Dynamic fit index cutoffs for categorical factor analysis with Likert-type, ordinal, or binary responses.

Area of Science:

• Psychometrics
• Psychological Measurement
• Statistical Modeling

Background:

• Scale validation is crucial in psychological research to ensure measurement accuracy.
• Current fit index guidelines often assume continuous data, which mismatches typical Likert-scale responses.
• Traditional guidelines can be too lenient with discrete data, failing to detect poor model fit.

Purpose of the Study:

• To evaluate the generalizability of traditional fit index guidelines to discrete response data.
• To propose and validate an extension of the dynamic fit index framework for discrete responses.
• To provide accessible tools for applying the proposed methods in psychological research.

Main Methods:

• A simulation study was conducted to compare traditional fit index guidelines with a proposed dynamic fit index framework for discrete responses.
• The study assessed the sensitivity of both methods in distinguishing between well-fitting and poorly fitting factor models.
• The proposed method was implemented in an R package and a Shiny application.

Main Results:

• Traditional fit index guidelines (e.g., RMSEA < 0.06, CFI > 0.95) do not generalize well to discrete response data.
• The proposed dynamic fit index framework effectively distinguishes between adequate and inadequate model fit for discrete responses.
• The new method demonstrated high sensitivity (≥90%) to misspecification, outperforming traditional methods with inconsistent sensitivity (<50%).

Conclusions:

• Existing fit index guidelines are inadequate for psychological research using discrete response data.
• The extended dynamic fit index framework offers a reliable solution for evaluating factor model fit with Likert-type scales.
• Accessible tools are now available to aid psychologists in conducting more rigorous scale validation.