Model; Scree Test

This study was undertaken to compare non-metric multidimensional scaling (MDS) and factor analysis (FA) as means of assessing dimensionality in relation to item response theory (IRT). FA assesses correlation matrices, while MDS performs an analysis of proximity measures. Seven data sets were generated; each differed from the others with respect to dimensionality. Each set consisted of 28 items and was either one- or two-dimensional, with two-dimensional data sets having interdimensional correlation coefficients of 0.01, 0.10, and 0.60. All sets were generated according to G. Masters' partial credit model (1982)--a Rasch model;:.4 item parameters were taken from Masters ' article and duplicated to produce the 28-item pool. Assessment of dimensionality through MDS was performed by stress by dimensionality graphs alone and in conjunction with plots of stress by dimensionality containing varying degrees of error. For the FA of each correlation matrix, the initial determination of dimensionality was performed through an examination of the matrix's scree plot. Results indicate that MDS may be a viable methodology for IRT researchers to use in assessing the dimensionality of ordered test or attitude data. Four data tables and 20 graphs are provided. (TJH) Reproductions supplied by EDRS are the best that can be made from the original document..4