The Factor-Augmented Regression Model (FARM) for Solving the Problem of High-Dimensional Data

Abstract

High-dimensional data analysis is a sub-topic of modern statistical applications that has become more significant when the number of explanatory variables grows bigger than the sample size. Such scenarios tend to make classic regression methods ineffective in the form of multicollinearity, high variance, and lack of the ability to estimate the parameters. This paper explores the effectiveness of the Factor-Augmented Regression Model (FARM) as an effective way of handling the issues of high-dimensional data. The given model splits the explanatory factors into latent variables and idiosyncratic elements that allow reducing the dimension but do not lose the necessary structural data. To maximize the prediction accuracy and the selection of the variables, the penalized estimation methods are used. The methodology is analyzed and approximated under the extensive simulation experiments in a high-dimensional data model, with varying sample sizes to assess the predictive performance. In addition, the model is used on real-world health-related data on body composition in order to determine its usefulness on enhancing the predictability of the model and to determine important predictors. The findings prove that Factor-Augmented Regression Model (FARM) is stable in its estimates and better predicting models than the conventional regression techniques in high dimensional situations. These results verify the appropriateness of the model in scientific applications that are based on data that are complex and large in scale.