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Consider a case study which consists of two predictors (Date and IndBin) and one response variable (Count). One predictor is ordinal (Date) and represents the day number within a season. The other predictor is categorical (IndBin) with two levels and describes an individual's characteristic. One level of IndBin is very predominant in frequency (about 90% of records). For each individual I have just one value of IndBin but the observational study goes on for several years. IndBin and Date are correlated because the rarer level of IndBin is more likely to occurr at the end of the season (in the last quartile of Date). In fact, the logistic regression of Date on IndBin results very significant.

Based on previous work I hypothesize that both Date and IndBin have a causal effect on Count. Thus, I want to investigate wether and how each one of these predictors affect a response variable (Count). I am using a negative binomial GLMM with zeroinflation but the question is not specific for this class of models. This is how the model loooks like:

Count ~ IndBin x Date + random = Year, zeroInflation = ~ IndBin x Date, family = "Negative Binomial"

Actually, I am somehow puzzled by the concept of confounding and control variables. I know that Date causes variation in IndBin (not vice versa) and an effect of Date on Count has largely been argued by observational studies. Date is therefore a confounding variable that I need to control in order to investigate the effect of IndBin (adjusting for Date) on Count. But on the other hand, IndBin and Date are very correlated and I have always been told that it is not good to keep correlated predictors in a model because it inflates their variance and therefore the type I error risk.

Do you have any general suggestion on how may I try to test the effect of each predictor on Count? I thought of building and comparing different models (e.g. by AIC) but I am not 100% sure on what are my a priori expectations. What would you do?

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