Mixed-Effects Logistic Regression Models for Indirectly Observed Discrete Outcome Variables

Area of Science:

• Statistics
• Psychometrics
• Organizational Psychology

Background:

• Clustered data analysis commonly employs mixed-effects models with random effects.
• Mixed-effects logistic regression predicts discrete outcomes with correlated observations.
• Existing models face challenges with measurement error in the dependent variable.

Purpose of the Study:

• To extend mixed-effects logistic regression for latent class dependent variables.
• To simultaneously address correlated observations and measurement error.
• To provide a robust statistical framework for complex psychological data.

Main Methods:

• Developed an extension of the mixed-effects logistic regression model.
• Incorporated a latent class variable as the dependent variable.
• Utilized maximum likelihood estimation via an Expectation-Maximization (EM) algorithm.

Main Results:

• The proposed model effectively handles correlated observations and measurement error.
• Maximum likelihood estimation is feasible using an EM algorithm with a specialized E step.
• The model's utility is demonstrated through an organizational psychology example.

Conclusions:

• The novel model offers a powerful approach for analyzing clustered data with latent structures.
• This method enhances the ability to model complex dependent variables in the presence of correlated errors.
• The findings have significant implications for statistical modeling in psychology and related fields.