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A Computer Program for Solving a Set of Conditional Maximum Likelihood Equations Arising in the Rasch Model for Questionnaires

Andersen, Erling B.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Computer Software, Data Analysis, Mathematical Models, Questionnaires, Rasch Model, Statistical Analysis


A computer program for solving the conditional likelihood equations arising in the Rasch model for questionnaires is described. The estimation method and the computational problems involved are described in a previous research report by Andersen, but a summary of those results are given in two sections of this paper. A working example is also provided to help the reader understand different computational steps of the program; these include (1) defining properties of the model, (2) computing estimates of the item parameters by taking the conditional distribution of the total set of responses given the individual score vectors as the likelihood function, (3) applying a goodness-of-fit test based on a grouping of possible score vectors, (4) developing technical, input-output, and main subroutines. Numerical examples are given of two actual executions of the program. The appendix, comprising nearly half of the report, lists the main program and subroutines.

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