Bayesian multiple Regression - compare regression coefficients
I would like to test whether the size of my regression coefficient varies across three different groups (A, B, and C). The goal is to find out whether the regression coefficient of weight predicting insulin levels differs across three groups of different age.
Therefore I computed two dummy variables: V_A: coding 1 for group A and zero otherwise, and variable V_B: coding 1 for group B and zero otherwise. Now in order to test whether the regression coefficients vary across groups I computed the variables: V_A_weight = V_A*weight and V_B_weight = V_B*weight.
In the Bayesian regression model I enter "insulin levels" as dependent variable, and "weight, V_A, V_B, V_A_weight and V_B_weight" as predictors. Because my main interest is to see whether a model including "V_A_weight and V_B_weight" is more plausible I assigned "weight, V_A, V_B" to the null model.
Is this procedure correct?
is it correct to only focus on the model including "V_A_weight and V_B_weight" as additional predictors?
do I need to include V_A and V_B at all into the regression model?
Any help would be very much appreciated!