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jMetrik and WINSTEPS are two Rasch measurement software applications that implement joint maximum likelihood estimation of Rasch, partial credit, and rating scale model parameters via a proportional curve fitting algorithm. We describe this algorithm in this paper and explain the handling of missing data and extreme cases. Results from a simulation study that manipulated sample size size and the number of test items indicate that both programs produce similar bias and root mean squared error values. In addition, root mean squared difference values indicate that estimates from each program are within 0.001 and 0.004 logits of each other depending on the model in question.