Fast Univariate Inference for Longitudinal Functional Models

We propose fast univariate inferential approaches for longitudinal Gaussian and non-Gaussian functional data. The approach consists of three steps: (i) fit massively univariate pointwise mixed-effects models; (ii) apply any smoother along the functional domain; and (iii) obtain joint confidence bands using analytic approaches for Gaussian data or a bootstrap of study participants for non-Gaussian data. Methods are motivated by two applications: (i) Diffusion tensor imaging measured at multiple visits along the corpus callosum of multiple sclerosis patients; and (ii) physical activity (PA) data measured by body-worn accelerometers for multiple days. An extensive simulation study indicates that model fitting and inference are accurate and much faster than existing approaches. Moreover, the proposed approach was the only one that was computationally feasible for the PA data application. Methods are accompanied by R software, though the method is “read-and-use,” as it can be implemented by any analyst who is familiar with mixed-effects model software. Supplementary files for this article are available online.