# Thread: Examining interaction in an exponential (Poisson) model with standard and robust SE's

1. ## Examining interaction in an exponential (Poisson) model with standard and robust SE's

Hello dear forum members!

For the purpose of my study I am using an exponential Poisson model with fixed-effects specification. In simple:

y = a + x1 + x2 + x1*x2 + e

When I use default standard errors, the interaction is significant. To examine its effect, I calculate the adjusted predictions at the respective values of the moderator and plot them -- see the first graph attached, for instance.

However, when I estimate the same model with cluster-adjusted (robust) SE's, as suggested by the literature, the interaction term becomes insignificant. I suspect that happens because of the increased SE's. Yet, the plot of the adjusted predictions for a model with robust SE's (see second graph attached) looks identical to the first one.

Frankly, I am not sure if I do or do not have a problem here. According to the graphs, the effects I am looking for are there, even though their magnitude is relatively weak.

In addition to the above elaborations, Professor Williams notes in his presentation (https://www3.nd.edu/~rwilliam/stats/Margins01.pdf, slide 44):

"People often ask what the marginal effect of an interaction term is. Stata’s margins command replies: there isn’t one. You just have the marginal effects of the component terms. The value of the interaction term can’t change independently of the values of the component terms, so you can’t estimate a separate effect for the interaction."

Does this imply that the significance of the interaction term matters not either?

Your feedback would be greatly appreciated

2. ## Re: Examining interaction in an exponential (Poisson) model with standard and robust

What is "exponential" Poisson? Does that mean you have a log link?

What is "cluster-adjusted" SE? Does that mean you had multiple observations for subject or cluster, so you are controlling for between subject variance as well? If so, then your written rationale jives with my understanding as well.

As for the mystery of marginal effect, I am in your boat. I think it is just another case of how people use terms. My personal understanding is that if you are interpreting a single effect then it is marginal (say 2x2 table, numbers are on the margins of the table). But if you are adjusting or controlling for something else (especially for an interaction), now instead of having a marginal distribution, the effects are based on a joint distribution, so you have conditional effects. Let me know if I need some corrections here as well, also, is your interaction cross-level. Interacts with individual and group levels, but you are not directly controlling for clusters, just using robust SE?

P.S., Robust SEs are typically wider, and if you did not change other approaches, that everything would be the same except wider confidence intervals.

3. ## Re: Examining interaction in an exponential (Poisson) model with standard and robust

Firstly, since my DV is of count type, I am relying on Poisson model, which is basically a GLM with logarithm as the (canonical) link function.

Secondly, my data set consists of a panel of doctors (N = 1752) observed from 2009 to 2015. Might be mistakenly, but for some reason I assumed I have to treat each doctor as a separate "cluster". But after reading your comments on observations per cluster, I find myself wrong in that vision. It's just anytime I see a paper with a non-linear model and a panel of observations across time, they seem to rely on robust (or clustered -- as the results are almost identical) SE's.

Thirdly, in relationship to the following comments of yours, "As for the mystery of marginal effect, I am in your boat. I think it is just another case of how people use terms. My personal understanding is that if you are interpreting a single effect then it is marginal (say 2x2 table, numbers are on the margins of the table). But if you are adjusting or controlling for something else (especially for an interaction), now instead of having a marginal distribution, the effects are based on a joint distribution, so you have conditional effects." is absolutely correct. And Williams' presentation is a pretty good reference to clarify on the differences between marginal, average, and adjusted effects.

Fourth, as for the level of interactions, in my case they are individual-level ones. So, if not for the literature, I wouldn't even consider robust SE's but simply use default ones.

Seems I need to brush up my understanding of SE's and their implications.

4. ## Re: Examining interaction in an exponential (Poisson) model with standard and robust

No, you seem to have a good general understanding of things. Think of SE as sampling variability, at least I do. So if you think about the interpretation of confidence intervals (95% intervals will contain effect, or more generically samples will), then if you have a bigger sample or less variance CI will be narrower. Controlling for within and between individual variance (clusters) means the variance will be bigger and CI wider. I will check out that link you referenced.

Thanks.

I think "margins" is a big or popular thing in STATA!

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