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2016 | OriginalPaper | Chapter

8. Adaptive Logistic Regression Modeling of Univariate Dichotomous and Polytomous Outcomes

Authors : George J. Knafl, Kai Ding

Published in: Adaptive Regression for Modeling Nonlinear Relationships

Publisher: Springer International Publishing

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Abstract

This chapter presents adaptive analyses of mercury level data, addressing how mercury level categorized as low and high (with cutoff 1.0 ppm near its median) and as low, medium, and high (with cutoffs 0.72 and 1.3 ppm near its tertiles) for \( \mathrm{n}=169 \) largemouth bass caught in the Lumber and Waccamaw Rivers of North Carolina depends on weight, length, and river. These analyses demonstrate adaptive logistic regression using fractional polynomials, including modeling of dichotomous and polytomous outcomes, extensions to adaptive multinomial and ordinal regression for polytomous outcomes, and how to model dispersions as well as means. Formulations are also provided for these alternative regression models, for associated k-fold LCV scores for unit dispersions models, extended quasi-likelihood cross-validation (\( {\mathrm{QLCV}}^{+} \)) scores for non-unit dispersions models based on extended quasi-likelihoods, for odds ratio (OR) functions generalizing the OR used in standard logistic regression, and for residuals and standardized or Pearson residuals. The example analyses demonstrate assessing whether the logits (or log odds) for an outcome are nonlinear in individual predictors, whether those relationships are better addressed with multiple predictors in combination compared to using singleton predictors, whether those relationships are additive in predictors, whether the predictors interact using geometric combinations, whether ordinal polytomous outcomes are better modeled with ordinal or multinomial regression, and whether there is a benefit to considering non-unit dispersions.

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Metadata
Title
Adaptive Logistic Regression Modeling of Univariate Dichotomous and Polytomous Outcomes
Authors
George J. Knafl
Kai Ding
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-33946-7_8

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