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Lack of fit tests for linear regression models with many predictor variables using minimal weighted maximal matchings

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  • Miller, Forrest R.
  • Neill, James W.

Abstract

We develop lack of fit tests for linear regression models with many predictor variables. General alternatives for model comparison are constructed using minimal weighted maximal matchings consistent with graphs on the predictor vectors. The weighted graphs we employ have edges based on model-driven distance thresholds in predictor space, thereby making our testing procedure implementable and computationally efficient in higher dimensional settings. In addition, it is shown that the testing procedure adapts to efficacious maximal matchings. An asymptotic analysis, along with simulation results, demonstrate that our tests are effective against a broad class of lack of fit.

Suggested Citation

  • Miller, Forrest R. & Neill, James W., 2016. "Lack of fit tests for linear regression models with many predictor variables using minimal weighted maximal matchings," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 14-26.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:14-26
    DOI: 10.1016/j.jmva.2016.05.005
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    References listed on IDEAS

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    1. Ronald Christensen & Yong Lin, 2015. "Lack-of-fit Tests Based On Partial Sums of Residuals," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(13), pages 2862-2880, July.
    2. Pascal Lavergne & Valentin Patilea, 2012. "One for All and All for One: Regression Checks With Many Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 41-52.
    3. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    4. Christensen, Ronald & Sun, Siu Kei, 2010. "Alternative Goodness-of-Fit Tests for Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 291-301.
    5. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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    Cited by:

    1. Stefan Wellek, 2021. "Testing for goodness rather than lack of fit of continuous probability distributions," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-12, September.
    2. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).

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