The polychoric instrumental variable (PIV) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small‐sample properties of the specification tests for testing the validity of instrumental variables (IVs). Second, we investigate the effects of using different numbers of IVs. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study. Simulation results show that the modified specification tests with all available IVs are able to detect model misspecification. In terms of estimation accuracy, the PIV approach where the IVs outnumber the endogenous variables by one produces a lower bias but a higher variation than the PIV approach with more IVs for correctly specified factor loadings at small samples.

中文翻译：

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在验证性因素分析中选择多色工具变量：替代性规范测试和工具变量的影响。

多变量工具变量（PIV）方法是最近提出的一种方法，用于将有序数据拟合到验证性因素分析模型中。在本文中，我们首先检查规格测试的小样本属性，以测试工具变量（IV）的有效性。其次，我们研究使用不同数量的静脉注射的影响。我们的结果表明，将连续数据导出的规格检验在应用于序数变量时，在所有样本量中均过大。本研究中提出了对序数数据的可能修改。仿真结果表明，具有所有可用IV的修改后的规范测试均能够检测模型的错误规范。在估算精度方面，