Abstract: Due to their flexibility in explaining a wide range of function classes, partially linear mixed models, which include both parametric and nonparametric components with random effects, are appropriate to construct estimation equations. Traditionally, spline or kernel approaches are used in conjunction with parametric estimation to infer the linear coefficient when there are repeated measures in a partially linear mixed model. Challenges such as computational complexity, which increase as the number of variables in the nonparametric function grows, can be overcome through the partially linear mixed model approach enhanced with machine learning. With the use of machine learning algorithms, complex interaction structures, nonsmooth terms, and high-dimensional variables can also be included. Thus, the linear variables and the response are adjusted nonparametrically for the nonlinear variables, and these adjusted variables satisfy a linear mixed model in which the linear coefficient can be estimated by standard linear mixed-effects methods. This method allows the nonparametric function to be estimated using machine learning techniques and then the other components of the model can be estimated separately using classical statistical techniques. While reducing computational complexity, enabling more reliable results, this approach improves model accuracy. It also offers significant advantages especially in datasets with high dimensionality and repeated measurements, where traditional statistical methods and machine learning techniques may fall short. When there is high correlation among independent variables in partially linear mixed regression models, classic statistical methods may fail to produce reliable estimates because of the multicollinearity. In datasets containing repeated measurements, the ridge approach can be applied to mitigate this effect. The ridge estimation method regulates multicollinearity and enhances model stability, while the machine learning component manages the complexity of the nonparametric part, providing a more flexible analytical process. Therefore, while the partially linear mixed model enhanced with machine learning increases model accuracy by estimating the nonparametric components through machine learning algorithms, this enables better modelling of high-dimensional datasets with repeated measurements and allows for more flexible and accurate analyses by relaxing the strict assumptions required by classical methods.

Keywords: Partially linear mixed model, multicollinearity, double machine learning, plug in method, ridge approach, Henderson method

Pages: 801-809