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A. Implementation of Maximum Likelihood Estimation of Item Parameters

A BASIC program will be used to illustrate the implementation of the maximum likelihood estimation of an item's parameters. In order to keep the size of the program to a minimum, many of the initial data processing tasks are assumed to have taken place. For example, the examinees have been grouped into 10 intervals with known ability levels, with the number of examinees and of correct responses in each group obtained. In a regular production computer program, the code to accomplish these tasks also would be present. The program has been structured with a short driver (kernel) section to control the overall flow of the program. The actual maximum likelihood estimation of the intercept and slope item parameters under a two-parameter logistic item characteristic curve model is implemented in a subroutine. Since this subroutine is one of the two building blocks of most IRT test analysis computer programs, it will be described in detail in this appendix and in less detail where it is used subsequently. Because computer programming languages do not allow Greek symbols, variable names were chosen to represent terms expressed in mathematics in order to convey the appropriate meaning. For example, CPT represents intercept, and an initial letter S in a variable name indicates a sum.