### Abstract

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 language | English (US) |
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Pages (from-to) | 239-247 |

Number of pages | 9 |

Journal | Journal of Modern Applied Statistical Methods |

Volume | 6 |

Issue number | 1 |

State | Published - May 2007 |

Externally published | Yes |

### Keywords

- 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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## Cite this

*Journal of Modern Applied Statistical Methods*,

*6*(1), 239-247.