Item response theory (IRT) true-score equating for the bifactor model is often conducted by first numerically integrating out specific factors from the item response function and then applying the unidimensional IRT true-score equating method to the marginalized bifactor model. However, an alternative procedure for obtaining the marginalized bifactor model is through projecting the nuisance dimensions of the bifactor model onto the dominant dimension. Projection, which can be viewed as an approximation to numerical integration, has an advantage over numerical integration in providing item parameters for the marginalized bifactor model; therefore, projection could be used with existing equating software packages that require item parameters. In this paper, IRT true-score equating results obtained with projection are compared to those obtained with numerical integration. Simulation results show that the two procedures provide very similar equating results.

中文翻译：

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用投影项目响应模型近似双因子IRT真实得分等式。

双因素模型的项目响应理论（IRT）真实得分等式通常是通过以下方式进行的：首先从项目响应函数中对特定因子进行数值积分，然后将一维IRT真实得分相等方法应用于边缘化的双因素模型。但是，获得边际化双因素模型的另一种方法是将双因素模型的有害尺寸投影到主导尺寸上。投影可以看作是数值积分的近似值，它在为边际化双因子模型提供项目参数方面优于数值积分。因此，可以将投影与需要项目参数的现有等同软件包一起使用。在本文中，将通过投影获得的IRT真实得分相等结果与通过数值积分获得的结果进行比较。仿真结果表明，这两个过程提供了非常相似的等效结果。