Psychometric properties of sum scores and factor scores differ even when their correlation is 0.98: A response to Widaman and Revelle.

Abstract

Commentary in Widaman and Revelle (2022) argued that sum scoring is justified as long as unidimensionality holds because sum score reliability is defined. My response begins with a review of the literature supporting the perspective we adopted in the original article. I then conduct simulation studies to assess the psychometric properties of sum scores created using Widaman and Revelle's justification relative to scores created by the weighted factor score approach in the original article. In my simulations, I generate data where sum and factor scores are correlated at 0.96 or 0.98 because high factor-sum score correlations are often used to support the contention that sum and factor scores have interchangeable psychometric properties. I explore (a) correlations between estimated scores and true scores, (b) classification accuracy of sum and factor scores, and (c) reliability of sum and factor scores. Results show that factor scores have (a) higher correlations with true scores (Δ = 0.02-0.04), (b) higher sensitivity (Δ = 4-8 percentage points), and (c) higher reliability (Δ = 0.04-0.07). Factor score performance metrics also have less sampling variability in most conditions. Psychometric properties of sum scores-even when highly correlated with factor scores-remain less desirable than those of factor scores. Additional considerations like models with multiple factors and measurement invariance are also discussed. Essentially, even if accepting Widaman and Revelle's justification for sum scoring, it is uncertain whether researchers generally would want to sum score after fitting a factor analysis unless sum and factor scores correlate at (and not merely close to) 1.00.