An Empirical Study of Various Indices for Determining Unidimensionality

Following a review of indices proposed to assess the unidimensionality of a set of items, Hattie (Note 1) identified 87 indices. The purpose of the present paper is to describe a simulation that determines the adequacy of various indices as decision criteria for assessing unidimensionality. A three-parameter, multivariate, logistic latent-trait model was used to generate item responses. Levels of difficulty, guessing, and discrimination, as well as the number of factors underlying the data, were varied. Many of the indices evaluated were highly intercorrelated. Some resulted in estimates outside their theoretical bounds, and most were particularly sensitive to the intercorrelations between factors. Indices based on answer patterns, reliability, component analysis, linear and nonlinear factor analysis, and on the one-parameter latent trait model were ineffective. Using the sum of absolute residuals from the twoparameter latent trait model, indices were obtained that were able to discriminate between cases with one latent trait and cases with more than one latent trait.