Bias correction of AIC in logistic regression models

The purpose of this article is to review the findings of Professor Fujikoshi which are primarily in multivariate analysis. He derived many asymptotic expansions for multivariate statistics which include MANOVA tests, dimensionality tests and latent roots under normality and nonnormality. He has made a large contribution in the study on theoretical accuracy for asymptotic expansions by deriving explicit error bounds. A large contribution has been also made in an important problem involving the selection of variables with introducing "no additional information hypotheses" in some multivariate models and the application of model selection criteria. Recently he is challenging to a high-dimensional statistical problem. He has been involved in other topics in multivariate analysis, such as power comparison of a class of tests, monotone transformations with improved approximations, etc.

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“…Similar criteria were also proposed by Satoh et al [93] in the growth curve model and by Yanagihara et al [111] in logistic regression models.…”

Section: Selection Of Variables In Multivariate Modelssupporting

confidence: 52%

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Siotani

Wakaki

2006

Journal of Multivariate Analysis

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“…The best logistic regression models were selected using the Akaike information criterion (AIC) [52]. Since AIC values in logistic models with small to moderate sample sizes may be biased [53,54], the Bayes information criterion (BIC) was also calculated [55]. In a first step, models with only one explanatory variable were generated and the models with the lowest AIC were selected.…”

Section: Calibration and Validation Of The Mortality Modelsmentioning

confidence: 99%

Radial Growth Patterns Associated with Tree Mortality in Nothofagus pumilio Forest

Rodríguez‐Catón

Villalba

Srur

et al. 2019

Forests

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Tree mortality is a key process in forest dynamics. Despite decades of effort to understand this process, many uncertainties remain. South American broadleaf species are particularly under-represented in global studies on mortality and forest dynamics. We sampled monospecific broadleaf Nothofagus pumilio forests in northern Patagonia to predict tree mortality based on stem growth. Live or dead conditions in N. pumilio trees can be predicted with high accuracy using growth rate as an explanatory variable in logistic models. In Paso Córdova (CO), Argentina, where the models were calibrated, the probability of death was a strong negative function of radial growth, particularly during the six years prior to death. In addition, negative growth trends during 30 to 45 years prior to death increased the accuracy of the models. The CO site was affected by an extreme drought during the summer 1978-1979, triggering negative trends in radial growth of many trees. Individuals showing below-average and persistent negative trends in radial growth are more likely to die than those showing high growth rates and positive growth trends in recent decades, indicating the key role of droughts in inducing mortality. The models calibrated at the CO site showed high verification skill by accurately predicting tree mortality at two independent sites 76 and 141 km away. Models based on relative growth rates showed the highest and most balanced accuracy for both live and dead individuals. Thus, the death of individuals across different N. pumilio sites was largely determined by the growth rate relative to the total size of the individuals. Our findings highlight episodic severe drought as a triggering mechanism for growth decline and eventual death for N. pumilio, similar to results found previously for several other species around the globe. In the coming decades, many forests globally will be exposed to more frequent and/or severe episodes of reduced warm-season soil moisture. Tree-ring studies such as this one can aid prediction of future changes in forest productivity, mortality, and composition. Author Contributions: R.V., M.R.-C., and A.S. planned and designed plot setup and collected samples for the research with the help of people mention in Acknowledgments; methodology, R.V., M.R.-C.; dendrochronological processing and formal analysis, M.R.-C.; resources and funding acquisition, R.V., M.R.-C., A.S., and A.P.W.; data curation, M.R.-C.; writing-original draft preparation, M.R.-C.; writing-review and editing, M.R.-C., R.V., A.S., and A.P.W.; supervision, R.V. and A.S. Funding:We are grateful for support from Consejo Nacional de Investigaciones Científicas y Técnicas for providing the postdoctoral fellowship (CONICET), Argentina and BNP-PARIBAS Foundation through THEMES Project. APW was supported by NSF awards 1602581 and 1743738.

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“…This model is also a GLM having a link function that is given by the logit function. For the logistic regression model, Yanagihara et al (2003) proposed a bias-corrected AIC derived by stochastic expansion of the maximum likelihood estimator (MLE) of an unknown parameter. In the present study, we apply this procedure to the Poisson regression model.…”

Section: Introductionmentioning

confidence: 99%

Bias-Corrected AIC for Selecting Variables in Poisson Regression Models

Kamo¹,

Yanagihara²,

Satoh³

2013

Communications in Statistics - Theory and Methods

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In the present paper, we consider the variable selection problem in Poisson regression models. Akaike's information criterion (AIC) is the most commonly applied criterion for selecting variables. However, the bias of the AIC cannot be ignored, especially in small samples. We herein propose a new bias-corrected version of the AIC that is constructed by stochastic expansion of the maximum likelihood estimator. The proposed information criterion can reduce the bias of the AIC from O(n −1 ) to O(n −2 ). The results of numerical 1 investigations indicate that the proposed criterion is better than the AIC.

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Bias correction of AIC in logistic regression models

Cited by 13 publications

References 9 publications

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Radial Growth Patterns Associated with Tree Mortality in Nothofagus pumilio Forest

Bias-Corrected AIC for Selecting Variables in Poisson Regression Models

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