| Applications in which several quantities are to be predicted using a common set of predictor variables are becoming increasingly important in various disciplines. However, three problems are associated with the application of the usual multivariate multiple regression model. First, the assumption that the regression coefficient matrix is of full rank. Second, the inclusion of a large number of predictors where some of them might be slightly correlated with the dependent variables or they may be redundant because of high correlations with other independent variables. Third, the model does not consider the correlations among the dependent variables which may reduces the prediction accuracy.;Multivariate variable selection procedures (stepwise regression and all-possible-regression) are usually used to solve the second problem, however the first and third problems are usually not considered by the multivariate multiple regression users. Reinsel & Velu (1998) propose a new technique that solves the two problems simultaneously. The variable selection procedure, which uses the reduced rank regression model, takes into account the interrelations among the multiple dependent variables in finding the "best" subset of predictors. This model is called the reduced rank regression (RRR) procedure.;This study is designed to compare, using Monte Carlo methods, several multivariate variable selection procedures and the reduced rank regression (RRR) procedure to select the "best" subset of predictors under various conditions: three levels of the sample size (n = 30, 60, 100, and 500), two levels of the total number of predictors ( k = 5 and 9), three levels of the correlation among the dependent variables (rhoy = .2, .5, and .8), three levels of the correlation among the independent variables (rhox = .1, .3, and .5), and two levels of the correlation between the set of the independent variables and the dependent variables (rhoZY = .1 and .4).;The results of the study demonstrated that the RRR procedure is superior to all other multivariate variable selection procedures studied. It is considered the best among the selection criteria under most of the study conditions although the Akaike's corrected information criterion (AICc) performed satisfactorily under some conditions. |
