# How do I interpret a regression model when there are impossible additive effects?

Let's say I have a model of count data as a function of the month of the year along with an additive effect of season (factor with 2 levels Wet and Dry which correspond to Jan - June and July to Dec respectively).

count ~ month + season


My regression will give some main effect estimates for the two parameters. Let's say I have a positive effect of wet season. How do I interpret this when the effect is on months that are not in the wet season?

• You’ll never have a December in the wet season, right?
– Dave
Sep 16, 2022 at 15:06
• If season is just defined in terms of month, then there doesn't seem much point in having both in the same model. month alone will capture the season effect + more fine-grained variation.
– mkt
Sep 16, 2022 at 15:49
• @Dave, that's right. So I guess in the model matrix I'd have zeroes for wet season beside the column for the month variable. Sep 19, 2022 at 8:38

If season is just defined in terms of month and consists of the same set of months each year, there isn't much point in having both in the same model because of the covariance between the two. month alone will capture the season effect as well as more fine-grained variation. This might be less of a problem if the dry/rainy seasons occurred in different months each year, but in general this isn't likely to work well.
Even ignoring the model problems I discussed earlier, the question doesn't really make sense. The parameter value for season distinguishes between dry and wet seasons. Assuming 'dry' is your reference category, then the season parameter value applies only to 'wet' periods (and vice versa). There's no effect of wet season applied to months not in the wet season. The question What is a contrast matrix? might help make this clearer, and I also suggest looking up 'dummy coding' on this site.