A Modified Order-Analysis Procedure for Determining Unidimensional Item Sets

184 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.Current latent-trait methods require that the latent space underlying a group's test performance be unidimensional. However, many tests yield multidimensional data, implying that more than one latent trait would be necessary to account for test performance. A possible solution to this problem of multidimensionality would be to isolate unidimensional subsets of items from the total set of test items and use item response theory with each subset. While factor analysis is the most commonly proposed procedure for determining dimensionality, a recently developed procedure called order analysis may also prove to be useful for isolating unidimensional item sets.In 1974, Krus and Bart outlined an order-analysis procedure for extracting unidimensional chains from multidimensional datasets. Cliff, in 1975, presented a number of consistency indices for simple orders. In 1976, Reynolds described a procedure using one of Cliff's indices, to extract unidimensional chains. Part of this thesis dealt with a comparison of three order-analysis procedures: Krus and Bart's procedure and Reynold's procedures using two of Cliff's consistency indices, c(,t1) and c(,t3). The comparisons were based on both simulated data with known factorial dimensionality and real data. The c(,t3) procedure reproduced the factor structure for the simulated datasets, while the other two procedures performed very poorly. However, for the real data, all three procedures failed to reproduce the factors. The poor performance of the c(,t3) procedure with the real data was presumed to be due to the oblique factor structure of these datasets.A second part of this thesis described the development and evaluation of ORDO, a new order-analysis procedure. ORDO represents a radical departure from other order-analysis procedures in that it extracts partial orders of items rather than simple orders. Simulated and real datasets were reanalyzed using ORDO, and the extracted item chains were highly similar to the extracted factors, even for datasets with correlated factors. The results suggest that ORDO represents a useful alternative to factor analysis in assessing the dimensionality of tests.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD