This is a rather specialized procedure for converting covariance matrices derived from scores of a multivariate analysis (such as principal component analysis, PCA) back to the coordinate system of the original landmarks. It is only needed for covariance matrices that have been imported from an external program into MorphoJ, for instance, after a quantitative genetic analysis.
An example of an application is quantitative genetics: the data are first set up in MorphoJ, a PCA is run, the dataset of PC scores is exported to a text file, and the genetic, phenotypic and environmental covariance matrices are estimated using other software (using all or a subset of the PCs). To perform morphometric analyses of these covariance matrices, they need to be imported into MorphoJ and converted back to the coordinate system of the original landmarks (e.g. Klingenberg et al. 2010).
Note: to convert a covariance matrix back to landmark coordinates, the covariance matrix must be attached to the dataset of scores from which it was derived.
To convert such a covariance matrix to landmark coordinates, click on the icon of the covariance matrix and select Convert Covariance Matrix to Landmark Coordinates from the Variation menu. A dialog box like the following will appear.
The two lists at the top of the dialog box are for selecting the set of variables to be used in the computation. This must be exactly the same set that was used in the external analysis that created the covariance matrix.
If the number of variables selected is the same as the dimensions in the covariance matrix, the message "The number of variables included is correct." is displayed below the two lists. If the number of variables selected does not match the number in the dataset, the message appears in red and indicates the number of variables to be included or excluded.
Finally, there are options for scaling the covariance matrix if the covariance matrix has been set to a different scale from that of the Procrustes units used in geometric morphometrics (e.g. by multiplying the scores by a factor of 1000 to reduce the effects of rounding error in the external analyses -- in that case, the covariances would be too big by a factor of one million!). There is a text field for entering a scale factor and there is a choice whether this is the factor that has been applied to the svores before producing the covariance matrix, whether it is the factor applied to the covariance matrix itself, or whether it is the factor that should be applied to the covariance matrix that was imported.
Clicking the Accept button will start the transformation and produce a new covariance matrix in the coordinate system of the original landmark coordinates. Clicking Cancel will abort the procedure.
Klingenberg, C. P., V. Debat, and D. A. Roff. 2010. Quantitative genetics of shape in cricket wings: developmental integration in a functional structure. Evolution 64:2935–2951.