Bookstein Fred L
Department of Statistics, University of Washington, Seattle, Washington.
Department of Anthropology, University of Vienna, Vienna, Austria.
Am J Phys Anthropol. 2017 Oct;164(2):221-245. doi: 10.1002/ajpa.23277. Epub 2017 Aug 2.
Currently the most common reporting style for a geometric morphometric (GMM) analysis of anthropological data begins with the principal components of the shape coordinates to which the original landmark data have been converted. But this focus often frustrates the organismal biologist, mainly because principal component analysis (PCA) is not aimed at scientific interpretability of the loading patterns actually uncovered. The difficulty of making biological sense of a PCA is heightened by aspects of the shape coordinate setting that further diverge from our intuitive expectations of how morphometric measurements ought to combine. More than 50 years ago one of our sister disciplines, psychometrics, managed to build an algorithmic route from principal component analysis to scientific understanding via the toolkit generally known as factor analysis. This article introduces a modification of one standard factor-analysis approach, Henry Kaiser's varimax rotation of 1958, that accommodates two of the major differences between the GMM context and the psychometric context for these approaches: the coexistence of "general" and "special" factors of form as adumbrated by Sewall Wright, and the typical loglinearity of partial warp variance as a function of bending energy. I briefly explain the history of principal components in biometrics and the contrast with factor analysis, introduce the modified varimax algorithm I am recommending, and work three examples that are reanalyses of previously published cranial data sets. A closing discussion emphasizes the desirability of superseding PCA by algorithms aimed at anthropological understanding rather than classification or ordination.
目前，对人类学数据进行几何形态测量（GMM）分析时，最常见的报告方式是从原始地标数据转换而来的形状坐标的主成分开始。但这种关注点往往让生物学家感到沮丧，主要是因为主成分分析（PCA）并非旨在对实际发现的载荷模式进行科学解释。形状坐标设置的一些方面进一步偏离了我们对形态测量应该如何组合的直观预期，这使得从生物学角度理解PCA变得更加困难。五十多年前，我们的一个姊妹学科——心理测量学，设法通过通常被称为因子分析的工具包，构建了一条从主成分分析到科学理解的算法路径。本文介绍了对一种标准因子分析方法（1958年亨利·凯泽的方差最大化旋转）的修改，该修改适应了这些方法在GMM背景和心理测量背景之间的两个主要差异：如休厄尔·赖特所阐述的“一般”和“特殊”形式因子的共存，以及部分弯曲方差作为弯曲能量函数的典型对数线性。我简要解释了生物统计学中主成分的历史以及与因子分析的对比，介绍了我推荐的修改后的方差最大化算法，并对三个先前发表的颅骨数据集重新分析的例子进行了研究。最后的讨论强调了用旨在实现人类学理解而非分类或排序的算法取代PCA的必要性。
