Self-modelling regression for longitudinal data with time-invariant covariates

The authors propose the use of self-modelling regression to analyze longitudinal data with time invariant covariates. They model the population time curve with a penalized regression spline and use a linear mixed model for transformation of the time and response scales to fit the individual curves. Fitting is done by an iterative algorithm using off-the-shelf linear and nonlinear mixed model software. Their method is demonstrated in a simulation study and in the analysis of tree swallow nestling growth from an experiment that includes an experimentally controlled treatment, an observational covariate and multi-level sampling.