This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum likelihood and Bayesian estimations of item parameters. Algorithms were developed and numerically illustrated for the one and two parameter logistic models. Results are comparable to conventional methods treating ability parameters as fixed. These new methods produce estimates when they do not exist under older methods. The Bayesian approach yields an approximation to the posterior covariance matrix, which can be used to make probabilistic statements about the uncertainty of the estimated parameters. User oriented computer packages need to be prepared before widespread application of these methods can be made. (Author/BS)