### Abstract

A semiparametric logistic regression model is proposed in which its nonparametric component is approximated with fixed-knot cubic B-splines. To assess the linearity of the nonparametric component, we construct a penalized likelihood ratio test statistic. When the number of knots is fixed, the null distribution of the test statistic is shown to be asymptotically the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. We set the asymptotic null expectation of this test statistic equal to a value to determine the smoothing parameter value. Monte Carlo experiments are conducted to investigate the performance of the proposed test. Its practical use is illustrated with a real-life example.

Original language | English (US) |
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Pages (from-to) | 461-475 |

Number of pages | 15 |

Journal | Journal of Applied Statistics |

Volume | 43 |

Issue number | 3 |

DOIs | |

State | Published - Feb 17 2016 |

### Keywords

- B-spline
- generalized linear model
- generalized partially linear model
- penalized likelihood ratio test
- semiparametric logistic regression

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty