B1518
Title: Matrix decomposition factor analysis with variable selection directly constrained by the number of zero columns
Authors: Naoya Shimada - Osaka University (Japan) [presenting]
Abstract: It is very important to select the variables to be used in factor analysis when there are many observed variables. We propose a new method for variable selection in factor analysis. The proposed method is based on matrix decomposition factor analysis, which treats all factor analysis model parameters (common and unique factors, loadings, and unique variances) as a fixed unknown matrix. This method treats parameters as grouped parameters by column (variable) and then uses the $L_0$ norm to constrain the number of variables used in the analysis. Three features distinguish this approach from previous studies. First, the tuning parameters that determine the number of variables to be selected are finite positive integers, and the optimal parameter values can be easily estimated by considering all possible values. Second, the number of variables to be used in the analysis can be ascertained prior to conducting the analysis. Third, the proposed method can derive a residual matrix that indicates the degree not accounted for in the model equation. Simulation were conducted to investigate the effectiveness of the proposed method.
