I compared multiple methods to estimate and test a difference in correlations (ρ_diff) between two variables that are repeatedly measured or originate from dyads. Fisher’s z transformed correlations are often used for testing ρ_diff. However, raw scores are typically used directly to compute correlations under this popular method, whose performance has not been evaluated with measurement error or nonnormality in data. Structural equation modeling (SEM) can handle measurement error via latent-variable modeling. To handle nonnormality for testing a difference in correlations in dependent groups, when measurement error was of no concern, I discussed SEM using maximum likelihood estimation (ML) with sandwich-type standard errors, ML with bootstrap percentile or bias-corrected confidence intervals, and Bayesian credible intervals. In addition, I also examined a mean- and variance-adjusted likelihood ratio test and the Bollen-Stine bootstrapping model fit test. When measurement error existed, ρ_diff was tested under a latent variable model. Furthermore, under the same SEM frameworks with complete data, I also assessed ρ_diff with ignorable missing data. A simulation study was conducted considering whether measurement error existed, whether data were normal, and whether data were complete. Empirical examples were used for illustration. Recommendations were then given based on the findings.

中文翻译：

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比较评估与依赖组相关性差异、测量误差、非正态性和不完整数据的方法。


我比较了多种方法来估计和测试重复测量或源自二元组的两个变量之间的相关性差异 (ρ _diff )。 Fisher 的 z 变换相关性通常用于测试 ρ _diff 。然而，原始分数通常直接用于在这种流行方法下计算相关性，其性能尚未通过测量误差或数据非正态性进行评估。结构方程建模 (SEM) 可以通过潜变量建模处理测量误差。为了处理非正态性以测试依赖组中相关性差异的情况，当不关心测量误差时，我讨论了使用最大似然估计 (ML) 和三明治型标准误的 SEM、使用引导百分位数或偏差校正置信区间的 ML，以及贝叶斯可信区间。此外，我还检查了均值和方差调整似然比检验以及 Bollen-Stine 自举模型拟合检验。当存在测量误差时，在潜变量模型下检验ρ _diff 。此外，在具有完整数据的相同SEM框架下，我还评估了可忽略缺失数据的ρ _diff 。考虑是否存在测量误差、数据是否正常、数据是否完整进行模拟研究。使用实证例子进行说明。然后根据调查结果提出建议。