Sample Size and the Recovery of Nominal Response Model Item Parameters

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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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In this study of polytomous items, the number of items and categories per item were varied to explore the effects on estimation of item parameters in the nominal response model. De Ayala and Sava-Bolesta's (1999) work suggested that the ratio of the sample size to the total number of item parameters was a key factor. They varied the total number of item parameters by increasing the sample size or changing the number of categories per item while leaving the number of items constant. In this study, the total number of item parameters, the sample size, and the number of categories were manipulated as separate factors. Increasing the nwnber of items had little effect on item parameter recovery, but increasing the number of categories increased the error variance of the parameter estimates. Error variance was also greater for more highly discriminating items and for skewed distributions of ability.