Outliers and multi-collinearity often have large influence in the model/variable selection process in linear regression analysis. To investigate this combined problem of multi-collinearity and outliers, we studied and compared Liu-type S (liuS-estimators) and Liu-type Least Trimmed Squares (liuLTS) estimators as robust model selection criteria. Therefore, the main goal of this study is to select subsets of independent variables which explain dependent variables in the presence of multi-collinearity, outliers and possible departures from the normality assumption of the error distribution in regression analysis using these models.