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Inferences from logistic regression models in the presence of small samples, rare events, nonlinearity, and multicollinearity with observational data

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  • Jason S. Bergtold
  • Elizabeth A. Yeager
  • Allen M. Featherstone

Abstract

The logistic regression model has been widely used in the social and natural sciences and results from studies using this model can have significant policy impacts. Thus, confidence in the reliability of inferences drawn from these models is essential. The robustness of such inferences is dependent on sample size. The purpose of this article is to examine the impact of alternative data sets on the mean estimated bias and efficiency of parameter estimation and inference for the logistic regression model with observational data. A number of simulations are conducted examining the impact of sample size, nonlinear predictors, and multicollinearity on substantive inferences (e.g. odds ratios, marginal effects) when using logistic regression models. Findings suggest that small sample size can negatively affect the quality of parameter estimates and inferences in the presence of rare events, multicollinearity, and nonlinear predictor functions, but marginal effects estimates are relatively more robust to sample size.

Suggested Citation

  • Jason S. Bergtold & Elizabeth A. Yeager & Allen M. Featherstone, 2018. "Inferences from logistic regression models in the presence of small samples, rare events, nonlinearity, and multicollinearity with observational data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(3), pages 528-546, February.
    • Handle: RePEc:taf:japsta:v:45:y:2018:i:3:p:528-546
    DOI: 10.1080/02664763.2017.1282441
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    References listed on IDEAS

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    1. Claeskens, Gerda & Aerts, Marc & Molenberghs, Geert, 2003. "A quadratic bootstrap method and improved estimation in logistic regression," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 383-394, February.
    2. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    3. Jason Dietrich, 2005. "The effects of sampling strategies on the small sample properties of the logit estimator," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(6), pages 543-554.
    4. E. Onukwugha & J. Bergtold & R. Jain, 2015. "A Primer on Marginal Effects—Part II: Health Services Research Applications," PharmacoEconomics, Springer, vol. 33(2), pages 97-103, February.
    5. Eberechukwu Onukwugha & Jason Bergtold & Rahul Jain, 2015. "A Primer on Marginal Effects—Part I: Theory and Formulae," PharmacoEconomics, Springer, vol. 33(1), pages 25-30, January.
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