Evaluating Structural Equation Models for Categorical Outcomes: A New Test Statistic and a Practical Challenge of...

Area of Science:

• Statistics
• Psychometrics
• Educational Measurement

Background:

• Assessing model fit is crucial in structural equation modeling (SEM) for categorical data.
• Traditional SEM fit statistics often focus on reproducing polychoric correlations.
• Limited-information fit statistics offer an alternative by assessing the reproduction of underlying categorical data.

Purpose of the Study:

• To apply the Cai-Monroe C2 statistic, a limited-information test, to SEM for categorical outcomes.
• To investigate the impact of the number of outcome variable categories on the root mean square error of approximation (RMSEA) fit index.
• To explore the interplay between limited-information fit statistics and RMSEA interpretation in categorical data analysis.

Main Methods:

• Application of the Cai-Monroe C2 statistic for limited-information model fit assessment.
• Analysis of structural equation modeling (SEM) for categorical outcome variables.
• Examination of the root mean square error of approximation (RMSEA) under varying category numbers.
• Empirical illustration using data from a large-scale educational survey.

Main Results:

• The Cai-Monroe C2 statistic provides a valuable limited-information approach for categorical SEM.
• The number of categories in an outcome variable significantly influences RMSEA values, complicating interpretation.
• The study demonstrates the practical application of these methods in educational research.

Conclusions:

• The C2 statistic offers a robust alternative for evaluating model fit with categorical data in SEM.
• Researchers must consider the number of categories when interpreting RMSEA for categorical outcomes.
• This research enhances the understanding and application of model fit assessment techniques in psychometrics and educational statistics.