<p>We investigate a flexible partially linear functional additive smoothed quantile regression model for analyzing hybrid high-dimensional heterogeneous data. The proposed model predicts a scalar response by both the parametric effects of high-dimensional scalar covariates and the nonparametric effects of a mixed multivariate functional predictor. The information of multivariate functional predictors is adequately compressed using multivariate functional principal component analysis, and the nonparametric effects of the principal component scores are modeled as additive components in the proposed model. We approximate additive components via B-spline basis functions and allow the number of principal component scores and scalar covariates to diverge to infinity with sample size, respectively. Double concave folded (group) penalties are adopted to select relevant components and estimate the effects. We apply convolution smoothing techniques to the quantile loss to address the challenges posed by its non-smoothness and the lack of strong convexity in the traditional quantile loss. The asymptotic properties of the resulting estimators are established. Simulation and application to Alzheimer’s disease study demonstrate the effectiveness of the proposed model.</p>