[statnet_help] Question about including an interaction effect in REM

[Carter T. Butts via statnet_help]

Hi, Choi

You can certainly include interaction effects by using products as 
covariates (just as you would in e.g. a regression context). You do, 
however, need to think carefully about what you expect these effects to 
do, and whether you want them to act as predictors for individual 
sending rates (CovSnd), predictors for individual receipt rates 
(CovRec), or predictors for pairwise specific events (CovEvent).  Also, 
it is important to distinguish between an effect that says that e.g. the 
log sending rate for an event from vertex i to vertex j varies with θ 
x_i y_i (a CovSnd interaction between x and y), and a model that says 
that the log sending rate for an event from vertex i to vertex j varies 
with θ x_i y_j.  Those are very different models, with the latter saying 
that the product between the sender's x value and the receiver's y value 
modifies the i->j interaction rate.  I'm not sure what you intend here, 
so I cannot tell whether you are doing what you want to be doing, but 
all of these are straightfoward to implement using appropriate covariate 
specifications.

Vis a vis testing hypotheses across models, the usual considerations 
apply as they would in other maximum likelihood scenarios (i.e., you can 
do it, depending on what assumptions/approximations you are willing to 
make, and the details may depend on your scenario).  For the most 
obvious base case, if you have two models A and B on independent data 
sets of reasonable size, then (coef_A - coef_B)/sqrt(se(coef_A)^2 + 
se(coef_B)^2) for respective coefficients coef_A from A and coef_B from 
B should be approximately standard normal (leading to a z-test for 
equality of coefficients).  If you want a Bayesian answer for the 
probability that coef_A > coef_B, fit both models using the BSIR method 
and look at the respective fraction of posterior draws (pairing A and B) 
for which coef_A is greater than coef_B.

Hope that helps,

-Carter

On 7/31/24 6:48 PM, SJ C via statnet_help wrote:

> Dear all,

>

> May I ask a question about including an interaction effect in REM?

> As illustrated in the code below, let's say I have two variables, 

> A.cat (categorical) and B.con (continuous).

>

>   rem.dyad(networkdata, n = 200, effects = c("CovSnd","CovRec", 

> "CovEvent",

>  "NIDRec","NIDSnd",

>  "NODSnd","NODRec",

>                                                  "PSAB-BA",

>                                                  "RRecSnd", "RSndSnd"),

>               covar = list(CovSnd = cbind(A.cat, B.con),

>                               CovRec= cbind(A.cat, B.con),

>                               CovEvent = abind(same.A.cat 

> <https://urldefense.com/v3/__http://same.A.cat__;!!CzAuKJ42GuquVTTmVmPViYEvSg!O4iVbsPlR-Obu67qMPZFlFsScm-aVJ4_EBM1ZUpI65bhpi_4Bg6N6plaSjMvp66VdzYzmS17AM3_VDJ8EVuWlLopOep2$>, 

> A.cat*B.con, along=0)),

>                               ordinal=TRUE, hessian = TRUE)

>

> To create their interaction effect, I formed a matrix by inserting 

> senders' A.cat values into all columns except the diagonal.

> Additionally, I did the same thing with senders' B.con values and 

> mean-centered them.

> Then, I multiplied these two matrices, which is represented as 

> A.cat*B.con in the code.

>

> My questions are:

> 1. Can the interaction term be inserted into the REM in the way 

> described above?

> 2. Should I also include A.cat and B.con(centered) as components in 

> the CovEvent code, along with A.cat*B.con?

>

> Besides these questions, I am also curious whether there are any 

> measures or indices that can compare the statistical significance of 

> coefficients between two REMs with the same parameters?

>

> It would be greatly appreciated if I can have any responses.

> Thank you!

>

> Sincerely,

> Choi

>

>

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