Bayesian Single-Index Quantile Regression for Binary Longitudinal Data

For binary longitudinal data, we propose a Bayesian analysis method for quantile single -index models of binary longitudinal data with random effects which using Bayesian methods and the relationship between quantile regression objective functions and asymmetric Laplacian distribution density functions.Some posterior distributions that are difficult to express were obtained using the Markov chain Monte Carlo method, which iteratively obtained samples that meet the objective posterior distribution.Using models to fit two simulation sets under different error distributions, using standard deviation, root mean square error, and bias information criteria as standards, the results indicate that our model fits better.Two real datasets illustrate this method.