Heterogeneous effects are prevalent in many economic settings. As thefunctional form between outcomes and regressors is often unknown a-priori, we propose a semiparametric negative binomial count data modelbased on the local likelihood approach and generalized product kernels,and apply the estimator to model demand for health care. The lo-cal likelihood framework allows us to leave the functional form of theconditional mean unspecified while still exploiting basic assumptions inthe count data literature (e.g., non-negativity). The generalized prod-uct kernels allow us to simultaneously model discrete and continuousregressors, which reduces the curse of dimensionality and increases itsapplicability as many regressors in the demand model for health careare discrete.