Polychotomous quantal response models are widely used in medical and econometric studies to analyze categorical or ordinal data. In this study, we apply the Bayesian methodology through a mixed-effects polychotomous quantal response model. For the Bayesian polychotomous quantal response model, we assume uniform improper priors for the regression coeffcients and explore the suffcient conditions for a proper joint posterior
distribution of the parameters in the models. Simulation results from Gibbs sampling estimates will be compared to traditional maximum likelihood estimates to show the strength that using the uniform improper priors for the regression coeffcients.
Motivated by investigating of relationship between BMI categories and several risk factors, we carry out the application studies to examine the impact of risk factors on BMI categories, especially for categories of "Overweight" and "Obesities". By applying the mixed-effects Bayesian polychotomous response model with uniform improper priors, we would get similar interpretations of the association between risk factors and BMI, comparing to literature fndings.
