Hierarchical Regression Without Phantom Factors

Abstract

In a recent note in the Teacher's Corner of this journal, de Jong (1999) proposed a method for computing hierarchical or fixed-order regressions in the context of latent variables. The essence of this approach is to decompose the predictor variables in the regression into orthogonal components based on a Cholesky decomposition and to regress the dependent variable on these orthogonal components. The components may be conceived of as phantom factors that do not have their own indicators. Because the idea of sequential entry of predictors in a latent variable regression framework seems generally to be unknown, the approach was developed by de Jong for latent variable regressions. However, it equally can be used for observed variable regression or path models. In this article we show that the phantom factors are unnecessary to achieve the objectives of a hierarchical regression. We give a direct approach that is equivalent to de Jong's approach.