Categorical semiparametric varying-coefficient models

Semiparametric varying-coefficient models have become a common fixture in applied data analysis. Existing approaches, however, presume that those variables affecting the coefficients are continuous in nature (or that there exists at least one such continuous variable) which is often not the case. Furthermore, when all variables affecting the coefficients are categorical/discrete, theoretical underpinnings cannot be obtained as a special case of existing approaches and, as such, requires a separate treatment. In this paper we use kernelbased methods that place minimal structure on the underlying mechanism governing parameter variation across categorical variables while providing a consistent and efficient approach that may be of interest to practitioners. One area where such models could be particularly useful is in settings where interactions among the categorical and real-valued predictors consume many (or even exhaust) degrees of freedom for fully parametric models (which is frequently the case in applied settings). Furthermore, we demonstrate that our approach behaves optimally when in fact there is no variation in a model's coefficients across one or more of the categorical variables (i.e. the approach pools over such variables with a high probability). An illustrative application demonstrates potential benefits for applied researchers.