Generation and Objective Rotation of Generalized Learning Curves Using Matrix Language Products

Two SAS macros are presented which perform Tucker's (1966) modified principal components approach to modeling generalized learning curves analysis up to a rotation of the components. The problem of rotation to a psychologically meaningful solution is considered. For example, when analyzing learning data, one may wish to rotate the components to satisfy Tucker's criteria for learning curves. For the modeling of other kinds of change, different rotational criteria may be appropriate. Graphical or hand rotation is often difficult for researchers. By using matrix manipulation languages currently available, it is possible for a researcher to develop a small number of candidate rotated solutions. Three SAS macros are described which determine whether dimensions should be reflected or rotated, perform objective rotations of the factor pattern matrix in line with Tucker's desiderata, and generate corresponding factor scores.