Linear models for the analysis and construction of instruments in a facet design.

Abstract

Linear models are described for the situation wherein a measurement instrument is constructed for all elements of the Cartesian product of several facets when the elements of each facet are not ordered. The structure of the covariance matrix of the instrument is derived from the models. By using covariance structure analysis, the models can be tested, and estimates of the parameters can be obtained. Models for 20 tests were formulated and tested and were constructed from a design with a behavioral and a situational facet measuring social anxiety in children; for 15 tests a model proved to fit the data. It is concluded that covariance structure analysis is useful for the analysis and construction of measurement instruments.We thank David A. Kenny, Fred N. Kerlinger, Wirn J. van der Linden, Wim E. Saris, and Pieter Vijn for their comments and Ineke Wesling for typing the manuscript.

Methods for questionnaire design: a taxonomy linking procedures to test goals

“…Each facet, in turn, consists of facet elements; facets are crossed in order to fully span the construct domain [ 106 ]. This design corresponds to the factorial design for experimentation [ 107 ]. Like the construct method, the facet design method is a hypothesis testing method, and the assumed structure is tested empirically.…”

Het facetontwerp als methode voor testconstructie

“…Naast de multidimensionele schaalanalysemethoden (bijvoorbeeld 'Smallest Space Analysis') die vooral aanhang vindt bij de facettheorieonderzoekers (Borg, 1994(Borg, , 1998, zijn de moderne psychometrische lineaire modellen (confirmatieve factoranalyse; Mellenbergh, Kelderman, Stijlen & Zondag, 1979; zie ook Hox, dit nummer) en logistische modellen (lineair logistische testmodel; Roskam, 1991) voorgesteld voor de analyse van de facetstructuur. Toepassingen van deze structurele relatiemodellen zijn onder andere te vinden bij Stouthard (1989), Broers (1993) en Stouthard en Peetsma (1999).…”

Searching for parsimony: are true-score models or factor models more appropriate?

“…One problem of MTMM as a special facet design concerns the covariances of its elements. For instance, Mellenbergh et al (1979) assume free covariances among the factors of the situational facets and among the factors of the reaction facets. Covariances between facets are not allowed.…”

“…The panel data allow not only to isolate the general attitude, but also these four elements of specific content. Our model is thus rooted in the tradition of the analysis of multitrait-multi-method (MTMM) design6 (Alwin, 1974: Browne, 1977Mellenbergh et al, 1979). 7 Empirical research should focus on some broadly defined general attitudes because the latter represent key concepts in micro-level theories.…”