General location multivariate latent variable models for mixed correlated bounded continuous, ordinal, and nominal...

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Analyzing correlated continuous and categorical data is complex, especially with missing values.
• Existing models may not adequately handle bounded continuous responses or non-ignorable missingness.

Purpose of the Study:

• To propose new multivariate latent variable models for analyzing correlated bounded continuous and categorical responses.
• To address models with and without non-ignorable missing values.
• To extend models for bounded continuous responses using beta and Dirichlet distributions.

Main Methods:

• Multivariate latent variable approach.
• Regression methods for jointly analyzing continuous, nominal, and ordinal responses.
• Maximum-likelihood estimation for regression parameters.
• Sensitivity analysis for missing data mechanisms.

Main Results:

• Developed general location models accommodating bounded continuous and categorical variables.
• Successfully applied models to BMI, Steatosis, Osteoporosis data, and Tehran household expenditure budgets.
• Demonstrated the utility of beta and Dirichlet distributions for bounded continuous responses.

Conclusions:

• The proposed models offer a flexible framework for analyzing complex correlated data with mixed response types and missing values.
• The methods provide robust tools for applications in health and economic research.
• Sensitivity analysis confirms model stability concerning missing data mechanisms.