A Comparison of Two Methods of Decomposing Item Difficulties

This paper compares two methods of estimating component difficulties for dichotomous test data. Simulated data are used to study the effects of sample size, collinearity, a measurement disturbance, and multidimensionality on the estimation of component difficulties. The two methods of estimation used in this study were conditional maximum likelihood estimation of parameters specified by the linear logistic test model (LLTM) and estimated Rasch item difficulties regressed on component frequencies. The results of the analysis indicate that both methods produce similar results in all comparisons. Neither of the methods worked well in the presence of an incorrectly specified structure or collinearity in the component frequencies. However, both methods appear to be fairly robust in the presence of measurement disturbances as long as there is a large number of cases (n = 1,000). For the case of fitting data with uncorrelated component frequencies, 30 cases were sufficient to recover the generating parameters accurately.