Model selection for generalized linear models with factor-augmented predictors

Model selection for generalized linear models with factor-augmented predictors is studied. It is found that the observed response variable may have serial correlations in empirical application. Time-series models are used depending on the dynamic pattern of the autocorrelation function of available. Cross-sectional dependence is studied and asymptotic results for approximate factor models are developed. This dependence is found to introduce identifiability problem in factor interpretations, while it does not affect the prediction. The constrained factor model, which serves as tools to achieve dimension reduction and simplifications in factor interpretation, impose certain prior specifications on the structure of the loading matrix. The research work also finds that sliced inverse regression (SIR) and the subsequent inverse regression methods are useful in analyzing high-dimensional data.