Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions.
Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions.
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DOI：
10.3390/jintelligence6030042
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发表时间：
2018-09-07
影响因子：
3.5
通讯作者：
Schulze, Julian
中科院分区：
文献类型：
--
作者：
Eid, Michael;Krumm, Stefan;Schulze, Julian
双因素模型是一种广泛应用于一般能力和特殊能力分析的模型。双因子模型的扩展还包括标准变量。在这种扩展的双因素模型中，一般和特定的因素可以与标准变量相关。此外，一般和特定因素对准则变量的影响可以在基于双因素测量模型的潜在多元回归模型中进行详细研究。本研究采用扩展的双因素模型预测数学和英语成绩的三个方面的智力（数字序列，言语类比，和展开）。我们表明，如果观察到的变量没有不同的负载，扩展的双因子模型是不确定的，不适用。此外，我们发现，在扩展的双因子模型的回归权重的标准误差可以是非常大的，从而导致无效的结论。给出了不可识别性的一个形式证明。随后，我们提出了替代方法预测标准变量的一般和具体因素。特别是，我们说明了如何（1）复合能力因子可以定义在扩展的一阶因子模型和（2）如何双因子（S-1）模型可以应用。详细讨论了一阶因子模型和双因子（S-1）模型在预测准则变量时的差异，并通过实例加以说明。
The bifactor model is a widely applied model to analyze general and specific abilities. Extensions of bifactor models additionally include criterion variables. In such extended bifactor models, the general and specific factors can be correlated with criterion variables. Moreover, the influence of general and specific factors on criterion variables can be scrutinized in latent multiple regression models that are built on bifactor measurement models. This study employs an extended bifactor model to predict mathematics and English grades by three facets of intelligence (number series, verbal analogies, and unfolding). We show that, if the observed variables do not differ in their loadings, extended bifactor models are not identified and not applicable. Moreover, we reveal that standard errors of regression weights in extended bifactor models can be very large and, thus, lead to invalid conclusions. A formal proof of the nonidentification is presented. Subsequently, we suggest alternative approaches for predicting criterion variables by general and specific factors. In particular, we illustrate how (1) composite ability factors can be defined in extended first-order factor models and (2) how bifactor(S-1) models can be applied. The differences between first-order factor models and bifactor(S-1) models for predicting criterion variables are discussed in detail and illustrated with the empirical example.