Assessing the Relative Importance of Predictors in Latent Regression Models

This study develops a method of measuring the i mportance of latent predictors and testing their importance ordering. A popular measure for relative importance, called dominance analysis, is extended to structural equation models such that the contribution to the variation of the outcome variable is attributed to each latent predictor. This measure is computed through the average R-squared change by adding a predictor into possible subset models, which can be derived from the model-implied correlation matrix of the latent variables. Besides presenting the dominance analysis measure for latent predictors, we calculate its confidence interval using bootstrap sampling and infer its statistical significance. Importance orderings of the latent predictors are formulated by order-constrained hypotheses, which can be evaluated using Bayes factors. Simulation studies demonstrate the performance of the proposed method. A real data example illustrates how to assess relative importance in latent regression models.