I am trying to determine if I can use the AIC/BIC criteria for model selection in the case of a multivariate probit model. I have two models with different specifications:
e.g. Model-1: mvprobit ( $Y_1 = a X_1 + b X_2 + c X_3), (Y_2 = a X_1 + b X_2 + c X_3 + \mathbf{s Y_1}), (Y_3 = a X_1 + b X_2 + c X_3 + \mathbf{s Y_1} + \mathbf{e Y_2})$.
Model-2: mvprobit ( $Y_1 = a X_1 + b X_2 + c X_3), (Y_3 = a X_1 + b X_2 + c X_3 + \mathbf{sY1}), (Y_2 = a X_1 + b X_2 + c X_3 + \mathbf{s Y_1} + \mathbf{e Y_3}$).
Here ($a, b, c, s$, and $e$ are coefficients: $Y_1, Y_2, Y_3$ are dependent variables in multivariate probit model).
Given these different model specifications, if I obtain AIC/BIC values from Model-1 and Model-2 and select the better-fit model based on the lowest AIC/BIC values, would this approach be justifiable?
Note that the data and the number of observations are the same for both models.
