Sağlam bir modelin makina öğrenmesi algoritmalarının ve istatistiksel metotların hibrit uygulamalarına boylamsal veriler için uyarlanması

Data structures in which the same characteristics are measured repeatedly at different time points are counted among the longitudinal data types. These datasets require the use of advanced modeling techniques because of the dependency structure amongst replicates. Linear mixed models (LMM) is an advanced regression method used in the analysis of such data sets. Although the LMM method provides many flexibility and advantages, the model setup is based on a number of assumptions that are challenging to provide in real data sets. Another method for analyzing the longitudinal data could be machine learning (ML) algorithms. However, many of them desire data to be independent and identically distributed (iid) which is not applicable for longitudinal data. Because of these limitations, hybrid methods including both LMM and ML have been developed to make precise estimations for longitudinal data in models with both random and fixed effects. However, these methods have model setups based on the assumption of a normal distribution of errors, which are not robust to the presence of heavy-tailed distributed data and outlier observations. This study aims to extend and robustfy hybrid methods including LMM and ML by introducing a heavy-tailed distribution into the model setting. While LMM performs parameter estimations related to the random effect with a robust approach; the ML algorithm performs the estimation of the fixed effect parameters with the proposed model. The model is tested on two real data sets and simulation studies with several conditions and it gives promising results in real datasets and especially in simulation trials involving heavy-tailed situations and outliers. Almost all of the results based on comparison criteria such as RMSE, AIC and BIC favor the proposed method. While this study expands one of the modern topics of statistics with a robust approach and a machine learning method; it will guide researchers who practice in this field with the open source and codes provided.