Interaction between two continuous covariates

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Interaction between two continuous covariates

Postby rodrossi » Wed Jun 09, 2021 8:32 pm

I want to test the interaction between two continuous environmental covariates (temperature and precipitation).
When I assemble the model in the design matrix, how should I put the interaction column between such variables?
I have read chapter 6 of the MARK Book and understand how it works with a continuous and a categorical covariate, however it does not exemplify what the matrix for interaction between two continuous ones looks like.
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Re: Interaction between two continuous covariates

Postby simone77 » Thu Jun 10, 2021 3:58 am

You can set the interaction between two continuous covariates by adding a third column that is the product of the other two (numeric) columns. I don't see any problem with that, it is just what happens behind the scenes when you run a GLM-like model in whatever other program. To avoid large numbers that may be cumbersome for the computation, you may want to shift your values to get 0 equal to the minimum value or some other transformation that makes their product values smaller. An alternative is to multiply the covariates by a scaling value, this is suggested in CH 11.2.2 when they speak about individual covariate, I think it should work for environmental covariates too.

Of course, you must keep in mind what transformations you did in order to correctly interpret the results (i.e. the beta values). In the MARK book, there are several points about the interpretation of betas (I recommend that you also read chapter 11 - one may get MARK to treat environmental covariates as individual covariates indeed) and how this depends on the way the design matrix is constructed and the values of the covariates.
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