A Multiple Imputation for Binary and Ordinal Responses: A Multivariate Probit Model Approach

Music City Center 

Handling missing data in studies with mixed multivariate responses is a critical challenge in statistical research. We propose a multiple imputation technique for datasets with binary and ordinal variables. This method, based on a multivariate probit model using Markov chain Monte Carlo, captures the correlation structure among variables while respecting their categorical nature. We evaluate the method under various missing data scenarios: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Comparisons with standard imputation techniques, such as multivariate normal-based and multiple imputations by chained equations (MICE), reveal that our approach outperforms existing methods. It better preserves the joint distribution of data and provides unbiased parameter estimates, particularly under complex missingness patterns. Our findings highlight the multivariate probit model's potential as a robust and flexible tool for multiple imputation in datasets with mixed ordinal and binary responses. This advancement enhances the reliability of statistical inference in applied research involving such data structures.

Multiple Imputation

Multinomial probit model

Markov chain Monte Carlo (MCMC)

Missing completely at random (MCAR)

Missing at random (MAR)

Missing not at random (MNAR). 

Section on Bayesian Statistical Science