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On quadratic logistic regression models when predictor variables are subject to measurement error

Author

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  • Stoklosa, Jakub
  • Huang, Yih-Huei
  • Furlan, Elise
  • Hwang, Wen-Han

Abstract

Owing to its good properties and a simple model fitting procedure, logistic regression is one of the most commonly used methods applied to data consisting of binary outcomes and one or more predictor variables. However, if the predictor variables are measured with error and the functional relationship between the response and predictor variables is non-linear (e.g., quadratic) then consistent estimation of model parameters is more challenging to develop. To address the effects of measurement error in predictor variables when using quadratic logistic regression models, two novel approaches are developed: (1) an approximated refined regression calibration; and (2) a weighted corrected score method. Both proposed approaches offer several advantages over existing methods in that they are computationally efficient and are straightforward to implement. A simulation study was conducted to evaluate the estimators’ finite sample performance. The proposed methods are also applied on real data from a medical study and an ecological application.

Suggested Citation

  • Stoklosa, Jakub & Huang, Yih-Huei & Furlan, Elise & Hwang, Wen-Han, 2016. "On quadratic logistic regression models when predictor variables are subject to measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 109-121.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:109-121
    DOI: 10.1016/j.csda.2015.09.012
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    References listed on IDEAS

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    1. Jakub Stoklosa & Wen-Han Hwang & Sheng-Hai Wu & Richard Huggins, 2011. "Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations," Biometrics, The International Biometric Society, vol. 67(4), pages 1659-1665, December.
    2. Wen-Han Hwang & Steve Y. H. Huang, 2003. "Estimation in Capture-Recapture Models When Covariates Are Subject to Measurement Errors," Biometrics, The International Biometric Society, vol. 59(4), pages 1113-1122, December.
    3. Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    4. Yih-Huei Huang & Chi-Chung Wen & Yu-Hua Hsu, 2015. "The Extensively Corrected Score for Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 911-924, December.
    5. Austin, Mike, 2007. "Species distribution models and ecological theory: A critical assessment and some possible new approaches," Ecological Modelling, Elsevier, vol. 200(1), pages 1-19.
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    1. Richard Huggins & Jakub Stoklosa & Cameron Roach & Paul Yip, 2018. "Estimating the size of an open population using sparse capture–recapture data," Biometrics, The International Biometric Society, vol. 74(1), pages 280-288, March.

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