July 19 – 22, 2020
Prague, Czech Republic
WORKSHOP on Facet Theory, Modern Multidimensional Scaling and Unfolding
Given by Prof. Ingwer Borg
on Sunday on July 19, 2020 from 14:00 till 18:00 incl. 1 coffee break
The workshop introduces these notions primarily by discussing various examples from published research. Special emphasis is given to familiarize the participants with data analysis software relevant in the FT context, in particular multidimensional scaling (MDS). This family of methods has seen many new developments in recent years that make it easy to address questions often asked by reviewers (for example, how MDS is related to factor analysis, or whether the fit of an MDS solution is “significant”) but also new features that enable the researcher to understand his/her findings in much more detail (for example, identifying points that do not fit well or imposing external theoretical constraints onto the solutions in confirmatory scaling). Almost all of these developments are available today in the R-package “smacof”.
About Facet Theory (FT)
Facet theory (FT) is a methodology for designing and analyzing empirical research in the social sciences. The objects of interest in the social sciences are almost always multi-faceted, and FT helps to articulate these facets systematically. Intelligence tests, for example, often use tasks presented in numerical, geometric, verbal language; they also require the test person to apply, find, or learn a rule that solves the task. The facets language and rule, each with three elements, define nine types of tasks. They guide the construction of concrete test items. The data they generate when using them in testing persons can all be coded on the range “very wrong … very right”. One can then ask whether the two facets are mirrored, facet by facet, in these data in the sense that they allow to discriminate the different item types statistically. For example, one can ask if an analysis of variance with the facets as factors would lead to significant main effects. Another, and less restrictive, correspondence hypothesis is that the different item types fall into different regions of an MDS representation of the item inter-correlations. These ideas are generalized in FT to domains with many more facets. Attitude research is a prominent example, where items are often constructed by referring to sub-samples from a population of item types that has hundreds of thousands of items. They are explicated and organized in a mapping sentence. This helps in systematically picking certain subsets of item types from this universe of content and in formulating concrete attitude items on job rewards that avoid distorting content.