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A characterization of the efficiency of individualized logistic regressions
Author(s) -
Bull Shelley B.,
Donner Allan
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315659
Subject(s) - covariate , logistic regression , mathematics , statistics , efficiency , multivariate statistics , econometrics , binary number , sample (material) , estimator , chemistry , arithmetic , chromatography
The use of individualized regressions, which reduces the polychotomous logistic regression model to several dichotomous models, has been proposed as a solution to some practical difficulties for binary covariates (Begg and Gray 1984, Biometrika , 71, 11–18). Its disadvantages, however, include loss of efficiency and the complexity of making comparisons among regressions. Using expressions for the large‐sample distribution of the maximum‐likelihood estimates, the efficiency of the individualized procedure relative to the polychotomous procedure is evaluated for the case in which the covariates are assumed to follow a multivariate normal distribution. The relative efficiency when the logistic slope vectors from different regressions are collinear can be substantially lower compared to the efficiency with orthogonal slope vectors. Further evaluations for binary covariates using collinear and orthogonal slope parametrizations lead to a similar characterization.