[statnet_help] Question about including an interaction effect in REM

[SJ C via statnet_help]

Dear Carter,

I really appreciate your detailed explanation!

I am expecting the interaction effect to "act as a predictor for individual
sending rates."
In addition, my interest is in "the log sending rate for an event from
vertex i to vertex j varying with θ x_i y_i (a CovSnd interaction between x
and y)."

If this is the case, how can I modify the code below that I previously
posted?

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
<http://same.a.cat/>, A.cat*B.con, along=0)),
                              ordinal=TRUE, hessian = TRUE)


Thank you for your kind support!

Sincerely,
Choi

2024년 8월 5일 (월) 오전 8:22, Carter T. Butts via statnet_help <
statnet_help at u.washington.edu>님이 작성:


> 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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