Assessing Influence Misspecification in Siena

In this example, I use Siena to create data and assess how homophily and influence interact each other under misspecification (removing and including influence effect). I use parameters similar to the ones I get by analyzing data from scenario I in ISA v6.

Only influence simulation

Parameters I use:

# simulation values (I use some of the values I get from our model)
n <- 200 # actors
M <- 10 # waves
c <- 10 # number of categories behavior, uniform distribution
# network
rate <- 2 # rate network change
dens <- -2 # density 
rec <- 2 # reciprocity 
tt <- 0.5 # transitivity 
c3 <- -0.3 # cycles
ego.b <- 0 # ego behavior covariate
alt.b <- 0 # alter behavior covariate
sim.b <- 0 # similarity behavior
# behavior
rate.b <- 1 # rate behavior change
lin.b <- 0.01 # linear trend
qu.b <- -0.20 # quadratic trend
avalt.b <- 1.5 # average alter 

# run simulation 
ss <- SimulateNetworksBehavior(n, M, c, rate, dens, rec, tt, c3, ego.b, alt.b, sim.b,
                               rate.b, lin.b, qu.b, avalt.b)

Average degrees  6.63 7.01 7.34 7.79 8.41 8.97 9.63 10.54 11.19 12.18 
Average behavior  4.55 4.46 4.58 4.5 4.66 4.88 5.03 5.23 5.22 5.24 

I use only the last four waves. The table below shows the estimates from different Siena specifications.

Observed autocorrelation from the simulated networks are kind of similar the ones we get from our ABM:

obs0[, moran_obs]

[1] 0.2559024 0.2453175 0.2539917

screenreg(list(m0, m1, m2), custom.model.names =  c("N", "N+S", "N+S+I"))

=======================================================================
                                  N            N+S          N+S+I      
-----------------------------------------------------------------------
constant network rate (period 1)     2.13 ***     2.13 ***     2.13 ***
                                    (0.11)       (0.11)       (0.12)   
constant network rate (period 2)     1.91 ***     1.91 ***     1.91 ***
                                    (0.10)       (0.10)       (0.10)   
constant network rate (period 3)     1.94 ***     1.95 ***     1.95 ***
                                    (0.11)       (0.11)       (0.10)   
outdegree (density)                 -1.97 ***    -1.97 ***    -1.97 ***
                                    (0.05)       (0.05)       (0.05)   
reciprocity                          1.96 ***     1.96 ***     1.96 ***
                                    (0.09)       (0.08)       (0.09)   
transitive triplets                  0.49 ***     0.49 ***     0.49 ***
                                    (0.02)       (0.02)       (0.02)   
3-cycles                            -0.26 ***    -0.26 ***    -0.26 ***
                                    (0.04)       (0.04)       (0.04)   
rate beh (period 1)                  1.10 ***     1.09 ***     0.99 ***
                                    (0.13)       (0.16)       (0.13)   
rate beh (period 2)                  0.87 ***     0.87 ***     0.81 ***
                                    (0.11)       (0.11)       (0.10)   
rate beh (period 3)                  1.06 ***     1.06 ***     0.97 ***
                                    (0.13)       (0.12)       (0.13)   
beh linear shape                     0.11 *       0.11         0.17    
                                    (0.06)       (0.06)       (0.09)   
beh quadratic shape                  0.01         0.01        -0.19 ** 
                                    (0.01)       (0.01)       (0.07)   
beh alter                                         0.01         0.01    
                                                 (0.01)       (0.01)   
beh ego                                           0.01         0.01    
                                                 (0.01)       (0.01)   
beh similarity                                    0.06         0.05    
                                                 (0.13)       (0.13)   
beh average alter                                              1.52 ** 
                                                              (0.49)   
-----------------------------------------------------------------------
Iterations                        2433         2548         2573       
=======================================================================
*** p < 0.001, ** p < 0.01, * p < 0.05

I compute the difference between the observed and simulated autocorrelation (Moran’s I) to assess goodness-of-fit. Both specificationsn (N and N+S) are very off: there is more autocorrelation than the estimated by the Siena model.

When I add the influence effect, differences are closer to zero.

Again, there seems to be not counfounding between selection and influence.

Other GOF statistics (N+S+I)

This is good fit. Reality and our ABM are another story.

Note: some statistics are not plotted because their variance is 0.
This holds for the statistic: 10.

Note: some statistics are not plotted because their variance is 0.
This holds for the statistics: 4 5 Inf.

Network misspecification

What happens if I misspecify the network. The selection coefficient increases but it is still very noisy. This suggests that most of the problem in our ABM is related to finding good fit of the network part or the behavior change (I am not sure what more important is).

screenreg(m3)

=============================================
                                  Model 1    
---------------------------------------------
constant network rate (period 1)     2.12 ***
                                    (0.11)   
constant network rate (period 2)     1.91 ***
                                    (0.10)   
constant network rate (period 3)     1.95 ***
                                    (0.11)   
outdegree (density)                 -1.32 ***
                                    (0.04)   
reciprocity                          2.01 ***
                                    (0.08)   
beh alter                            0.01    
                                    (0.01)   
beh ego                              0.00    
                                    (0.01)   
beh similarity                       0.13    
                                    (0.13)   
rate beh (period 1)                  0.99 ***
                                    (0.13)   
rate beh (period 2)                  0.82 ***
                                    (0.11)   
rate beh (period 3)                  0.98 ***
                                    (0.13)   
beh linear shape                     0.16    
                                    (0.09)   
beh quadratic shape                 -0.19 ** 
                                    (0.07)   
beh average alter                    1.52 ** 
                                    (0.49)   
---------------------------------------------
Iterations                        2514       
=============================================
*** p < 0.001, ** p < 0.01, * p < 0.05