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How To Pick The Best Regression Equation: A Review And Comparison Of Model Selection Algorithms

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Abstract

This paper reviews and compares twenty-one different model selection algorithms (MSAs) representing a diversity of approaches, including (i) information criteria such as AIC and SIC; (ii) selection of a “portfolio” or best subset of models; (iii) general-to-specific algorithms, (iv) forward-stepwise regression approaches; (v) Bayesian Model Averaging; and (vi) inclusion of all variables. We use coefficient unconditional mean-squared error (UMSE) as the basis for our measure of MSA performance. Our main goal is to identify the factors that determine MSA performance. Towards this end, we conduct Monte Carlo experiments across a variety of data environments. Our experiments show that MSAs differ substantially with respect to their performance on relevant and irrelevant variables. We relate this to their associated penalty functions, and a bias-variance tradeoff in coefficient estimates. It follows that no MSA will dominate under all conditions. However, when we restrict our analysis to conditions where automatic variable selection is likely to be of greatest value, we find that two general-to-specific MSAs, Autometrics, do as well or better than all others in over 90% of the experiments.

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  • Jennifer L. Castle & Xiaochuan Qin & W. Robert Reed, 2009. "How To Pick The Best Regression Equation: A Review And Comparison Of Model Selection Algorithms," Working Papers in Economics 09/13, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:09/13
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/0913.pdf
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    Cited by:

    1. Thomas Pave Sohnesen & Niels Stender, 2017. "Is Random Forest a Superior Methodology for Predicting Poverty? An Empirical Assessment," Poverty & Public Policy, John Wiley & Sons, vol. 9(1), pages 118-133, March.
    2. Castle, Jennifer L. & Doornik, Jurgen A. & Hendry, David F., 2012. "Model selection when there are multiple breaks," Journal of Econometrics, Elsevier, vol. 169(2), pages 239-246.
    3. Graham Bird & Alex Mandilaras & Helen Popper, 2012. "Explaining Shifts in Exchange Rate Regimes," School of Economics Discussion Papers 1312, School of Economics, University of Surrey.
    4. Steven L. Scott & Hal R. Varian, 2015. "Bayesian Variable Selection for Nowcasting Economic Time Series," NBER Chapters, in: Economic Analysis of the Digital Economy, pages 119-135, National Bureau of Economic Research, Inc.
    5. Hal R. Varian, 2014. "Big Data: New Tricks for Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 28(2), pages 3-28, Spring.
    6. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-33, February.
    7. Lu, Quanying & Li, Yuze & Chai, Jian & Wang, Shouyang, 2020. "Crude oil price analysis and forecasting: A perspective of “new triangle”," Energy Economics, Elsevier, vol. 87(C).

    More about this item

    Keywords

    Model selection algorithms; Information Criteria; General-to-Specific modeling; Bayesian Model Averaging; Portfolio Models; AIC; SIC; AICc; SICc; Monte Carlo Analysis; Autometrics;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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