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Activity Number:
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31
- Categorical Data
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Type:
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Contributed
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Date/Time:
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Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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Abstract #328705
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Presentation
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Title:
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Log Binomial Regression When the Maximum Likelihood Solution Is on the Boundary of the Parameter Space
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Author(s):
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Chao Zhu* and David W Hosmer and Jim Stankovich and Karen Wills and Leigh Blizzard
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Companies:
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Menzies Institute of Medical Research, University of Tasmania and University of Massachusetts and School of Medicine, University of Tasmania and Menzies Institute of Medical Research, University of Tasmania and Menzies Institute of Medical Research, University of Tasmania
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Keywords:
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Regression;
Binomial;
Log link;
Boundary point
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Abstract:
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Fitting a log binomial model to binary outcome data makes it possible to estimate risk and relative risk for follow-up data, and prevalence and prevalence ratios for cross-sectional data. However, the fitting algorithm may fail to converge from appropriate starting values when the maximum likelihood (ML) solution is on the boundary of the allowable parameter space. In the simplest case of a single covariate, the ML solution can be estimated using standard statistical software after re-parametrization of the covariate values. Petersen and Deddens (2010) sketched an extension of the re-parametrization method for multiple covariates, and labelled it the exact method. We provide the details necessary to implement the exact method. The ML solution by the exact method for data with number of covariates equal to the number of distinct unit probability covariate vectors (those combinations of covariate values with a fitted probability of unity) represent a special case for which a proof is provided. The properties of the exact estimator are investigated by simulation, and the results are compared with those of alternative estimation methods.
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Authors who are presenting talks have a * after their name.
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