Quadratic Inference Function Sample Clauses

Quadratic Inference Function. Although GEEs consistently estimate regression parameters even when the correlation structure is misspecified, the estimator of the regression parameter can be inefficient under such misspecification. Qu et al. [69] introduced a quadratic inference function (QIF) method, which is essentially a generalized method of moments approach based on an extended GEE. The QIF method provides an alternate estimation approach for longitudinal data, which does not require direct estimation of the correlation pa- rameter and remains optimal even under misspecification of the correlation structure. Additionally, Qu et al. proposed using the QIF approach as a measure of goodness- of-fit. Let yij be an outcome variable and xij denote a p × 1 vector of covariates observed at the jth measurement occasion for subject i, where j = 1, . . . , mi and i = 1, . . . , n. Further, let yi = (yi1, . . . , yimi )′ be an mi × 1 vector of outcomes for subject i and β be a p × 1 vector of regression parameters. Assume that the E (yit) = µ (x′itβ) and let µi = (µi1, . . . , µimi ). Finally, let Vi be the covariance matrix of the vector yi. As seen in the GEE approach to modeling longitudinal data, the optimal estimating equation is given by the quasi-likelihood equation n opt ∂β i g = ∑ ∂µi V −1 (y i=1 − µ ) . When using the GEE approach, Vi is often unknown and a working variance model Vi = ϕA1/2 (µ ) Ri (α) A1/2 (µ ) with working correlation matrix R (α) is used during