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Bayesian analysis of latent factor quantile regression model
Journal of the Korean Data & Information Science Society 2022;33:755-73
Published online September 30, 2022;  https://doi.org/10.7465/jkdi.2022.33.5.755
© 2022 Korean Data and Information Science Society.

Minjung Kyung1

1Department of Statistics, Duksung Women’s University
Correspondence to: This work was supported by the Duksung Women’s University research grants 3000006527.
1 Associate professor, Department of Statistics, Duksung Women’s University, Seoul 132-714, Korea.
E-mail: mkyung@duksung.ac.kr
Received July 26, 2022; Revised September 2, 2022; Accepted September 16, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Quantile regression model has been known as a strong tool even for non-normal and non-homoscedasticity response. Factor regression constructs a common structure inherent among explanatory variables to solve the multicollinearity among explanatory variables and is considered for a dimension reduction. We suggest a Bayesian inference for the latent factor quantile regression with LASSO prior to construct a significant factor loading matrix of intrinsic interests among infinite latent structures. Also, we consider shrinkage priors on selected factors with large variance. The estimated factor loading matrix with the estimates of the other parameters can be inversely transformed into linear parameters of each explanatory variable and can be used as prediction models for new observations. To choose the number of factors, we consider the linear relationship with dependent variable based on the adjusted Bayesian information criteria of quantile regression. We apply the proposed method to Boston housing dataset, which is available in R, ”mlbench” package. We observe that the estimated regression coefficients and the estimated variance are smaller than estimates from other compared methods and the calculated MSE of predicted values of Bayesian latent factor quantile regression model is smaller than the common quantile regression models with shrinkage methods.
Keywords : Adjusted Bayesian information criteria, Bayesian inference, latent factor model, quantile regression, shrikage priors.