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Entropy
Volume 22
Issue 9
10.3390/e22090965
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Article

Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression

by
Alex Pijyan
1,
Qi Zheng
2,
Hyokyoung G. Hong
1,* and
Yi Li
3
1
Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA
2
Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY 40202, USA
3
Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(9), 965; https://doi.org/10.3390/e22090965
Submission received: 1 August 2020 / Revised: 26 August 2020 / Accepted: 28 August 2020 / Published: 31 August 2020
(This article belongs to the Special Issue Big Data Analytics and Information Science for Business and Biomedical Applications)
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Abstract

Predictive models play a central role in decision making. Penalized regression approaches, such as least absolute shrinkage and selection operator (LASSO), have been widely used to construct predictive models and explain the impacts of the selected predictors, but the estimates are typically biased. Moreover, when data are ultrahigh-dimensional, penalized regression is usable only after applying variable screening methods to downsize variables. We propose a stepwise procedure for fitting generalized linear models with ultrahigh dimensional predictors. Our procedure can provide a final model; control both false negatives and false positives; and yield consistent estimates, which are useful to gauge the actual effect size of risk factors. Simulations and applications to two clinical studies verify the utility of the method.
Keywords: estimation consistency; generalized linear models; high dimensional predictors; model selection; stepwise regression estimation consistency; generalized linear models; high dimensional predictors; model selection; stepwise regression

Share and Cite

MDPI and ACS Style

Pijyan, A.; Zheng, Q.; Hong, H.G.; Li, Y. Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression. Entropy 2020, 22, 965. https://doi.org/10.3390/e22090965

AMA Style

Pijyan A, Zheng Q, Hong HG, Li Y. Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression. Entropy. 2020; 22(9):965. https://doi.org/10.3390/e22090965

Chicago/Turabian Style

Pijyan, Alex, Qi Zheng, Hyokyoung G. Hong, and Yi Li. 2020. "Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression" Entropy 22, no. 9: 965. https://doi.org/10.3390/e22090965

APA Style

Pijyan, A., Zheng, Q., Hong, H. G., & Li, Y. (2020). Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression. Entropy, 22(9), 965. https://doi.org/10.3390/e22090965

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