The theoretical detect index of dimensionality and its application to approximate simple structure

摘要: In this paper, a theoretical index of dimensionality, called the DETECT index, is proposed to provide foundation for procedure. The purpose assess certain aspects latent dimensional structure test, important practitioner and research alike. Under reasonable modeling restrictions referred as “approximate simple structure”, proven be maximized at thecorrect dimensionality-based partition where number item clusters in corresponds substantivelyseparate dimensions present test by “correct” meant that each cluster contains only items correspond same separate dimension. It argued separation into achieved appropriate from applied perspective desiring are interpretable substantively distinct between homogeneous within cluster. Moreover, maximum value measure amount multidimensionality present. estimation discussed genetic algorithm developed effectively execute DETECT. study facilitated recasting two factor analytic concepts multidimensional response theory setting: dimensionally an approximate test.