Analysis of Deviance in Generalized Partial Linear Models

We develop analysis of deviance tools for generalized partial linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance, which admit an additivity property that reduces to ANOVA decompositions in the Gaussian case. Chi-square tests based on integrated likelihood functions are proposed to formally test whether the nonparametric term is significant. Simulation results are shown to illustrate the proposed chi-square tests. The methodology is applied to German Bundesbank Federal Reserve data.