Investigating interaction

Question

Please I need to check for interaction before building an explanatory model (logistic regression). I have 16 interaction terms in total. Please how what is the best way to go about it. Will I need to put all the interaction terms together with the main effects at once, then drop the insignificant interaction parameters and do the likelihood test (model including all interaction parameters compared to model with all insignificant interaction parameter removed). Or I need to put in each of the interaction terms in different models and compare model with no interaction parameter with model with each interaction parameter separately.

Answer 1

It sounds like you desire to perform stepwise model building. I suggest you not do this. Here's why:

• Your $p$-values no longer mean “the probability of observing the test statistic given the null hypothesis.” Instead, they are probabilities based on a chain of conditionals that at each step of model building include functions of variables that are and are not included in the final presented model, so your resulting $p$-values (under their regular interpretation) are badly biased to be small.
• CIs around your model estimates are also badly biased to be small.
• The $F$ test statistic does not have an $F$ (or a $\chi^{2}$) distribution, but rather a distribution that, like the $p$-values, is conditional upon a series of models that include variables not present in the final model.
• $R^{2}$ values are badly biased to be high because the degrees of freedom are dramatically deflated, usually being based upon the number of parameters of the final model, rather than the number of parameters employed in the stepwise procedure.
• Your model coefficients are biased to be inflated away from zero.
• Stepwise regression model building tends towards overfitting, preferring to include including the most heteroscedastic predictors.
• Many true predictor variables will be excluded, and many false predictor variables will be included.

Not really sure what the benefits of stepwise model building are, but that is one doozy-list of drawbacks.