Table 1.
A selection of different masculinity concepts and their statistical properties.
Fig 1.
Path models corresponding to different multivariate methods of estimating masculinity.
(a) The morphological pattern underlying perceived masculinity can be estimated by a multivariate regression of the morphometric variables (X1…X5) on a masculinity rating. (b) The morphological effects of steroid hormones can be estimated by a multivariate regression of the morphometric variables on a measure of hormone level. (c) The difference between average male and average female shape is equivalent to a regression of morphology on sex (as a binary variable). (d) Allometric and non-allometric components of sexual dimorphism can be estimated by regressing morphology on both size and sex. (e) A discriminant function is computationally equivalent to a multiple regression of sex on the morphological measurements.
Fig 2.
The statistical distribution of two morphometric variables for two groups of individuals (males and females) is shown by two equal frequency ellipses and the corresponding means.
(a) The mean difference vector (solid line) is spanned by the two mean configurations. The discriminant function (dashed line) maximizes the squared distance between the group means relative to the variation of the scores within the groups. When the two covariance matrices are the same (as in this example), it is the optimal direction to discriminate the two groups and to classify individuals with unknown group membership. (b) The mean difference vector can be decomposed into an allometric component (which, for many morphometric data sets, is close to the direction of maximum variance within the groups) and a non-allometric component (orthogonal to the allometric direction).
Fig 3.
Landmark configuration used for studying face shape and perceived masculinity.
(a) Face with the 33 landmarks (open circles) and 37 semilandmarks (filled circles) used in the morphometric analysis. (b) The shape features determining perceived masculinity are visualized by deformation grids from the mean shape to shapes predicted for deviations of ±20 rating scores from the average.
Fig 4.
Sexual dimorphism is visualized by deformation grids between average female and average male facial shape, together with two-fold extrapolations of these shape differences.
Fig 5.
Decomposition of sexual dimorphism into an allometric and a non-allometric component.
The corresponding deformation grids are two-fold extrapolations of the actual dimorphism.
Fig 6.
Visualization of discriminant functions between male and female face shapes using (a) five and (b) ten principal components (PCs) of the full set of shape coordinates.