Question

Given the following OLS equation:

P2*21

Where D is a dummy variable, state the possible statistical problems with this equation and a possible remedy.

Answer 1

Possible statistical problems with this multivariate equation could be:

1) There exists a confounding effect between the predictor variables X11 and X21. The confounding is confirmed by checking the relationship between D1 and X11 first, and then including X21 too in the model. As a rule of thumb, if the inclusion of X21 changes the coefficient of X11 compared to the univariate case by more than 10%, there exists a confounding effect between the 2 predictor variables X11 and X21.

To get rid of confounding, we can perform stratification, in which we fix the levels of the confounders and produce groups within which the confounders do not vary. Then evaluate the outcome associated with each stratum of the confounder. Then, estimators are used to provide adjusted results according to the different strata.

2) The 2 predictor variables could also be collinear with each other, in which case the predictors themselves are inter-correlated, which introduces some level of redundancy into the model. This is measured through the Variance Inflation Factors (a value different from 1 signifies collinearity).

To get rid of collinearity, we can remove the variables with Variance Inflation Factors (VIF), which hardly reduces the R-squared given the information added by their presence was redundant. One can also use Principal Components Analysis to cut the predictors into a smaller set of non-collinear components.