ESTIMATING THE PARAMETERS OF THE

For some situations the beta-binomial distribution might be used to describe the marginal distribution of test scores for a particular population of examinees. To use this distribution it is necessary to estimate two parameters which characterize the beta-binomial model. One method of estimating these parameters is to approximate the maximum likelihood estimates using some appropriately chosen iterative technique. When the number of examinees is small, how-ever, it is not clear that this method of estimation is justified since the iterative approximations might not converge to the maximum likeli-hood estimate. Using Monte Carlo techniques, this paper compares the Newton-Raphson approximation to the maximum likelihood estimate with several other possible procedures. It is found that the Newton-Raphson method should be used when it yields admissible (positive) results. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1979, 39 FOR certain types of tests for which an item sampling model applies and when the items are scored dichotomously, the beta-binomial distribution (BBD), also known as the negative hypergeometric or Polya distribution, may be useful when describing the marginal distri-bution of observed scores for a particular population of examinee