Reconsidering the Conditions for Conducting Confirmatory Factor Analysis

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Confirmatory Factor Analysis (CFA) relies on established conventions for application.
• These rules, concerning sample size, item representation, and factor loading estimation, can lead to unjustified decisions by overlooking practical significance and validity.
• Existing guidelines may not adequately address the nuances of model stability.

Purpose of the Study:

• To investigate the interplay between sample size, number of items per factor, and factor loading strength in Confirmatory Factor Analysis (CFA).
• To demonstrate how these factors compensate for each other, affecting parameter estimation stability.
• To highlight scenarios where poor model decisions are made and undetected by goodness-of-fit indices.

Main Methods:

• A Monte Carlo simulation study was conducted.
• The simulation manipulated sample size, number of items per factor, and the strength of factor loadings.
• The stability of parameter estimation in CFA was assessed under various conditions.

Main Results:

• Significant compensatory effects were observed between sample size, number of items, and factor loading strength.
• Certain combinations of these factors can lead to unstable parameter estimates that are not flagged by standard goodness-of-fit measures.
• The study identified specific conditions where arbitrary rule-following in CFA can result in invalid factor model conclusions.

Conclusions:

• Researchers must be cautious about blindly adhering to conventional rules when validating factor models.
• Applied researchers should consider conducting their own simulation studies tailored to their specific factor model.
• Such simulations can help determine conditions ensuring stable parameter estimation and reliable model validation.