Empirical Comparison Between Factor Analysis and Multidimensional Item Response Models

Area of Science:

• Psychometrics
• Statistical Modeling
• Data Analysis

Background:

• Numerous factor analysis and multidimensional item response models exist for dichotomous data.
• Existing literature offers various methods for estimating item parameters within these models.

Purpose of the Study:

• To review and compare different factor analysis and multidimensional item response models for dichotomous variables.
• To evaluate the performance of various item parameter estimation methods.
• To compare models using both item response theory and factor analysis formulations.

Main Methods:

• Brief review of existing factor analysis and multidimensional item response models.
• Simulation study comparing parameter estimation methods.
• Analysis using both item response theory and factor analysis frameworks.

Main Results:

• Common factor analysis on tetrachoric correlations demonstrates comparable performance to multidimensional item response models for multidimensional data.
• Parameter estimates from factor analysis formulations were evaluated against item response theory formulations.

Conclusions:

• Common factor analysis provides a robust and potentially simpler alternative for analyzing multidimensional dichotomous data.
• The findings suggest that factor analysis methods are a viable and effective approach in psychometric research.