Three-mode {parafac} factor analysis in applied research.

Abstract

Applied research milieus are inherently multivanate As researchers employ more elaborate and comprehensive data collection schemes to reflect this complexity, sophisticated analytic techniques will play an ever-important role m unraveling the intricacies of the applied context. Starting with the seminal work of Tucker in three-mode factor analysis, this article examines a specific statistical development m multimode analysis, called the parallel factors model (PARAFAC) A substantive example of the PARAFAC analysis is provided The example investigates the structure of affective reactions to physical activities, in this case, trampohmng Following Eckblad's sector model for affect, the connotative meaning of affective descriptors is assumed to be associated with the assimilation resistance offered by the particular stimulus set encountered This laboratory-based notion guides the structural account of individual differences in affective reaction to trampohmng exercises investigated in this study Harshman's PARAFAC analysis is applied to the three-mode data set" 10 affective response scales by 10 trampoline exercises by 34 young trampohmsts Three unrestricted two-dimensional solutions (with all modes orthogonally constrained, with the scales and exercise modes orthogonally constrained, and with all modes unconstrained) reliably conform to Eckblad's hypothesized assimilation resistance model About 20 years ago, Tucker (1963, 1966) nents and three-mode common factor methpresented his three-mode factor analysis ods Tucker's conceptualization of individual model, which opened up new possibilities for differences in his three-mode model remains the analysis of complex data sets His inno-one of the more general and interesting provations included a more easily generalized two-posals for «-mode generalization. This article mode factor analysis logic, three-mode matrix examines the logic and analytic solution of the operations and their implications based on the three-mode model within the context of recent Kronecker product operator, and computation work on parallel proportional profiles (called algorithms for three-mode principal compo-PARAFAC, Harshman, 1981). PARAFAC is based on a statistical three-mode model that, when coupled with scaling preprocessing methods, overcomes some of the difficulties associated This arucle is based on a paper presented at the Otago *"& Tucker's original algorithms. Application Symposium on Motor Memory and Control, September of the PARAFAC three-mode method focuses 8-10, 1982, Dunedm, New Zealand on a sport psychology study that seeks to ex-We gratefully acknowledge the assistance of Les Gray, hcate the stmcture of se lf. re ported affect for State Director of Coaching for Trampohmng, Queensland, ., , c , . Australia, for his technical adv.ee a Prescribed set of trampohmng exercises. This article benefited from earlier reviews by M Cohn,

A new efficient method for determining the number of components in PARAFAC models

“…which clearly gives the absolute minimum of Equation (4). As the problem of minimizing Equation (4) has a unique solution (provided that A, B and C have full column rank, as is assumed here but which will be relaxed later), the Tucker3 core G will be identical to the superdiagonal binary array T if the PARAFAC model fits perfectly.…”

“…Let G be the least squares Tucker3 core given the loading matrices A, B and C; that is, the minimum of Equation (4). As the intrinsic core T provides a perfect-fitting model, we have…”

What Accounts for the Appeal of Complementary/Alternative Medicine, and What Makes Complementary/Alternative Medicine "Alternative"?

“…38 This study, however, represents, to our knowledge, the first time PARAFAC has been applied to study health-related views and beliefs.…”

CATTELL'S parallel proportional profiles

“…So far in the social and behavioral sciences quite a few researchers in diverse disciplines have found the model useful in describing their data, e.g. in the area of sensory perception, 59 brain activity, 60,61 tone perception, 62 personality development, 63 speech production, 64 growth curves, 65 evaluating teacher effectiveness, 66 facial expressions, 67 parenting, 68 psychology of attribution, 69 animal psychology, 70 marital issues, 71 spectrum of affect, 72 consonant confusion, 73 metaphor appreciation, 26 , emotions and stress 74 …”