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Varying-coefficient models (with discussion). (English) Zbl 0796.62060
The authors consider generalizations of linear models which are linear in the regressors but their coefficients are permitted to change smoothly as functions of other variables. Such a model has the form \[ \eta = B_ 0 + X_ 1 B_ 1 (R_ 1) + X_ 2 B_ 2(R_ 2) + \cdots + X_ p B_ p(R_ p). \] Here \(\eta\) is a parameter of a random variable \(Y\), and the coefficients of \(X_ i\)’s are altered by \(R_ i\)’s through the unspecified functions \(B_ i(R_ i)\).
The authors present general algorithms for estimating the model flexibility. These varying coefficients models include generalized additive models as well as dynamic generalized linear models as special cases. Some illustrative examples are given and their applications to the proportional hazards model for survival data are also discussed. The paper ends with interesting and useful comments and discussions by other researchers in this area.

MSC:
62J12 Generalized linear models (logistic models)
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