I have a question about the construction of a multivariate regression model. I have one major predictor (continuous: IV1) and 3 continuous dependent variables. As we are registering our study on OSF before collecting data (and as I am not an expert in statistics), I would prefer having your advice before registering a mistake.
The particularity of my study is that I collect data from two populations (categorical: IV2). For this analysis, we are not specifically interested by this variable (i.e., we are not interested in the main effect of IV2). However, we are afraid that the relationship between our IV1 and the DVs differs depending on the population (i.e., we are afraid that the IV1*IV2 interaction will be significant).
I have a question on how I should build my a priori multivariate regression model. IV1 is mandatory but I am not sure how I should handle IV2. My initial plan was first to run a model with the interaction term. If the interaction is significant, I would run univariate effects of IV1 for each level of IV2. If the interaction is not significant, I would rerun a model including only the main effect of IV1 and I would estimate univariate effects if the multivariate main effect of IV1 is significant.
However, a colleague advice me to build 3 models (one model with the main effect IV1, one with main effects of IV1 and IV2 and then one with main effects + the interaction term) and to select the model based upon the AIC value.
I have thus two questions:
1) Do you think that I should select my model based upon the result of the interaction or the AIC (or a third way not described here)?
2) If you suggest that the AIC is the best solution, can you recommend me a package that can be used in R? I have read several publications on this topic (e.g., Seghouane, 2011) since standard AIC should not be used in multivariate analyses but I am not sure what is the standard package to use.
Thank you very much for your help!