A design-sensitive approach to fitting regression models with complex survey data
This survey article reviews generalized linear models of the form \(y_k = f(\mathbf{x}_k^T\mathbf{\beta}) + \epsilon_k\) in the context of survey sampling, summarizing earlier work of the author [J. Stat. Plann. Inference 129, No. 1--2, 263--277 (2005; Zbl 1058.62014)]. \(\mathrm{E}(\epsilon_k|\mathbf{x}_k) = 0\) is not assumed, but instead only uncorrelatedness, \(\mathrm{E}(\mathbf{x}_k \epsilon_k) = 0\). Weighted estimating equations, interpretations of parameters and relations to standard estimating approaches [\textit{W. A. Fuller}, Sankhyā, Ser. C 37, No. 3, 117--132 (1975; Zbl 0395.62009)] and [\textit{D. A. Binder}, Int. Stat. Rev. 51, 279--292 (1983; Zbl 0535.62014)] are discussed. While results from the two approaches are identical for many important cases, the cumulative logistic model is one instance where approaches diverge.
scientific article; zbMATH DE number 6828646
scientific article