Diagnostics for the scale of functional predictors in generalized linear models

Elizabeth J. Malloy, Edward J. Bedrick, Tim Goldsmith

Research output: Contribution to journalArticlepeer-review


We develop diagnostics for fixed-effects generalized linear models (GLMs) with functional predictors. As a first step, we extend the GLM to allow a functional predictor to depend on a vector of parameters. A power transformation and a cubic spline transformation are the two primary models considered. We discuss methods for fitting the models, then derive the score test and a graphical tool for assessing the need for a transformation in models with functional predictors. These methods are natural extensions of the Box-Tidwell score test and constructed residual plots used to examine nonlinearities in classical GLMs. We consider both penalized and nonpenalized maximum likelihood methods and use two data sets to illustrate the methods.

Original languageEnglish (US)
Pages (from-to)480-489
Number of pages10
Issue number4
StatePublished - Nov 2007
Externally publishedYes


  • Box-Tidwell method
  • Constructed residual plots
  • Penalized likelihood
  • Score test
  • Transformation model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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