Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)
Introduction In this chapter, the logistic model is extended to handle outcome variables that have dichotomous correlated respon ...
Objectives Upon completing this chapter, the learner should be able to: State or recognize examples of correlated responses. St ...
Presentation I. Overview Modeling outcomes with dichotomous correlated responses FOCUS Examples of correlated responses: Differ ...
Assumption: Responses correlated within clusters independent between clusters : 8 >> >>< >> >> : Igno ...
Infant Care Study: Sample Data From three infants: five (of nine) observations listed for each IDNO MO OUTCOME BIRTHWGT GENDER D ...
In general, with longitudinal data, independent variables may be either Time-dependent or Time-independent Outcome variable ge ...
95% confidence interval 95 %CI¼exp½ 0 : 2214 1 : 96 ð 0 : 8558 Þ ¼ð 0 : 23 ; 6 : 68 Þ Wald test H 0 :b 3 ¼ 0 Z¼ 0 : 2214 0 : ...
Wald test H 0 :b 3 ¼ 0 Z¼ 0 : 7764 0 : 4538 ¼ 1 : 711 ;P¼ 0 : 0871 Comparison of analysis approaches: dOR and 95% CI for DIARRH ...
Correlation structure: Framework for estimating: Correlations Regression coefficients Standard errors Primary interest ...
III. Data Layout Basic data layout for correlated analysis: Ksubjects niresponses for subjecti The basic data layout for a corre ...
IV. Covariance and Correlation Covariance and correlation are measures of relationships between variables. Covariance Population ...
Positive correlation On average, asXgets larger,Ygets larger; or, asXgets smaller,Ygets smaller. Negative correlation On average ...
Perfect linear relationship Y¼b 0 þb 1 X, for a givenX XandYindependent)r¼ 0 BUT r¼ 0 ) XandYindependent or XandYhave nonlinear ...
V. Generalized Linear Models General form of many statistical models: Y¼fðX 1 ;X 2 ;...;XpÞþE; where:Yis random X 1 ,X 2 ,...,Xp ...
Exponential family distributions include: Binomial Normal Poisson Exponential Gamma Generalized linear model gðmÞ¼b 0 þ~ p h¼ 1 ...
Link function: gðmÞ¼b 0 þ~bhXh g‘‘links’’EðYÞwithb 0 þ~bhXh Logistic regression (logit link) gðmÞ¼log m 1 m ¼logitðmÞ Alte ...
IfYinot independent but MV normal + Lspecified IfYinot independent andnot MV normal + Quasi-likelihood theory Quasi-likelihood: ...
Correlated vs. independent Identical model but Different assumptions GEE: Generalization of quasi- likelihood Specify a ...
Corresponding 2 2 correlation matrix C¼ 1 corrðY 1 ;Y 2 Þ corrðY 1 ;Y 2 Þ 1 " Diagonal matrix: has 0 in all non- diagonal entri ...
Block diagonal matrix: subject- specific correlation matrices form blocks (Bi) B 1 0 B 2 0B 3 2 6 4 3 7 5 where Bi¼ith block We ...
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