This meeting was a follow-up to the first 'TRIC' conference held in Epe (Netherlands) in August 1993. 1 That meeting was organized to bring together chemometricians and psychometricians who turned out to be involved in the use of very similar methods for the analysis of three-way data. The aim of that conference was to allow a high technical level and to evoke thorough discussions on possibly very technical issues related to these and other three-way methods. The conference succeeded very well in this and it was agreed that a follow-up should be organized some three years later, but now in America. The locale for this was found about two years ago, when Barry Wise volunteered to organize the next meeting in his beautiful home town-and he successfully did. The meeting was visited by 32 attendees of 14 different nationalities, from ten different countries. In total, 23 oral presentations (of 45 min each) were given and nine posters were presented.
The oral presentations were often interrupted for questions as well as discussions, thus ensuring very lively sessions. Questions were quite often related to terminology: an important benefit of a meeting like this one is that it clears up the confusion caused by different terminology in the two disciplines brought together; it was thus revealed that what is termed differently in the two disciplines may very well be equivalent or at least closely related. In the present meeting, interest was focused on more three-way methods than in the first TRIC meeting. There was considerable interest in the Tucker3 model and also in methods for somewhat special types of three-way data. An important point of interest of the present meeting was computational efficiency and also modeling particular data features (using constraints or penalties). These subjects seem to reflect the gradual maturation of threeway methods: for successful applications we need an efficient algorithm and we may want to incorporate data features into our analysis. Actually, several such successful applications were demonstrated at the meeting, all of them in chemistry, which may reflect that the most convincing applications of three-way methods can be found in this discipline. Since the first contributions on three-way methods emerged in psychometrics, one may nevertheless assume the existence of useful applications in psychology as well, which hopefully will be presented at the next TRICAP meeting, planned for the year 2000, in Denmark (for more information on this, refer to the authors of this report).
We will now continue with a brief overview of the meeting, not disregarding some of the most salient remarks by the speakers.
P. M. Kroonenberg and W. J. Heiser and later R. Bro and R. A. Harshman discussed the use of constraints in multiway analysis. Examples were orthogonality and non-negativity constraints and constraining components to be fixed in order to estimate lower-order interaction effects and main effects in ANOVA models. Kroonenberg's talk, by which the meeting was opened, also offered a very good introduction to three-way methods in general.
P. Paatero advocated a new algorithm called the multilinear engine for estimating large general multilinear models. In the multilinear engine the structural model and auxiliary constraints result in a very general, flexible and efficient algorithm amenable to largely any multilinear problem.