Joint modeling of mixed skewed longitudinal responses using convolution of normal and log-normal distributions: a Bayesian approach

Abstract

This paper investigates the joint modeling of mixed ordinal and continuous longitudinal responses using a random effects model and applying a conditional approach. For the ordinal responses, a latent variable model with a logistic distribution is employed. To address skewness in the data, the model incorporates normal and log-normal convolution (NLNC) for both the error term and the random effects in the longitudinal model. Parameter estimation is carried out within a Bayesian framework using Gibbs sampling. The performance of the proposed model is evaluated through simulation studies, comparing it to joint models of mixed ordinal and continuous longitudinal responses assuming skew-normal or normal distributions. The results indicate that joint models using skew-normal or normal distributions can lead to biased parameter estimates, whereas the NLNC joint model performs better overall. Additionally, the proposed method is applied to analyze data from the British Household Panel Survey (BHPS), using life satisfaction and annual income as the correlated ordinal and continuous longitudinal responses, respectively, with annual income showing significant skewness. The results demonstrate that the proposed model provides the best fit for capturing the substantial skewness in the data.