A test for the linearity of the nonparametric part of a semiparametric logistic regression model

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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 languageEnglish (US)
Pages (from-to)461-475
Number of pages15
JournalJournal of Applied Statistics
Volume43
Issue number3
DOIs
StatePublished - 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

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