| Abstract: | A numerical specification of ‘size’ and ‘shape’ is of interest for making interpretations in morphometrics. Starting from a, possibly large, set m 1,…, mr of size measurements, e.g. m 1= height, m 2= sitting height, etc., a preliminary analysis provides the set x 1,…,xp of size measurements to be used, e.g. x 1= m 1? m 2= subischial leg length, x 2= m 2= sitting height, and x 3= head circumference. In general these xj are constructed as appropriately scaled linear combinations of the original measurements. A constant term should not be included because size measurements have to be 0 if all xj are 0. Our theory requires a (compromise) vector μof means and a matrix Σof (co)variances. Size being specified as an optimalsize characteristic of the form c ′ x , the remaining morphological information is expressed by, at most, p? 1 components of shapeof the form d ′ x. Relations with Darroch-Mosimann 9] Darroch, J. N. and Mosimann, J. E. 1985. Canonical and Principal Components of Shape. Biometrika, 72: 241–252. Crossref], Web of Science ®] , Google Scholar]are indicated. An application to human growth is made and other applications are suggested. Don't read my book, think for yourself. C. R. Rao, personal communications, 1981 |
