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ERIC Number: ED049289
Record Type: Non-Journal
Publication Date: 1971-Feb
Pages: 3
Abstractor: N/A
Reference Count: N/A
On an Extension of the Rasch Model to the Case of Polychotomously Scored Items.
Vogt, Dorothee K.
The Rasch model for the probability of a person's response to an item is extended to the case where this response depends on a set of scoring or category weights, in addition to person and item parameters. The maximum likelihood approach introduced by Wright for the dichotomous case is applicable here also, and it is shown to yield a unique solution. The method of estimating the three sets of parameters consists in using the person-by-category responses summed over items and the item-by-category responses summed over persons to yield a system of (N+k)m linear equations in the (N+k)m unknown parameters. (N=number of people, k=number of items, m=number of categories) They are solved iteratively using a Newton-Raphson procedure. The matrix of Nm person-by-category estimates and the matrix of km item-by-category estimates each have eigenvectors whose components are proportional to the scoring weights. The other factors yield the "ability" estimators and "easiness" estimators respectively. Computer programs for the estimation procedure have been developed. (Author)
Publication Type: N/A
Education Level: N/A
Audience: N/A
Language: N/A
Sponsor: N/A
Authoring Institution: N/A