In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given.
Li, Chin-Shang and Tu, Wanzhu
"A Spline-Based Lack-of-Fit Test for Independent Variable Effect,"
Journal of Modern Applied Statistical Methods:
1, Article 22.
Available at: http://digitalcommons.wayne.edu/jmasm/vol6/iss1/22