Journal ArticleDOI
On the existence of maximum likelihood estimates in logistic regression models
Adelin Albert,Ja. Anderson +1 more
TLDR
For multinomial logistic regression models, this article proved existence theorems by considering the possible patterns of data points, which fall into three mutually exclusive and exhaustive categories: complete separation, quasicomplete separation and overlap.Abstract:
SUMMARY The problems of existence, uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature (Haberman, 1974, Chapter 2; Wedderburn, 1976; Silvapulle, 1981). For multinomial logistic regression models, we prove existence theorems by considering the possible patterns of data points, which fall into three mutually exclusive and exhaustive categories: complete separation, quasicomplete separation and overlap. Our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables.read more
Citations
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Journal ArticleDOI
Bias reduction of maximum likelihood estimates
TL;DR: In this paper, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function, and the effect is to penalize the likelihood by the Jeffreys invariant prior.
Book
Flexible Imputation of Missing Data
TL;DR: The problem of missing data concepts of MCAR, MAR and MNAR simple solutions that do not (always) work multiple imputation in a nutshell and some dangers, some do's and some don'ts are covered.
Journal ArticleDOI
A solution to the problem of separation in logistic regression
Georg Heinze,Michael Schemper +1 more
TL;DR: A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation and produces finite parameter estimates by means of penalized maximum likelihood estimation.
Journal ArticleDOI
A weakly informative default prior distribution for logistic and other regression models
TL;DR: In this paper, the authors propose a new prior distribution for logistic regression models, called Cauchy prior, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-t prior distributions on the coefficients.
Journal ArticleDOI
Back to the Future: Modeling Time Dependence in Binary Data
TL;DR: Monte Carlo analysis demonstrates that, for the types of hazards one often sees in substantive research, the polynomial approximation always outperforms time dummies and generally performs as well as splines or even more flexible autosmoothing procedures.
References
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Regression models and life tables (with discussion
TL;DR: The drum mallets disclosed in this article are adjustable, by the percussion player, as to balance, overall weight, head characteristics and tone production of the mallet, whereby the adjustment can be readily obtained.
Journal ArticleDOI
Logistic disease incidence models and case-control studies
Ross L. Prentice,R. Pyke +1 more
TL;DR: In this article, it was shown that the odds ratio estimators and their asymptotic variance matrices can be obtained by applying the original logistic regression model to the case-control study as if the data had been obtained in a prospective study.
Journal ArticleDOI
Separate sample logistic discrimination
TL;DR: In this article, the problem of logistic discrimination when all or most of the observations are qualitative is discussed and the results of Aitchison & Silvey (1958) on constrained maximum likelihood estimation are extended to the situation where separate samples are taken from each population.