A Comparative Study of Ridge Robust and Reciprocal Lasso Estimators for Semiparametric Additive Partial Linear Models Under Multicollinearity

Abstract

Estimating parameters in Semiparametric Additive Partial Linear Models (SAPLMs) accurately proves quite difficult under high-dimensional data and related explanatory variables. Multicollinearity among predictors not only increases the variance of parameter estimates but also makes statistical interpretation more difficult, especially when the number of variables exceeds the sample size. We contrast two strong estimating techniques (Ridge regression with R/W robust estimators and the Reciprocal Lasso method) to solve these problems. Our work assesses their efficacy in overcoming multicollinearity while concurrently choosing important variables. We evaluate the techniques by means of three criteria, namely: Average Absolute Deviation Error (AADE), Mean Squared Error (MSE), and coefficient of determination (R2), using actual educational data on elements influencing the academic performance of special needs students. Results show that the Reciprocal Lasso approach offers more accurate predictions and improved variable selection capacity than both Ridge robust methods regarding the practical aspect, in terms of simulation methods, it was observed that the Lasso method is preferable when the sample size is less than the number of explanatory variables, the Ridge with W robust method is preferable when there is a moderate correlation between the explanatory variables, and the Ridge with R robust method is preferable when there is a strong relationship between the explanatory variables.