Farnell D J J, Richmond S, Galloway J, Zhurov A I, Pirttiniemi P, Heikkinen T, Harila V, Matthews H, Claes P
School of Dentistry, Cardiff University, Heath Park, Cardiff CF14 4XY, United Kingdom.
School of Dentistry, Cardiff University, Heath Park, Cardiff CF14 4XY, United Kingdom.
Comput Methods Programs Biomed. 2021 Mar;200:105935. doi: 10.1016/j.cmpb.2021.105935. Epub 2021 Jan 8.
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.
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.
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 R).
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.
多水平统计模型体现了研究对象群体（或本研究中的形状）内层次结构或聚类的存在。相较于单水平方法，这是一个明显的优势，因为单水平方法无法做到这一点。本文采用多水平偏最小二乘回归（mPLSR）来研究威尔士和芬兰样本中青少年在青春期随年龄变化的面部形状，样本涵盖男性和女性。
获取了威尔士和芬兰12至17岁不同年龄段男性和女性受试者的3D面部图像。使用“meshmonk”软件为每个形状规则地定义1000个3D点。这里使用了一个三级模型，包括第1级（性别/种族）；第2级，排除性别、种族和年龄后的所有“受试者”变异；以及第3级，年龄。mPLSR的数学形式在附录中给出。
mPLSR预测的12岁至17岁面部形状差异与先前多水平主成分分析（mPCA）的结果高度吻合；随着年龄增长，颊脂减少，鼻子、眉毛和下巴等特征变得更大且更明显。还观察到了种族和性别的差异。从该模型可以预测出不同年龄、性别和种族的合理模拟面部。通过考虑合适的模型拟合度量（RMSE和R），我们的模型对面部形状数据提供了良好的表示。
在我们的数据集中，针对同一受试者在不同年龄的重复测量只能通过mPCA在离散年龄的模型最低水平进行间接建模。相比之下，mPLSR将年龄明确建模为连续协变量，这是mPLSR相对于mPCA的一个显著优势。这些研究表明，诸如mPLSR之类的多变量多水平方法可用于描述此类与年龄相关的密集3D点数据变化。mPLSR未来可能在预测特定年龄失踪人员的面部形状或为影响新受试者群体面部形状的综合征模拟形状方面有很大用途。
