3WayPack
Program Descriptions

CONTENTS

OVERVIEW 3WayPack

The collection of programs which together constitute 3WayPack have been designed for the analysis of three-way data. Data are considered to be three-way if they can be classified or indexed by three types of entities. An obvious example is a data set consisting of scores of (1) subjects on several (2) variables measured at different (3) points in time.

3WayPack consists at present of three main programs for three-mode component analysis TUCKALS3, TUCKALS2, and TRILIN, which are the ones most developed. Additional more recent programs are those for three-mode correspondence analysis ANACOR3, three-mode analysis for multi-mode covariance matrices T3COVAR, Procrustes analysis PROCRUS, simultaneous component analysis SIMULCOMP, and three-mode mixture method of clustering MIXCLUS3. These programs, written in Fortran90 and compatible with Windows 32-bits processing, form the backbone of the package and will be collectively referred to as the analysis programs. The two interface programs, IF3 and POSTPROC (or OPP), are written in Pascal, and therefore are still subject to DOS limitations. In addition, there is the preprocessing program PREPROC3 (or PP3), which also performs a three-way analysis of variance and there are three Fortran90 Win32 programs which carry out the actual postprocessing, RESIDUAL (calculation of residuals and perfectly fitting data), T3ROTATE (rotations of core and components), AND JOINTPLT (construction and plotting of joint biplots for two modes given a component of the third mode). These three programs will be referred to as the postprocessing programs. The three-mode correspondence analysis program consists of both an "analysis" part and a "postprocessing" part.

INTERFACE3

Interface3 is a user interface to simplify the use of analysis programs for three-way data on Personal Computers. In its present form it has an interface for INTERFACE3 is the control centre for all analysis. It has menu part to specify all options After settin up the options INTERFACE3 will write the set-up file to disk and start an analysis program. When the analysis program is finished INTERFACE3 retake control and it will offer the opportunities to view and/or print the output, to create quality graphs and to start the browser of your choice. In addition, the interface can call the postprocessing programs to further enhance the analysis, such as rotating components and or the core array, calculating residuals, and constructing joint biplots.

Availability

The program suite is designed to be run under a Windows environment, even though the menu systems uses DOS. The analysis programs and postprocessing programs are Win32 program and can use all available memory. Because the Fortran programs can also run independently of the Pascal menu program, they can be compiled for other systems and used as stand-alone programs. In such a case several input files have to be by an editor according to the specifications in the manuals of the programs. Copies of the software and the manuals can be ordered from Pieter M. Kroonenberg, The Three-Mode Company, Leiden Institute of Education and Child Studies, Leiden University, Wassenaarseweg 52, 2333 AK Leiden, The Netherlands. kroonenb at fsw.leidenuniv.nl, Tel: *31-71-5273446/5273434, Fax: *31-71-5273945

PREPROC3

PREPROC3 is a program for preprocessing three-way data. It is, however, also a proper three-way program in its own right; for instance, it can perform three-way analysis of variance with one observation per cell, estimate missing data, etc.

The program can perform functions such as
1. Swapping the dimensions of a three-way array;
2. Estimating missing data according to Anova models;
3. Centring three-way arrays;
4. Normalising three-way arrays;
5. Printing all means from a three-way Anova model;
6. Computing and printing three-way Anova summary tables.

If PREPROC3 changes the data in any way it creates a new data file in the same directory where the original data file resides. Simultaneously, PREPROC3 also creates a data definition file for this data set, so that the modified data can directly be used in IF3. A new data file is created whenever the options 1, 2, 3, 4 from the above list are requested.

TUCKALS3

TUCKALS3 is a program for three-mode principal components with dimension reduc- tion along all three ways. Its core matrix will have as its dimensions the number of components of each of the three ways (i.e. PxQxR). The program can also be used for a simple singular value decomposition if K=1, and a weighted (or replicated) principal component analysis if R=1.

TUCKALS2

TUCKALS2 is a program for three-mode principal components with dimension reduc- tion along two of the three ways. Its extended core matrix will have as its dimensions the number of components of way 1 and way 2, and the number of levels of way 3 (i.e. PxQxK). The program can also be used for a simple singular value decomposition if K=1, or can be used to fit the IDIOSCAL model, if the input is a set of K symmetric matrices with (squared) distances.

TRILIN

TRILIN is a program for three-mode component analysis without a core matrix. It fits the parallel factor analysis model (PARAFAC), which is also called the canonical decomposition model (candecomp). The PARAFAC model is an extension of the principal component model in which the components are equal for each level of the third way except for proportionality constants. It can be seen as a Tucker2 model with diagonal core, or a Tucker3 model with superdiagonal core given that all ways have equal numbers of components. The program can also be used for the INDSCAL model, if the input is a set of K symmetric matrices with (squared) distances.

POSTPROC

With the programs in POSTPROC, the output of the three-way analysis programs can be analysed further. The components and core matrix (TUCKALS) or component weights (TRILIN), and the overall sum of squares are written to the file jobname.cpc by the three-way analysis programs. This information is the basis for the three postprocessing programs T3ROTATE (rotation/transformation of component matrices), RESIDUAL (computations of residuals and residual-fitted data plots), and JOINTPLT (joint (bi)plots of components of two ways given a component of the third), which can be selected from the type of POSTPROC screen. If you want to use more than one postprocessing program, you have to select the postprocessing option in the main menu screen of the relevant three-way analysis program every time. No rotations or joint plots can be made for output from TRILIN, as such operations are incompatible with the Parafac model fitted by TRILIN.

T3ROTATE

This program will rotate the components of any of the three ways. The rotations (or rather) transformations available are
1. Varimax rotation on the orthonormal components (equivalent to the Harris-Kaiser cluster rotation);
2. Oblimin transformation of the orthonormal components;
3. Optimally constant first component. This option can sometimes be used to facilitate interpretation, especially of reference modes for joint plots.

RESIDUAL

This program will calculate standardized residuals and plot these against the fitted data. You may choose to do the plotting per frontal slice or for the entire data set. This program also provides an option to write either the residuals and/or the fitted data to a file. Note that the fitted data are such that they perfectly fit the model, and thus can be used for simulation etc.

JOINTPLT

This program constructs joint (bi)plots for two modes given the third, so that the third is the reference mode. In addition, it can compute the coordinates for interactive biplots, but not yet the interactive biplots themselves. These coordinates can in some data sets be considered component scores.

TRIADIC

TRIADIC is a program for three-mode component analysis without a core matrix. The program fits the Parallel factor analysis model (PARAFAC), but it uses a non-standard algorithm, so-called triadic fitting. This procedure allows for easy inclusion of constraints on the components. Unfortunately, it is not yet available for general use, but it is hoped that it will be included in the next release of 3waypack.

MIXCLUS

MIXCLUS is a set of two cluster analysis programs which are based on the mixture method of clustering model developed by Kaye E. Basford. At present only the two-way version is more or less operational under IF3, and only available on special request. Please check with The Three-Mode Company.
| Algemene en Gezinspedagogiek | Centre for Child & Family Studies | Leiden Institute of Education and Child Studies | The Three-Mode Company | TOP |
P.M. Kroonenberg
Leiden Institute of Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945
E-mail: kroonenb at fsw.leidenuniv.nl
Created: 4-04-1997
Last Updated: 1-2-2003