Estimation of an IRT Model by Mplus for Dichotomously Scored Responses Under Different Estimation Methods

Area of Science:

• Psychometrics
• Statistical modeling

Background:

• Item response theory (IRT) and factor analysis (FA) are widely used in psychometric research.
• Understanding the relationships between IRT and FA parameterizations is crucial for applied researchers and students.
• Mplus software offers various estimation methods and parameterizations that can impact model results.

Purpose of the Study:

• To evaluate the recovery of model parameters and standard errors for the two-parameter IRT model using different Mplus estimation methods.
• To provide clear information on the relationships between IRT and FA parameterizations (Theta and Delta) in Mplus.
• To facilitate understanding for practitioners, instructors, and students regarding IRT and FA in Mplus.

Main Methods:

• Comparison of parameter and standard error recovery for the two-parameter IRT model across different Mplus estimation methods.
• Description of Theta and Delta parameterizations in Mplus for unidimensional and multidimensional models.
• Analysis of dichotomous and polytomous response data with and without the scaling constant D.

Main Results:

• Evaluates the performance of various Mplus estimation methods for binary response IRT models.
• Details the connections between IRT and Mplus FA parameterizations using accessible mathematical expressions.
• Highlights practical implications for applying IRT and FA in Mplus.

Conclusions:

• Different estimation methods in Mplus can influence parameter recovery in IRT models.
• The Theta and Delta parameterizations provide a bridge between IRT and FA, enhancing model interpretability.
• This work offers practical guidance for researchers and students using Mplus for IRT and FA analyses.