David J. Weiss, Principal Investigator

Estimation Methods for Correlation Matrices

  There is a growing understanding of the links between time factor analysis and item response theory (e.g., Lord & Novick, 1968; McDonald, 1967, 1999; Mislevy, 1986; Takane and de Leeuw, 1987). Overlooked thus far is the utility of applying the estimation methods of item factor analysis (e.g., Christoffersson, 1975; Joreskog, 1990, 1994; Muthen, 1978, 1984) to the estimation of the parameters of the equivalent item response models. This project investigated parameter recovery of the unidimensional 2-parameter normal ogive item response model (and the equivalent unidimensional item factor analysis model) under a number of estimation methodsÑa number of which have not yet been studied for the item response model. Using computer simulated dichotomous item responses, factors such as sample size, test length, and item and person parameter distributions were manipulated in order to determine which of these estimation methods provide satisfactory estimates under given time response matrix conditions.

  One finding anticipated from this work was that the least squares approaches would provide more accurate estimates for smaller sample sizes and test lengths than the maximum likelihood and weighted least squares approaches. Should the item factor analysis approaches be shown to be viable methods of estimation for time response models, numerous alternative estimation methods would become available, in addition to the dominant marginal maximum likelihood approach.