Equating Tests Under The Nominal Response Model

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Abstract
Under item response theory, test equating involves finding the coefficients of a linear trans formation of the metric of one test to that of another. A procedure for finding these equating coefficients when the items in the two tests are nominally scored was developed. A quadratic loss function based on the differences between response category probabilities in the two tests is employed. The gradients of this loss function needed by the iterative multivariate search procedure used to obtain the equating coefficients were derived for the nominal response case. Examples of both hori zontal and vertical equating are provided. The empirical results indicated that tests scored under a nominal response model can be placed on a com mon metric in both horizontal and vertical equatings.