Bayesian Local Influence Analysis For Nonlinear Mixed Effects Quantile Regression

The longitudinal data is widespread in the field of medicine, economics and education, etc, it is one of the hot topics of modern statistical research, nonlinear mixed effects model is a powerful tool for longitudinal data, because it can depict the nonlinear relationship between dependent variables and independent variables with fixed effects and random effects. At the same time, with the improving of the social demand, people begin to understand the importance of quantile regression in longitudinal data analysis, because quantile regression can study the relationship between the dependent variables and the independent variables in different quantiles, especially when the distributions of the dependent variables are asymmetric distributions, quantile regression can reflect more information than the classical mean regression. Therefore, nonlinear mixed effects quantile regression gets more and more attentions.In this article, we will use bayesian approach to statistical inference for nonlinear mixed effects quantile regression, the main research contents include:(1)Using Laplace distribution to show the check function of quantile regression, using the probability density function of the Laplace distribution as the likelihood function. Then, using bayesian formula to calculate the posterior distribution of parameters, usingthe Gibbs algorithm to sample from the posterior distribution of unknown parameters and random effects according to the ideas of the MCMC sampling, then use the sample averages to approximate the unknown parameters.(2) According to the bayesian local influence analysis method, discusses the nonlinear mixed effects of bayesian quantile regression model analysis. Based on the φ- distance, bayesian factor and the posterior mean distance, for assessing minor perturbation to the prior, the sampling distribution and observations to evaluate the sensitivity of the model, and presents a concise formula for computing the diagnostic statistics.(3) Through a simulation and a real data to illustrate the feasibility of the proposed approach in this article.