Estimating Functional Linear Mixed-Effects Regression Models

The functional linear model is a popular tool to investigate the relationship between a scalar/functional response variable and a scalar/functional covariate. We generalize this model to a functional linear mixed-effects model when repeated measurements are available on multiple subjects. Each subject has an individual intercept and slope function, while shares common population intercept and slope function. This model is flexible in the sense of allowing the slope random effects to change with the time. We propose a penalized spline smoothing method to estimate the population and random slope functions. A REML-based EM algorithm is developed to estimate the variance parameters for the random effects and the data noise. Simulation studies show that our estimation method provides an accurate estimate for the functional linear mixed-effects model with the finite samples. The functional linear mixed-effects model is demonstrated by investigating the effect of the 24-hour nitrogen dioxide on the daily maximum ozone concentrations and also studying the effect of the daily temperature on the annual precipitation.