A test for the linearity of the nonparametric part of a semiparametric logistic regression model |
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Authors: | Chin-Shang Li |
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Affiliation: | Division of Biostatistics, Department of Public Health Sciences, University of California, Davis, CA, USA |
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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. |
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Keywords: | B-spline generalized linear model generalized partially linear model penalized likelihood ratio test semiparametric logistic regression |
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