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

广义线性混合模型（GLM）是广义线性模型的扩展，它将随机效应引入线性预测因子。它们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，生态学和环境科学。GLP-S是分析重复测量和聚类观测的有用模型，然而，已经开发的大多数估计方法都是基于随机效应的正态性假设。该假设提供了一种方便的方法来估计固定效应，但可能会损害估计效率。本研究计划提出了研究算法，推理方法，预测，拟合优度，模型选择和识别的GLCLT，不强加参数假设的随机效应。

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.