Cole David A, Ciesla Jeffrey A, Steiger James H
Department of Psychology and Human Development, Vanderbilt University.
Psychol Methods. 2007 Dec;12(4):381-398. doi: 10.1037/1082-989X.12.4.381.
In practice, the inclusion of correlated residuals in latent-variable models is often regarded as a statistical sleight of hand, if not an outright form of cheating. Consequently, researchers have tended to allow only as many correlated residuals in their models as are needed to obtain a good fit to the data. The current article demonstrates that this strategy leads to the underinclusion of residual correlations that are completely justified on the basis of measurement theory and research design. In many designs, the absence of such correlations will not substantially harm the fit of the model; however, failure to include them can change the meaning of the extracted latent variables and generate potentially misleading results. Recommendations include (a) returning to the full multitrait-multimethod design when measurement theory implies the existence of shared method variance and (b) abandoning the evil-but-necessary attitude toward correlated residuals when they reflect intended features of the research design.
在实践中，在潜变量模型中纳入相关残差往往被视为一种统计上的花招，即便不是一种彻头彻尾的欺骗形式。因此，研究人员倾向于在其模型中只允许纳入为使模型与数据良好拟合所需数量的相关残差。本文表明，这种策略会导致基于测量理论和研究设计完全合理的残差相关性被纳入不足。在许多设计中，缺少此类相关性不会对模型拟合造成实质性损害；然而，不纳入它们可能会改变所提取潜变量的含义，并产生潜在的误导性结果。建议包括：（a）当测量理论表明存在共同方法方差时，回归到完整的多特质多方法设计；（b）当相关残差反映研究设计的预期特征时，摒弃对它们那种“虽有害但必要”的态度。
