Likelihood-based quantile mixed effects models for longitudinal data with multiple features via MCEM algorithm

Abstract

In longitudinal data analysis, many data features are frequently encountered in practice. For example, variates are usually measured with censoring, substantial errors and non-normal feature, etc. In such case, it is impossible to give a precise result by conducting statistical inference of separate analysis. The joint modeling may be a considerable alternative. The superiority of joint modeling is that it can implement a simultaneous analysis for longitudinal mixed models with random effects, censoring, nor-normal errors, errors in covariates and heavy-tailed feature by pooling all data information together. However, most of traditional modeling methods aim at depicting the average variation of outcome variable conditionally on covariates, which may result in non-robust estimation results when suffering outliers or non-normal errors. Quantile regression provides an attractive alternative to model longitudinal data with multiple data features, which can draw a complete picture of the conditional distributions of outcome variable and bring out robust estimation results. In this paper, we conduct the likelihood-based joint quantile regression for longitudinal mixed models by accounting for the above multiple data features simultaneously. Based on the asymmetric Laplace distribution (ALD), the Monte Carlo Expectation-Maximization (MCEM) algorithm is employed to address the estimation problem. Finally, some Monte Carlo simulations are conducted and an AIDS data analysis is provided to illustrate the developed procedures.