Reduced bias estimation of the log odds ratio

Asma Saleh ()
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Asma Saleh: University College London

Statistical Papers, 2024, vol. 65, issue 8, No 20, 5293-5331

Abstract: Abstract Analysis of binary matched pairs data is problematic due to infinite maximum likelihood estimates of the log odds ratio and potentially biased estimates, especially for small samples. We propose a penalised version of the log-likelihood function based on adjusted responses which always results in a finite estimator of the log odds ratio. The probability limit of the adjusted log-likelihood estimator is derived and it is shown that in certain settings the maximum likelihood, conditional and modified profile log-likelihood estimators drop out as special cases of the former estimator. We implement indirect inference to the adjusted log-likelihood estimator. It is shown, through a complete enumeration study, that the indirect inference estimator is competitive in terms of bias and variance in comparison to the maximum likelihood, conditional, modified profile log-likelihood and Firth’s penalised log-likelihood estimators.

Keywords: Bias reduction; Binary matched pairs; Indirect inference; Maximum likelihood; Modified profile likelihood; Adjusted responses; 62F10; 62F12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01593-7

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