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http://dx.doi.org/10.5351/KJAS.2020.33.4.365

Bayesian analysis of latent factor regression model  

Kyung, Minjung (Department of Statistics, Duksung Women's University)
Publication Information
The Korean Journal of Applied Statistics / v.33, no.4, 2020 , pp. 365-377 More about this Journal
Abstract
We discuss latent factor regression when constructing a common structure inherent among explanatory variables to solve multicollinearity and use them as regressors to construct a linear model of a response variable. Bayesian estimation with LASSO prior of a large penalty parameter to construct a significant factor loading matrix of intrinsic interests among infinite latent structures. The estimated factor loading matrix with estimated other parameters can be inversely transformed into linear parameters of each explanatory variable and used as prediction models for new observations. We apply the proposed method to Product Service Management data of HBAT and observe that the proposed method constructs the same factors of general common factor analysis for the fixed number of factors. The calculated MSE of predicted values of Bayesian latent factor regression model is also smaller than the common factor regression model.
Keywords
Bayesian latent factor model; LASSO prior; Gibbs sampling;
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1 Aguilar, O. and West, M. (2000). Bayesian dynamic factor models and portfolio allocation, Journal of Business and Economic Statistics, 18, 338-357.   DOI
2 Bartlett, M. S. (1951). The effect of standardization on a 2 approximation in factor analysis, Biometrika, 38, 337-344   DOI
3 Bhattacharya, A. and Dunson, D. B. (2011). Sparse Bayesian infinite factor models, Biometrika, 98, 291-306.   DOI
4 Hair, J. F., Black, W. C., Babin, B. J., and Anderson, R. E. (2014). Multivariate Data Analysis : Pearson New International Edition (7th ed), Pearson.
5 Hoerl, A. E. and Kennard, R. W. (1950). Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12, 55-67.   DOI
6 Hotelling, H. (1957). The relations of the newer multivariate statistical methods to factor analysis, British Journal of Statistical Psychology, 10, 69-79.   DOI
7 Jeffers, J. N. R. (1967). Two case studies in the application of principal component analysis, Applied Statistics, 16, 225-236.   DOI
8 Kendall, M. G. (1957). A Course in Multivariate Analysis, Griffin, London.
9 Kyung, M., Gill, J., Ghosh, M., and Casella, G. (2010). Penalized regression, standard errors, and Bayesian lassos, Bayesian Analysis, 5, 369-412.   DOI
10 Park, T. and Casella, G. (2008). The Bayesian lasso, Journal of the American Statistical Association, 103, 681-686.   DOI
11 Raftery, A. E. (1995). Bayesian model selection in social research, Sociological Methodology, 25, 111-163.   DOI
12 Tibshirani, R. (1996). Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B, 58, 267-288.
13 West, M. (2003). Bayesian factor regression models in the "Large p, Small n" paradigm, in: J.M. Bernardo, M. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith, M. West (Eds.), Bayesian Statistics, Vol. 7, OxfordUniversity Press, Oxford, 723-732