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

Chin-Shang Li

Journal of Applied Statistics, 2016, vol. 43, issue 3, 461-475

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.

Date: 2016
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DOI: 10.1080/02664763.2015.1070803

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