Estimating functional linear mixed-effects regression models

A new functional linear mixed model is proposed to investigate the impact of functional predictors on a scalar response when repeated measurements are available on multiple subjects. The advantage of the proposed model is that under the proposed model, each subject has both individual scalar covariate effects and individual functional effects over time, while it shares the common population scalar covariate effects and the common population slope functions. A smoothing spline method is proposed to estimate the population fixed and random slope functions, and a REML-based EM algorithm is developed to estimate fixed effects and variance parameters for random effects. Simulation studies illustrate that for finite samples the proposed estimation method can provide accurate estimates for the functional linear mixed-effects model. The proposed model is applied to investigate the effect of daily ozone concentration on annual nonaccidental mortality rates and also to study the effect of daily temperature on annual precipitation.