有限混合線性混合效應（FM-LME）模型已成為處理具異質性之長期追蹤資料分群的常用工具。然而，FM-LME 模型中傳統的常態假設對於溫和型離群值或受污染數據可能較為敏感。本研究透過考慮群組隨機效應與個體內誤差服從多變量污染常態（MCN）分配，進一步擴展了 FM-LME 模型，此後將其簡稱為有限混合污染常態線性混合效應（FM-CNLME）模型。與多變量常態分配相比，MCN 分配額外包含兩個參數：一個用於控制溫和型離群值的比例，另一個則用於指定污染程度，進而提升參數估計結果的穩健性。在推論模型參數及隱藏資料方面，本研究發展兩套方法：最大概似（ML）估計與貝氏（Bayesian）推論。一個有效率的交替預期條件最大化（AECM）演算法被提供以執行最大概似估計。從完全貝氏觀點，結合吉布斯採樣（Gibbs sampler）與 Metropolis-Hastings（M-H）演算法的馬可夫鏈蒙地卡羅（MCMC）採樣程序被發展以進行後驗推估。數值結果顯示，在處理具有群體結構與污染觀測值的複雜長期追蹤資料時，相較於現有的模型，FM-CNLME 模型能有效識別潛在分群、達成更好的資料擬合優度，並在估計參數和計算配適值上提供更高的精確度。最後，本研究所提出的模型與方法亦應用於實證資料，以證明其在實務上的價值與效率。

Finite mixtures of linear mixed-effects (FM-LME) models have become a commonly used tool for clustering longitudinal data with heterogeneity. However, the conventional assumption of normality in the FM-LME model may be sensitive to mild outliers or contaminated points. This thesis extends the FM-LME model by considering the multivariate contaminated normal (MCN) distributions for component random effects and within-subjects errors, referred to as the finite mixtures of contaminated normal linear mixed-effects (FM-CNLME) model henceforth. Comparing with the multivariate normal distribution, the MCN distribution has two extra parameters: one for controlling the proportion of mild outliers and the other for specifying the degree of contamination, improving the robustness of the estimation results. Regarding the inference of parameters as well as latent data in the model, we develop two approaches: maximum likelihood (ML) estimation and Bayesian inference. For carrying out ML estimation, an efficient alternating expectation conditional maximization (AECM) algorithm is provided. From a fully Bayesian viewpoint, Markov Chain Monte Carlo (MCMC) sampling procedure, which combines the Gibbs sampler and Metropolis-Hastings (M-H) algorithm, is developed to perform posterior inference. Numerical results show that, when dealing with complex longitudinal data that have grouped structures and contaminated observations, the FM-CNLME model can effectively identify hidden groups, achieves better fitness of data, and offer more accurate estimation of parameters as well as fitted responses compared with the existing model. Our proposed model and methods are applied to real-data examples to demonstrate their practical values and efficiency.

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