title: Lack-of-fit Tests for Generalized Linear Models via Splines.
abstract: Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the non-parametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use.
authors.affiliation: Division of Biostatistics, Department of Public Health Sciences, University of California, Davis, CA 95616.
authors.forename: Chin-Shang
authors.initials: CS
authors.lastname: Li