Applied Psychometrics: Estimator Considerations in Commonly Encountered Conditions in CFA, SEM, and EFA Practice

Abstract

The goal of this work was: 1) to present the assumptions for use of the estimators used in CFA/SEM and EFA, and their advantages/disadvantages; 2) to highlight that the variables were treated either as continuous or as ordinal categorical during the estimation process should be consistently treated for the rest of the study analyses (keeping a consistent level of measurement). Two estimator groups exist 1) Maximum Likelihood and 2) Least Squares. Robust alternatives exist in both groups. Desirable estimator properties include consistency, non-biasness, efficiency, scale freeness, and scale invariance. Scholars propose selecting an estimator considering: 1) measurement level; 2) non-normality; 3) model type. Not considering these could affect parameter significance, chi-square tests, and model fit. A plausible under-highlighted issue is the impact of the level of measurement implied during the estimation process on the level of measurement assumed for the same variables across the study. E.g., when an ordinal categorical level is assumed using categorical estimators, the same variables should be treated as ordinal categorical for the rest of the study: 1) using ordinal reliability; 2) omitting means; 3) using tetrachoric/polychoric correlation for the nomological network. Therefore, the selection of an estimator impacts all the analytic strategies of the study.