Reliability estimates for three factor score predictors

TL;DR

This paper compares the reliability of three factor score predictors using simulation studies and provides scripts for their computation, highlighting the regression predictor's superior reliability.

Contribution

It introduces and compares reliability estimates for three factor score predictors, including new simulation-based methods and computational scripts.

Findings

Regression factor score predictor has the highest reliability.

Reliability estimates for Bartlett's and McDonald's predictors are lower.

Simulation studies validate the comparative reliability assessments.

Abstract

Estimates for the reliability of Thurstone's regression factor score predictor, Bartlett's factor score predictor, and McDonald's factor score predictor were proposed. As in Kuder-Richardson's formula, the reliability estimates are based on a hypothetical set of equivalent items. The reliability estimates were compared by means of simulation studies. Overall, the reliability estimates were largest for the regression score predictor, so that the reliability estimates for Bartlett's and McDonald's factor score predictor should be compared with the reliability of the regression score predictor, whenever Bartlett's or McDonald's factor score predictor are to be computed. An R-script and an SPSS-script for the computation of the respective reliability estimates is presented.