Covariance matrices are used in a wide range of morphometric analyses, e.g. principal component analysis, and they are the basis for applications in quantitative genetics, the study of modularity and integration, and many other conexts.
MorphoJ can generate covariance matrices from datasets of shape data after Procrustes superimposition (and perhaps other analyses). It is also possible to compute pooled within-group covariance matrices as a joint estimate of the variation within several groups (defined by the values of one or more classifiers).
To generate covariance matrices, one or more datasets are needed. The datasets may either contain raw data for which a Procrustes fit has already been done or results from previous analyses (e.g. residuals from regression, etc.). Covariance matrices can be generated for several datasets at the same time. If you want to generate a covariance matrix just for one dataset, it is helpful to select the dataset in the Project Tree tab.
To start, select Generate Covariance Matrix from the Preliminaries menu.
A dialog box like the following will appear:
The top two boxes contain the lists for selecting or excluding datasets. In the screen shot, a dataset 'skulls, averaged' is currently selected, and three additional datasets are available in the projuect. Covariance matrices will be generated for all those that are in the lost of selected datasets. Datasets can be moved between the lists by selecting them and using the Include or Exclude buttons.
The list of data types (lower left) shows all the types of dataavailable in any of the selected datasets. Select the data types for which covariance matrices should be produced. If several datasets are selected, MorphoJ will generate covariance matrices for all of the selected data types that are available in each dataset.
If no data of a suitable type is found in the selected datasets, a warning message appears in the lower-left corner of the dialog box. (For instance, this may happen if no Procrustes fit has yet been done for a dataset with raw coordinate values; in this case, perform the Procrustes fit first.)
Unless you want to compute pooled within-group covariances (see below), click the Execute button to start the computation. The new covariance matrices will appear in the Project Tree, each attached to the dataset from which it is derived.
To abort the procedure and close the dialog box, click Cancel.
In the lower-right part of the dialog box, there is a button for specifying whether pooled within-group covariances should be computed. If this button is clicked to the 'on' status, the list below it is activated (inactive in the screen shot). The list contains all the classifiers that are common to all selected datasets. Whether classifiers in different datasets are the same is decided by the name of the classifier (notice: this comparison is case-sensitive, so that 'species' and 'Species' are considered as two different names). If a dataset contains several classifiers with the same name, only the first is considered.
You can select several classifiers simultaneously as a grouping criterion, which will then be used in combination. For instance, if the classifier 'species' contains the levels 'human' and 'chimp' and the classifier 'sex' contains the levels 'male' and 'female', four groups will be formed: male humans, male chimps, female humans and female chimps (if all four combinations occur in the dataset).