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Theory & Methods: Fisher’s Information on the Correlation Coefficient in Bivariate Logistic Models
Author(s) -
Smith Murray D.,
Moffatt Peter G.
Publication year - 1999
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00086
Subject(s) - bivariate analysis , mathematics , statistics , censoring (clinical trials) , fisher information , estimator , econometrics , correlation coefficient , logistic regression , bivariate data , correlation , fisher transformation , geometry
From a theoretical perspective, the paper considers the properties of the maximum likelihood estimator of the correlation coefficient, principally regarding precision, in various types of bivariate model which are popular in the applied literature. The models are: ‘Full‐Full’, in which both variables are fully observed; ‘Censored‐Censored’, in which both of the variables are censored at zero; and finally, ‘Binary‐Binary’, in which both variables are observed only in sign. For analytical convenience, the underlying bivariate distribution which is assumed in each of these cases is the bivariate logistic. A central issue is the extent to which censoring reduces the level of Fisher’s information pertaining to the correlation coefficient, and therefore reduces the precision with which this important parameter can be estimated.