Abstract

A weighted version of the tau-equivalent model of measurement is proposed for overcoming a shortcoming of the original and essential versions of this model resulting from the assumption of equal true scores. Because of this assumption the original version cannot be expected to do well in items with considerably varying variances. The proposed version includes weights reflecting the easiness of items. In a small simulation study the original and weighted versions of the model were applied to items characterized by variances of either equal or varying sizes for demonstrating the usefulness of the weighted version. As expected, only the weighted version of the tau-equivalent model did well in all item sets. Furthermore, the results obtained by the weighted version in combination with maximum likelihood estimation appeared to be closer to the expectations than the results obtained by asymptotic distribution-free estimation and robust estimation.

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