A spline-based lack-of-fit test for independent variable effect in poisson regression

Chin-Shang Li, Wanzhu Tu

Research output: Contribution to journalArticlepeer-review


In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given.

Original languageEnglish (US)
Pages (from-to)239-247
Number of pages9
JournalJournal of Modern Applied Statistical Methods
Issue number1
StatePublished - May 2007
Externally publishedYes


  • B-splines
  • Likelihood ratio test
  • Loglinear model
  • Penalized likelihood
  • Poisson regression model

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability


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