Linear mixed models for longitudinal shape data with applications to facial modelling

We present a novel application of methods for analysis of high-dimensional longitudinal data to a comparison of facial shape over time between babies with cleft lip and palate and similarly aged controls. A pairwise methodology is used that was introduced in Fieuws and Verbeke (2006) in order to apply a linear mixed-effects model to data of high dimensions, such as describe facial shape. The approach involves fitting bivariate linear mixed-effects models to all the pairwise combinations of responses, where the latter result from the individual coordinate positions, and aggregating the results across repeated parameter estimates (such as the random-effects variance for a particular coordinate). We describe one example using landmarks and another using facial curves from the cleft lip study, the latter using B-splines to provide an efficient parameterization. The results are presented in 2 dimensions, both in the profile and in the frontal views, with bivariate confidence intervals for the mean position of each landmark or curve, allowing objective assessment of significant differences in particular areas of the face between the 2 groups. Model comparison is performed using Wald and pseudolikelihood ratio tests.