A Factored Regression Model for Composite Scores With Item-Level Missing Data

Composite scores are an exceptionally important psychometric tool for behavioral science research applications. A prototypical example occurs with self-report data, where researchers routinely use questionnaires with multiple items that tap into different features of a target construct. Item-level missing data are endemic to composite score applications. Many studies have investigated this issue, and the near-universal theme is that item-level missing data treatment is superior because it maximizes precision and power. However, item-level missing data handling can be challenging because missing data models become very complex and suffer from the same "curse of dimensionality" problem that plagues the estimation of psychometric models. A good deal of recent missing data literature has focused on advancing factored regression specifications that use a sequence of regression models to represent the multivariate distribution of a set of incomplete variables. The purpose of this paper is to describe and evaluate a factored specification for composite scores with incomplete item responses. We used a series of computer simulations to compare the proposed approach to gold standard multiple imputation and latent variable modeling approaches. Overall, the simulation results suggest that this new approach can be very effective, even under extreme conditions where the number of items is very large (or even exceeds) the sample size. A real data analysis illustrates the application of the method using software available on the internet.