Analysing Three-way Profile Data Using the Parafac and Tucker3 Models Illustrated with Views on Parenting

In this paper two major models for three-way profile data, i.e., the Parafac model and the Tucker3 model are discussed from the point of view of application. Topics treated are handling the data before analysis, model choice, choice of dimensionality, model fit, algorithmic hazards during the analyses, and interpretation and validation of the results. These issues are discussed in some detail so that prospective users can take guidance for analysing their own data. The data provided by Japanese girls and their parents about the parenting style in their family are the major vehicle for demonstrating the issues touched upon. The general results from these data are that parental styles consisted of three groups of behaviours: Acceptance, Control and Rejection, and Discipline. Within families the parenting behaviours of fathers and mothers are seen as parallel rather than at cross purposes, both by the daughters and the parents themselves. Moreover, daughters and parents largely agree about the parenting style itself. Notwithstanding, there are also families in which daughters and parents disagree about the parenting style in particular about Acceptance and Control, but not about Discipline.