In this paper, Professors Prasad Naik and Chih-Ling Tsai, with co-author Peide Shi from Nuclear Safety Solutions Ltd., examine the problem of jointly selecting the number of components and variables in finite mixture regression models.

Inverse regression methods facilitate dimension-reduction analyses of high-dimensional data by extracting a small number of factors that are linear combinations of the original predictor variables. But the estimated factors may not lend themselves readily to interpretation consistent with prior information.

in this paper, Professors Prasad Naik and Chih-Ling Tsai derive a new model selection criterion for single-index models, AIC, by minimizing the expected Kullback-Leibler distances between the true and candidate models.

The pro-posed criterion selects not only relevant variables but also the smoothing parameter for an unknown link function. Thus, it is a general selection criterion that provides a unifies approach to model selection across both parametric and nonparametric functions. Monte Carlo studies demonstrate that AIC performs satisfactorily in most situations.

In data-rich marketing environments (e.g., direct marketing or new product design), managers face an ever-growing need to reduce the number of variables effectively. To accomplish this goal, Professors Prasad Naik and Chih-Ling Tsai and co-author Michael Hagerty introduce a new method called sliced inverse regression (SIR), which finds factors by taking into account the information contained in both the dependent and independent variables.