Dimensional analyses of complex data

In this article, scales constructed using principal components and Rasch measurement methods are compared. The context of the comparison is scale definition under difficult circumstances—when constructs are unclear and sample sizes marginal. Three data sets of increasing complexity and decreasing stability were used. Responses for the least complex data set were dichotomous; the remaining two were polytomous. Results of Rasch and principal components analyses were identical when data were stable and the structure unidimensional. With less stability and more complexity, the defined scales were still similar for the two analytic approaches. Effects of item positions on the scales were noted and are discussed.