I am trying to understand whether the use of several linear models using the same variable as a response variable (but differing in one of the specified predictors) constitutes a case of multiple hypothesis testing.
My research is investigating the relationship between a continuous response variable (Y) and several continuous predictor variables (A, B, C, D). Additionally, I want to investigate if these relationships are dependent on two categorical variables (W, Z). Using a linear model, my ideal model specification would include 3-way interactions between each of my continuous predictors and the categorical predictors:
Y ~ A * W * Z + B * W * Z + C * W * Z + D * W * Z
Due to sample size limitations, I cannot fit all interactions of interest in the same model and instead have to specify each of them in separate models:
Model 1) Y ~ A * W * Z
Model 2) Y ~ B * W * Z
Model 3) Y ~ C * W * Z
Model 4) Y ~ D * W * Z
Does this constitute a case of multiple hypothesis testing for which corrections of significant p-values must be done? E.g., if the interaction between A and W (A * W) has a significant effect in Model 1), must its p-value be adjusted?
If so, which kind of correction is advisable?