Estimation in Marginal Models GEE and Robust Estimation

Estimation in Marginal Models (GEE and Robust Estimation)

GEE • Since there is no convenient specification of the joint multivariate distribution of Y for marginal models when the responses are discrete, we require an alternative to MLE • GEE is based on the concept of “estimating equations” and provides a very general approach for analyzing correlated responses that can be discrete or continuous

GEE • The essential idea behind GEE is to generalize and extend the usual likelihood equations for a GLM with a univariate response by incorporating the covariance matrix of the vector of responses Y • For the case of linear models, the GLS estimator (also called Generalized Least Square estimator) for the vector of regression coefficients is a special case of the GEE approach

What we need to specify for implementing GEE Model for the mean Known variance function Working correlation matrix: model for the pariwise correlations among the responses

Working covariance matrix V is called the working covariance matrix to distinguish for the true underlying covariance of Y

GEE minimize GEE equations Solution of the GEE equation

Properties of GEE estimates • The GEE estimator is consistent whether or not the within subject associations/correlations have been correctly modelled • That is, for GEE estimator to provide a valid estimate of the true beta, we only require that the model for the mean response has been correctly specified

Asymptotic distribution of GEE estimator • In large sample, the GEE estimator is multivariate normal True covariance matrix

Sandwich estimate of bread meat Consistent estimate of the true Covariance matrix of Y

Link to stata command xtgee for continuous data substitute into GEE equations, got • xtgee, identity link, corr(exch) • Use Weighted Least Square for

• xtgee, identity link, corr(exch), robust • Use Sandwich Estimator for

Link to stata commands xtgee for binary data • Substitute into GEE equation, but no closed-form solution, need iteration. • Difference between using robust or not analogous to continuous data • xtgee, logit link, corr(exch), robust