Multilevel principal components analysis of three-dimensional facial growth in adolescents

The study of age-related facial shape changes across different populations and sexes requires new multivariate tools to disentangle different sources of variations present in 3D facial images. Here we wish to use a multivariate technique called multilevel principal components analysis (mPCA) to study three-dimensional facial growth in adolescents.

These facial shapes were captured for Welsh and Finnish subjects (both male and female) at multiple ages from 12 to 17 years old (i.e., repeated-measures data). 1000 "dense" 3D points were defined regularly for each shape by using a deformable template via "meshmonk" software. A three-level model was used here, namely: level 1 (sex/ethnicity); level 2, all "subject" variations excluding sex, ethnicity, and age; and level 3, age. The technicalities underpinning the mPCA method are presented in Appendices.

Eigenvalues via mPCA predicted that: level 1 (ethnicity/sex) contained 7.9% of variation; level 2 contained 71.5%; and level 3 (age) contained 20.6%. The results for the eigenvalues via mPCA followed a similar pattern to those results of single-level PCA. Results for modes of variation made sense, where effects due to ethnicity, sex, and age were reflected in modes at appropriate levels of the model. Standardised scores at level 1 via mPCA showed much stronger differentiation between sex and ethnicity groups than results of single-level PCA. Results for standardised scores from both single-level PCA and mPCA at level 3 indicated that females had different average "trajectories" with respect to these scores than males, which suggests that facial shape matures in different ways for males and females. No strong evidence of differences in growth patterns between Finnish and Welsh subjects was observed.

mPCA results agree with existing research relating to the general process of facial changes in adolescents with respect to age quoted in the literature. They support previous evidence that suggests that males demonstrate larger changes and for a longer period of time compared to females, especially in the lower third of the face. These calculations are therefore an excellent initial test that multivariate multilevel methods such as mPCA can be used to describe such age-related changes for "dense" 3D point data.