Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

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Detailed Outline


Abbreviated Outline


I. Overview (pages 304–305)
A. Focus: Goodness of fit (GOF) – assessing the
extent to which a logistic model estimated
from a dataset predicts the observed
outcomes in the dataset.
B. Considers how well a given model, considered
by itself, fits the data.
C. Provides a summary measure over all subjects
that compares the observed outcome (Yi)for
subjectito the predicted outcomeðY^iÞfor this
subject obtained from the fitted model.
D. Widely used measure is thedeviance;
however, for binary logistic regression, use of
deviance is problematic. Alternative measure:
Hosmer–Lemeshow(HL) statistic.
II. Saturated vs. Fully Parameterized Models
(pages 305–312)
A. Saturated model
i. Providesperfect prediction of the (0, 1)
outcomefor each subject in the dataset
ii. Contains as many parameters as the
number of “subjects” in the dataset
iii. Uses data layout insubjects-specific (SS)
format
iv. Classical model used as gold standard for
assessing GOF
B. Fully parameterized model
i. Contains the maximum number of
covariates that can be defined from the
basic predictors (X) being considered for
the model.
ii. The number of parameters (kþ1) equals
the number (G) of distinctcovariate
patterns(orsubgroups) that can be
defined from the basic predictors.
iii. Uses data layout inevents–trials (ET)
format.
iv. Providesperfect predictionof the observed
proportion of cases withinsubgroups
defined by distinct covariate patterns ofX.
v. An alternative gold standard model for
determining GOF.
C. Example:n¼40, 2 basic predictors:E(0, 1),
V(0, 1)
i. Fully parameterized model (G¼ 4
covariate patterns,k¼3 variables):
logit PðXÞ¼aþbEþgVþdEV

Detailed Outline 329
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