Assessing Test Dimensionality Using an Index Based on Nonlinear Factor Analysis.

ABSTRACT A new index for assessing the dimensionality underlying a set of test items was investigated. The incremental fit index (IFI) is based on the sum of squares of the residual covariances. Purposes of the study were to: (1) examine the distribltion of the IFI in the null situation, with truly unidimensional data; (2) examine the rejeccion rate of the IFI under various simulation conditions of a two-dimensional test structure; and (3) compare the performance of the IFI with the T-statistic of W. Stout (1987). Data sets were computer-generated for sample sizes of BOO and 1,000 with test lengths of 15 and 45 items each. The IFI based on the sum of the squares of tho residual covariances of the one-dimensional and two-dimensional non-linear factor analyses of dichotomous test data did show fairly high rejectiar rates of unidimensionality when two-dimensf.onal data were generated. The results suggest that the statistic has the potential for use in the assessment of unidimensionality of test data and in the determination of the number of dimensions underlying a test. The T-statistic seemed best suited for long tests having large sample sizes, while the IFI might be preferable for smaller test lengths or smaller samples. Five tables present study data. A 23-item list of references is included. (SLD)