### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

*Journal of Modern Applied Statistical Methods*,

*6*(1), 239-247.

**A spline-based lack-of-fit test for independent variable effect in poisson regression.** / Li, Chin-Shang; Tu, Wanzhu.

Research output: Contribution to journal › Article

*Journal of Modern Applied Statistical Methods*, vol. 6, no. 1, pp. 239-247.

}

TY - JOUR

T1 - A spline-based lack-of-fit test for independent variable effect in poisson regression

AU - Li, Chin-Shang

AU - Tu, Wanzhu

PY - 2007/5

Y1 - 2007/5

N2 - 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.

AB - 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.

KW - B-splines

KW - Likelihood ratio test

KW - Loglinear model

KW - Penalized likelihood

KW - Poisson regression model

UR - http://www.scopus.com/inward/record.url?scp=48249115994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48249115994&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:48249115994

VL - 6

SP - 239

EP - 247

JO - Journal of Modern Applied Statistical Methods

JF - Journal of Modern Applied Statistical Methods

SN - 1538-9472

IS - 1

ER -