Orthosim 3 and its utility program, SPSS-to-Orthosim provide a solution for orthogonal procrustes rotation of a comparison matrix toward a target matrix.
Orthosim 3 calculates four different kinds of similarity coefficient between a comparison and target matrix - both "as they are" on input to the program, and after the comparison matrix has been orthogonally rotated against the target matrix so as to minimize the sum of squared deviations between the comparison matrix and target matrix values. For exploratory factor analysis (EFA) vectors (factors), the program allows an investigator to choose between two kinds of approaches to the problem - that using a "procrustes" approach whereby the matrices are expressed in the same unit-metric space (coordinates of -1 and +1 , irrespective of the initial sizes of the loadings/coordinate values - they are stretched or shrunk accordingly so as to occupy a joint unified metric space), and a non-procrustes approach whereby the comparison and target matrices remain unadjusted, and the comparison matrix is rotated against the target "as is". Both orthogonal or obliquely rotated matrices may be presented to the program. However, oblique matrices will be "transformed" to orthogonal ones, prior to the factor comparison methodology being applied to these orthogonal versions.
When submitting Multidimensional Scaling vectors (coordinate dimensions) for comparison, both matrices are initially centered (their coordinate-space origins are equated), are row-normalized (the "procrustes" approach which expresses each matrix in a normalized unit metric space which preserves the distance relations), then any coordinate "reflections" undone as part of the orthogonal rotation to maximum congruity. This is known as "configural similarity" (Borg and Groenen, 1997). The reason for these specific transformations is that MDS solutions are arbitrary in terms of their location, scale, and orientation of variables in geometric space.It is the distance relations between variables which are critical in MDS; such relations can be preserved while allowing the origin, scale, and reflection of solutions to vary. Hence, the extra transformations required prior to congruential rotation.
SPSS-to-Orthosim converts SPSS 11-onwards factor loading and factor correlation matrices into the fixed-format .vf (simple ASCII text) files required for input into Orthosim. The SPSS tables are required to be exported (or cut and paste) from the SPSS output viewer (or .spo file) to an Excel format file (.xls or .xlsx). This may be achieved either by using the export facility in SPSS or simply cutting and pasting the tables between SPSS and Excel. Comprehensive step-by-step online HTML help is provided to assist the user.
The original programs were written back in early 2003 - and it shows! I've tried to update them where possible/where necessary. Indeed Orthosim itself is old, hamstrung by having to call an external Fortran program that began life in 1998! The ASCII text input file format is so clumsy - but reflects the old days of fixed-format ASCII files used by Fortran 77! Frankly, the whole caboodle needs reprogramming in Delphi, with formatted output using a rich-text document utility coupled with pdf output or .docx output. However, I just don't have the time to devote to this task, and in reality Orthosim is 'niche' software, only used by those with a very specific need for congruential/configural rotation.
So, I've done my best to make both Orthosim and SPSS-to-Orthosim usable for Windows 7 upwards, especially taking into account the new security permissions/constraints of Windows 10. The help pages sometimes use images from old versions of Excel .. I've not bothered remaking them with Office 365 Excel - as nothing changes except the Office Excel 'look'.
Anyway, SPSS-to-Orthosim is easy to use and does 'the business'. It creates the necessary fixed-format ASCII file required as input for Orthosim.
Installations created with: Installation software:
Installation Note The installations install example files used in the helpfile in the subdirectory C:\Users\Public\Orthosim. The first time either program is run, it automatically opens that subdirectory for you. From then on, should you open your own files in a different path, the program remembers the last used path.