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Diagnostics for the Scale of Functional Predictors in Generalized Linear Models

Summary: ´╗┐[This abstract is based on the authors' abstract.] Diagnostics are developed for fixed-effects generalized linear models (GLMs) with functional predictors, after first extending the GLM to permit a functional predictor to depend on a vector of parameters. Methods for fitting both a power transformation model and a cubic spline transformation model are discussed, and the score test and a graphical tool for assessing the need for a transformation in models with functional predictors are then determined. These methods are extensions of the methods used to examine nonlinearities in classical GLMs. Both penalized and nonpenalized maximum likelihood methods are considered.

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  • Topics: Statistics
  • Keywords: Residual analysis, Box plots, Likelihood methods, Transformation, Linear models
  • Author: Malloy, Elizabeth J.; Bedrick, Edward J.; Goldsmith, Tim
  • Journal: Technometrics