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Unformatted text preview: PUBH 7430 Lecture 13 J. Wolfson Division of Biostatistics University of Minnesota School of Public Health October 18, 2011 ”In statistics, as in art, never fall in love with your model.” Seen on a fortune cookie... Marginal models for correlated data Setup • Y 1 , Y 2 , . . . , Y K independent vectors of correlated observations • Predictor matrices X 1 , X 2 , . . . , X K • Model mean μ i = E ( Y i  X i ) via g ( μ i ) = X i β Generalized Estimating Equations 1 Select the mean function 2 Fix a variance function 3 Assume a “working” correlation structure 4 Use sandwich variance estimator to “fix up” variance estimates and: • Produce coefficient estimates ˆ β • Compute CIs/pvalues/etc. GEE as a marginal model • GEE is known as a marginal modeling approach. • Marginal model: Model where comparisons between clusters are of primary interest. • GEE most useful for comparing effects of covariates which do not vary within clusters. • In contrast to conditional models (generally associated with random effects... later), where comparisons within clusters are of interest. Marginal models for correlated data What is the difference between: 1 “Naive” GLM 2 “Naive” GLM w/ sandwich variance estimates 3 GEE w/ independence working correlation matrix 4 GEE w/ Exch/AR1/unstructured/etc. working correlation matrix with respect to: 1 Estimates ˆ β of β 2 Estimates d Var ( ˆ β ) of Var ( ˆ β ) ⇒ Estimates of confidence intervals/pvalues for ˆ β Properties of estimators Consistency “As the sample size increases, the probability that our estimate is far from the true value gets small.” ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●...
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This note was uploaded on 11/21/2011 for the course PUBH 7430 taught by Professor Prof.eberly during the Fall '04 term at Minnesota.
 Fall '04
 Prof.Eberly

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