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Model Selection Using Information Theory and the MDL Principle

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  • Robert A. Stine

    (University of Pennsylvania)

Abstract

Information theory offers a coherent, intuitive view of model selection. This perspective arises from thinking of a statistical model as a code, an algorithm for compressing data into a sequence of bits. The description length is the length of this code for the data plus the length of a description of the model itself. The length of the code for the data measures the fit of the model to the data, whereas the length of the code for the model measures its complexity. The minimum description length (MDL) principle picks the model with smallest description length, balancing fit versus complexity. Variations on MDL reproduce other well-known methods of model selection. Going further, information theory allows one to choose from among various types of models, permitting the comparison of tree-based models to regressions. A running example compares several models for the well-known Boston housing data.

Suggested Citation

  • Robert A. Stine, 2004. "Model Selection Using Information Theory and the MDL Principle," Sociological Methods & Research, , vol. 33(2), pages 230-260, November.
    • Handle: RePEc:sae:somere:v:33:y:2004:i:2:p:230-260
    DOI: 10.1177/0049124103262064
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    References listed on IDEAS

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    1. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    2. Thomas C. M. Lee, 2001. "An Introduction to Coding Theory and the Two‐Part Minimum Description Length Principle," International Statistical Review, International Statistical Institute, vol. 69(2), pages 169-183, August.
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    Cited by:

    1. Foster, Dean P. & Stine, Robert & Young, H. Peyton, 2011. "A Markov Test for Alpha," Working Papers 11-49, University of Pennsylvania, Wharton School, Weiss Center.
    2. Mattia Prosperi & Jiang Bian & Iain E. Buchan & James S. Koopman & Matthew Sperrin & Mo Wang, 2019. "Raiders of the lost HARK: a reproducible inference framework for big data science," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-12, December.

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