### Abstract

The negative binomial (NB) is frequently used to model overdispersed Poisson count data. To study the effect of a continuous covariate of interest in an NB model, a flexible procedure is used to model the covariate effect by fixed-knot cubic basis-splines or B-splines with a second-order difference penalty on the adjacent B-spline coefficients to avoid undersmoothing. A penalized likelihood is used to estimate parameters of the model. A penalized likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the continuous covariate effect. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. The smoothing parameter value is determined by setting a specified value equal to the asymptotic expectation of the test statistic under the null hypothesis. The power performance of the proposed test is studied with simulation experiments.

Original language | English (US) |
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Pages (from-to) | 1013-1025 |

Number of pages | 13 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 85 |

Issue number | 5 |

DOIs | |

State | Published - Mar 24 2015 |

### Keywords

- B-spline
- overdispersion
- penalized likelihood ratio test
- semiparametric negative binomial regression

### ASJC Scopus subject areas

- Applied Mathematics
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty