ABSTRACT Structural misspecifications in factor analysis include using the wrong number of factors and omitting cross loadings or correlated errors. The impact of these errors on factor loading estimates is understudied. Factor loadings underlie our assessments of the validity and reliability of indicators. Thus knowing how structural misspecifications affect a factor loading is a key issue. This paper develops analytic conditions of when misspecifications affect Bollen’s (1996) model implied instrumental variable, two stage least squares (MIIV-2SLS) estimator of a factor loading. It shows that if an indicator equation is correctly specified, then correlated errors among other measures, mixing up causal indicators with reflective, omitting cross loadings, and omitting direct effects between indicators leave the MIIV-2SLS estimator of the factor loading unchanged. Alternatively, if the indicator or the scaling indicator equation is misspecified, then the loading is unlikely to be robust. The results are illustrated with hypothetical and empirical examples.

中文翻译：

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当好的载荷变坏时：因子分析的稳健性

摘要 因子分析中的结构性错误指定包括使用错误数量的因子以及遗漏交叉载荷或相关误差。这些错误对因子负荷估计的影响尚未得到充分研究。因素负荷是我们评估指标有效性和可靠性的基础。因此，了解结构错误指定如何影响因子加载是一个关键问题。本文开发了错误指定何时影响 Bollen (1996) 模型隐含工具变量、因子加载的两阶段最小二乘 (MIIV-2SLS) 估计量的分析条件。它表明，如果一个指标方程被正确指定，那么其他措施之间的相关误差，将因果指标与反射性指标混合，省略交叉载荷，并省略指标之间的直接影响，使因子负荷的 MIIV-2SLS 估计量保持不变。或者，如果指标或比例指标方程指定错误，则加载不太可能稳健。结果用假设的和经验的例子来说明。