Interpreting continuous var by continuous var interactions for FE Poisson model

[Mansi Jain]

Hi all,

I'm looking at the effect of fire occurrence on the number of visits to National Forests and National Parks. I've divided up these parks into spatial units, with multiple units from each park. This gave me panel date with 10 years and 350 IDs, and I'm using an FE Poisson model to conduct my analysis.

I'm not sure how to interpret some of the results, particularly for places where there is an interaction between two continuous variables. For more context, both of the interacted continuous variables range from 0 to 1. I know normally people use margins and try to assess the marginal effect of a change in one of the interacted variables at different baseline values of the other, but I'm also reading that people don't do that for FE Poisson models. Could someone help me figure out how I should interpret the coefficient estimate for this interaction? To add to this, I think I'm generally confused about interpreting Poisson results. I get that the interpretation for a coefficient estimate, say beta, is to say that one unit change in that variable results in a change in the log of the Y variable by beta amount, but I'm getting tangled up in the conversation about incidence rate ratios and am not sure how to make this sentence more interpretable.

Thank you so much!

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions -Stata code in code delimiters, sample data and output.

Rather than marginal effects, I might use margins with predicted values. Then you can calculate the change for a given change in a rhs variable at specific values of the interacting variable.

[Joao Santos Silva]

Dear Mansi Jain,

In Poisson regression, the coefficients can be interpreted as (semi-) elasticities. If you use xtpoisson, you cannot use margins to compute partial effects.

Best wishes,

Joao

[Mansi Jain]

Thank you very much, Phil Bromiley and Joao Santos Silva!

One quick question -- why as semi elasticities rather than as elasticities? I know that in a normal log linear relationship the conventional wisdom is that when the coefficients are small, roughly below 0.1, we can interpret the coefficient to mean that a 1% change in the x var results in a beta% change in y-var, but if the coefficient is much bigger we need to do some manual calculations. Is it a semi-elasticity in the same sense?

Thank you!

[Joao Santos Silva]

Dear Mansi Jain,

It is a semi-elasticity if the regressor is not in logs (for example, a dummy) and indeed you need to make the adjustment if the estimate is not "small".

Best wishes,

Joao