Background and Objectives

Multilevel statistical models represent the existence of hierarchies or clustering within populations of subjects (or shapes in this work). This is a distinct advantage over single-level methods that do not. Multilevel partial-least squares regression (mPLSR) is used here to study facial shape changes with age during adolescence in Welsh and Finnish samples comprising males and females.

Methods

3D facial images were obtained for Welsh and Finnish male and female subjects at multiple ages from 12 to 17 years old. 1000 3D points were defined regularly for each shape by using “meshmonk” software. A three-level model was used here, including level 1 (sex/ethnicity); level 2, all “subject” variations excluding sex, ethnicity, and age; and level 3, age. The mathematical formalism of mPLSR is given in an Appendix.

Results

Differences in facial shape between the ages of 12 and 17 predicted by mPLSR agree well with previous results of multilevel principal components analysis (mPCA); buccal fat is reduced with increasing age and features such as the nose, brow, and chin become larger and more distinct. Differences due to ethnicity and sex are also observed. Plausible simulated faces are predicted from the model for different ages, sexes and ethnicities. Our models provide good representations of the shape data by consideration of appropriate measures of model fit (RMSE and R²).

Conclusions

Repeat measures in our dataset for the same subject at different ages can only be modelled indirectly at the lowest level of the model at discrete ages via mPCA. By contrast, mPLSR models age explicitly as a continuous covariate, which is a strong advantage of mPLSR over mPCA. These investigations demonstrate that multivariate multilevel methods such as mPLSR can be used to describe such age-related changes for dense 3D point data. mPLSR might be of much use in future for the prediction of facial shapes for missing persons at specific ages or for simulating shapes for syndromes that affect facial shape in new subject populations.

中文翻译：

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通过多级偏最小二乘回归探索青少年面部形状随年龄的变化

背景和目标

多级统计模型表示对象群体（或本研究中的形状）内存在层次结构或聚类。与单级方法相比，这是一个明显的优势。这里使用多级偏最小二乘回归（mPLSR）来研究威尔士和芬兰男性和女性样本中青春期面部形状随年龄的变化。

 方法

获得了 12 至 17 岁多个年龄段的威尔士和芬兰男性和女性受试者的 3D 面部图像。使用“meshmonk”软件定期为每个形状定义 1000 个 3D 点。这里使用了三级模型，包括级别1（性别/种族）； 2 级，所有“主体”变异，不包括性别、种族和年龄；第三级，年龄。 mPLSR 的数学形式在附录中给出。

 结果

mPLSR预测的12岁和17岁之间的面部形状差异与之前的多级主成分分析（mPCA）结果非常吻合；随着年龄的增长，颊部脂肪会减少，鼻子、眉毛和下巴等特征会变得更大、更清晰。还观察到种族和性别造成的差异。根据模型预测不同年龄、性别和种族的合理模拟面孔。通过考虑模型拟合的适当度量（RMSE 和R ² ），我们的模型提供了形状数据的良好表示。

 结论

我们的数据集中同一对象在不同年龄的重复测量只能通过 mPCA 在离散年龄的模型的最低级别间接建模。相比之下，mPLSR 将年龄明确地建模为连续协变量，这是 mPLSR 相对于 mPCA 的强大优势。这些研究表明，mPLSR 等多元多级方法可用于描述密集 3D 点数据的此类与年龄相关的变化。 mPLSR 未来可能会在预测特定年龄失踪人员的面部形状或模拟影响新受试者群体面部形状的综合症形状方面发挥很大作用。