Bhargava and Ishizukaʹs BI-Method: A Neglected Method for Variable Selection

Quite often in data reduction, it is more meaningful and economical to select a subset of variables instead of reducing the dimensionality of the variable space with principal components analysis. The authors present a neglected method for variable selection called the BI-method (R. P. Bhargava & T. Ishizuka, 1981). It is a direct, simple method that uses the same criterion—trace information—used in ordinary regression analysis. The authors begin by discussing the nature and properties of the BI-method and then show how it is different from other existing variable selection methods. Because the BI-method originally was applied to small datasets that had little or no relevance to psychology or education, the authors apply it to large datasets with relevance to the psychological and educational literature. Of particular interest was the application of the BI-method to select a subset of items from a large item pool. Two practical psychometric examples with 49 and 108 items, respectively, showed that item subsets selected with the BI-method reflected the underlying structure of the whole item pool and that the scales based on those item subsets showed good reliability and predictive validity. The appropriateness of this item selection method within the context of the domain-sampling model is discussed.