Beta Principal Component Regression Model with Application

Rammah Oday  Hassan

Rammah Oday Hassan Assistant Lecturer of Statistic at Administration and Economics of Babylon University, Iraq

Keywords: Beta Regression, Principal Component Regression, Multicollinearity, Beta Principal Component Regression

Abstract

The main goal of regression analysis is to estimate the effect relationship between independent variables and the dependent variable. Consequently, the type of response variable data determines the type of regression model to be used. If the dependent variable data is continuous and represents proportions confined between (0, 1), the Beta regression model is considered a good choice for representing such a relationship. However, at times, the Beta regression model encounters issues that make the estimated relationship unstable. This instability is due to the presence of some econometric problems that cause the estimators to be inaccurate. One such issue is multicollinearity. This problem arises when there is a strong correlation between the explanatory variables, which particularly affects the estimators of the parameters (β) by reducing their accuracy. Multicollinearity leads to an unusual inflation of parameter variances, making the estimators less reliable. In this paper, we will present a new method that integrates the Beta regression model with Principal Component Regression to develop a hybrid regression model. This hybrid model will be more suitable for estimation in the presence of multicollinearity issues. Simulation examples and real data are used to evaluate the performance of the proposed method in comparison with existing methods.

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