The joint quantile regression modeling of mixed ordinal and continuous responses with its application to an obesity risk data

In clinical medical health research, individual measurements sometimes appear as a mixture of ordinal and continuous responses. There are some statistical correlations between response indicators. Regarding the joint modeling of mixed responses, the effect of a set of explanatory variables on the conditional mean of mixed responses is usually studied based on a mean regression model. However, mean regression results tend to underperform for data with non-normal errors and outliers. Quantile regression (QR) offers not only robust estimates but also the ability to analyze the impact of explanatory variables on various quantiles of the response variable. In this paper, we propose a joint QR modeling approach for mixed ordinal and continuous responses and apply it to the analysis of a set of obesity risk data. Firstly, we construct the joint QR model for mixed ordinal and continuous responses based on multivariate asymmetric Laplace distribution and a latent variable model. Secondly, we perform parameter estimation of the model using a Markov chain Monte Carlo algorithm. Finally, Monte Carlo simulation and a set of obesity risk data analysis are used to verify the validity of the proposed model and method.