Semi-parametric mixture models: algorithms, model comparison and checking, and joint longitudinal models for disease progression

广义线性混合模型(GLMM)是广义线性模型的推广，它在线性预报器中引入了随机效应。它们被广泛应用于各个领域，从纵向数据分析、流行病学到图像处理、生态和环境科学。GLMM是分析重复测量和聚类观测的有用模型，然而，已开发的大多数估计方法都是基于随机效应的正态分布假设。这一假设为估计固定效应提供了一种方便的方法，但可能会影响估计效率。这项研究计划对不对随机效应施加参数假设的广义最小二乘模型的算法、推理方法、预测、拟合度、模型选择和识别进行研究。

Generalized linear mixed models (GLMMs) are an extension of generalized linear models that introduce random effects to the linear predictor. They are widely used in various fields, from longitudinal data analysis, epidemiology to image processing, ecology and environmental sciences. GLMMs are useful models for analyzing repeated measurements and clustered observations, however, the majority of estimation methods that have been developed are based on the normality assumption of random effects. This assumption provides a convenient way to estimate the fixed effects but may compromise estimation efficiency. This research plan proposes to investigate algorithms, inferential methods, predictions, goodness-of-fit, model selection and identification for GLMMs that do not impose parametric assumptions for the random effects.