P-value H_0: RMSEA >= 0.080 NA NA
Robust RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA
P-value H_0: Robust RMSEA <= 0.050 NA
P-value H_0: Robust RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000 0.000
Parameter Estimates:
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured
Regressions:
Estimate Std.Err z-value P(>|z|)
advice ~
gender -0.019 0.040 -0.463 0.643
years -0.018 0.002 -9.354 0.000
cowork ~
advice 0.691 0.019 36.651 0.000
gender 0.013 0.040 0.323 0.747
years 0.013 0.002 7.248 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|)
.advice 0.000
.cowork 0.000
Thresholds:
Estimate Std.Err z-value P(>|z|)
advice|t1 0.956 0.022 43.812 0.000
cowork|t1 1.037 0.022 48.049 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.advice 1.000
.cowork 0.523
Scales y*:
Estimate Std.Err z-value P(>|z|)
advice 1.000
cowork 1.000