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




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.

Suggested Citation

  • 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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    Cited by:

    1. Alex Mandilaras & Graham Bird, 2008. "Foreign exchange pressures in Latin America: does debt matter?," Journal of International Development, John Wiley & Sons, Ltd., pages 613-627.
    2. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, pages 1-33.
    3. 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.
    4. Jennifer Castle & David Hendry & Jurgen A. Doornik, 2010. "Evaluating Automatic Model Selection," Economics Series Working Papers 474, University of Oxford, Department of Economics.

    More about this item


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

    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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