Principal component regression with variational bayesian principal component analysis approach to handle multicollinearity and missing data

NABILA AZARIN BALQIS; SUCI ASTUTIK; SOLIMUN; NURJANNAH; HENNY PRAMOEDYO

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Principal component regression with variational bayesian principal component analysis approach to handle multicollinearity and missing data

Author(s)

NABILA AZARIN BALQIS University of Brawijaya, Department of Statistics, East Java, Indonesia

SUCI ASTUTIK University of Brawijaya, Department of Statistics, East Java, Indonesia

SOLIMUN University of Brawijaya, Department of Statistics, East Java, Indonesia

NURJANNAH University of Brawijaya, Department of Statistics, East Java, Indonesia

HENNY PRAMOEDYO University of Brawijaya, Department of Statistics, East Java, Indonesia

Abstract

Principal Component Regression (PCR) is a combination method of Principal Component Analysis (PCA) and linear regression that aims to deal with multicollinearity in regression data. Classical PCA has the disadvantage that when faced with missing data. Missing data becomes a weakness in PCA where the resulting principal component will lose a lot of information so that the principal component cannot really describe the original variable properly. The method that can be used to deal with these problems and overcome overfitting is Variational Bayesian Principal Component Analysis (VBPCA). This study aims to modeling PCR using VBPCA with Ordinary Least Square (OLS) as a regression parameter estimation method to overcome multicollinearity at various levels of missing data proportions. The data used in this study are secondary data and simulation data which has been contaminated with collinearity in the predictor variables with various levels of the proportion missing data of 1%, 5%, and 10%. The results of this study indicate that in estimating the PCR parameters with VBPCA method using OLS, the estimated regression parameter coefficients have a constant value at the proportion of missing data up to 5%. This is influenced by missing data where the greater proportion of missing data, then the estimation results of the regression parameters are less constant and have a large standard error value of the regression parameters. Multicollinearity in secondary data and simulation data can be optimally overcome as indicated by the smaller standard error value of the regression parameter for the PCR method using VBPCA. VBPCA can handle the proportion of missing data to less than 10%. This is due to the large proportion of missing data as evidenced by the larger MAPE value, the cross validation ( ) and the adjusted value which are getting smaller as the proportion of missing data increases.

Publication Details

Page(s) 5545-5561

DOI DOI not available

Published Journal: Journal of Theoretical and Applied Information Technology, Volume: 100, Issue: 19, Year: 2022

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Keywords

PCR, multicollinearity, missing data, VBPCA

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