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Maximum Likelihood Analysis of Logistic Regression Models with Incomplete Covariate Data and Auxiliary Information

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  • Nicholas J. Horton
  • Nan M. Laird

Abstract

Summary. This article presents a new method for maximum likelihood estimation of logistic regression models with incomplete covariate data where auxiliary information is available. This auxiliary information is extraneous to the regression model of interest but predictive of the covariate with missing data. Ibrahim (1990, Journal of the American Statistical Association85, 765–769) provides a general method for estimating generalized linear regression models with missing covariates using the EM algorithm that is easily implemented when there is no auxiliary data. Vach (1997, Statistics in Medicine16, 57–72) describes how the method can be extended when the outcome and auxiliary data are conditionally independent given the covariates in the model. The method allows the incorporation of auxiliary data without making the conditional independence assumption. We suggest tests of conditional independence and compare the performance of several estimators in an example concerning mental health service utilization in children. Using an artificial dataset, we compare the performance of several estimators when auxiliary data are available.

Suggested Citation

  • Nicholas J. Horton & Nan M. Laird, 2001. "Maximum Likelihood Analysis of Logistic Regression Models with Incomplete Covariate Data and Auxiliary Information," Biometrics, The International Biometric Society, vol. 57(1), pages 34-42, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:34-42
    DOI: 10.1111/j.0006-341X.2001.00034.x
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    References listed on IDEAS

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    1. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    2. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz, 1999. "Monte Carlo EM for Missing Covariates in Parametric Regression Models," Biometrics, The International Biometric Society, vol. 55(2), pages 591-596, June.
    3. Stuart R. Lipsitz & Joseph G. Ibrahim & Garrett M. Fitzmaurice, 1999. "Likelihood Methods for Incomplete Longitudinal Binary Responses with Incomplete Categorical Covariates," Biometrics, The International Biometric Society, vol. 55(1), pages 214-223, March.
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    1. Sinha, Sanjoy K. & Laird, Nan M. & Fitzmaurice, Garrett M., 2010. "Multivariate logistic regression with incomplete covariate and auxiliary information," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2389-2397, November.
    2. Liu, Li & Xiang, Liming, 2019. "Missing covariate data in generalized linear mixed models with distribution-free random effects," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 1-16.

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