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

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  • Chin-Shang Li

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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  • Chin-Shang Li, 2016. "A test for the linearity of the nonparametric part of a semiparametric logistic regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 461-475, March.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:3:p:461-475
    DOI: 10.1080/02664763.2015.1070803
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    1. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    4. Göran Kauermann & Gerhard Tutz, 2001. "Testing generalized linear and semiparametric models against smooth alternatives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 147-166.
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