By David W. Hosmer, Stanley Lemeshow
This e-book discusses the way to version a binary end result variable from a linear regression research standpoint. It develops the logistic regression version and describes its use in tools for modelling the connection among a dichotomous end result variable and a suite of covariates. dialogue of the translation of this version follows. The textual content contains a number of info units that are the resource of the examples and workouts. The e-book additionally makes use of a couple of software program programs, together with BMDP, EGRET, GLIM, SAS, and SYSTAT, to investigate facts units.
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Additional resources for Applied Logistic Regression (Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics Section)
In linear regression the hat matrix is H = X(Xℜ′ X)-1Xℜ′; for example, = Hy. The linear regression residuals, (y ), expressed in terms of the hat matrix are (I H)y where I is the J Ã J identity matrix. Using weighted least squares Â < previous page < previous page next page > next page > page_150 page_151 Page 151 linear regression as a model, Pregibon (1981) derived a linear approximation to the fitted values which yields a hat matrix for logistic regression. This matrix is where V is a J Ã J diagonal matrix with general element v = .
Goodness-of-fit is assessed over the constellation of fitted values determined by the covariates in the model, not the total collection of covariates. Â , xp), and let J denote the number of distinct values of x observed. If some subjects have the same value of x then J < n. Â , J. It follows that Σmj = n. Let yj denote the number of positive responses, y = 1, among the mj subjects with x = xj. It follows that Σyj = n1, the total number of subjects with y = 1. The distribution of the goodness-of-fit statistics is obtained by letting n become large.
The degrees of freedom for tests are based on the difference in the number of variables in competing models, not on the number of covariate patterns. However, the number of covariate patterns may be an issue when the fit of a model is assessed. Goodness-of-fit is assessed over the constellation of fitted values determined by the covariates in the model, not the total collection of covariates. Â , xp), and let J denote the number of distinct values of x observed. If some subjects have the same value of x then J < n.
Applied Logistic Regression (Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics Section) by David W. Hosmer, Stanley Lemeshow