Measurement invariance is the condition that an instrument measures a target construct in the same way across subgroups, settings, and time. In psychological measurement, usually only partial, but not full, invariance is achieved, which potentially biases subsequent parameter estimations and statistical inferences. Although existing literature shows that a correctly specified partial invariance model can remove such biases, it ignores the model uncertainty in the specification search step: flagging the wrong items may lead to additional bias and variability in subsequent inferences. On the other hand, several new approaches, including Bayesian approximate invariance and alignment optimization methods, have been proposed; these methods use an approximate invariance model to adjust for partial measurement invariance without the need to directly identify noninvariant items. However, there has been limited research on these methods in situations with a small number of groups. In this paper, we conducted three systematic simulation studies to compare five methods for adjusting partial invariance. While specification search performed reasonably well when the proportion of noninvariant parameters was no more than one-third, alignment optimization overall performed best across conditions in terms of efficiency of parameter estimates, confidence interval coverage, and type I error rates. In addition, the Bayesian version of alignment optimization performed best for estimating latent means and variances in small-sample and low-reliability conditions. We thus recommend the use of the alignment optimization methods for adjusting partial invariance when comparing latent constructs across a few groups.

测量不变性是仪器以相同方式跨子组、设置和时间测量目标构造的条件。在心理测量中，通常只能实现部分而不是完全的不变性，这可能会使后续的参数估计和统计推断产生偏差。尽管现有文献表明正确指定的部分不变性模型可以消除此类偏差，但它忽略了规范搜索步骤中的模型不确定性：标记错误的项目可能会导致后续推理中的额外偏差和可变性。另一方面，已经提出了几种新方法，包括贝叶斯近似不变性和对齐优化方法；这些方法使用近似不变性模型来调整部分测量不变性，而无需直接识别非不变项。然而，在少数群体的情况下，对这些方法的研究有限。在本文中，我们进行了三个系统的模拟研究，以比较调整部分不变性的五种方法。虽然当非不变参数的比例不超过三分之一时，规范搜索表现得相当好，但在参数估计效率、置信区间覆盖率和 I 类错误率方面，对齐优化总体上在各种条件下表现最佳。此外，贝叶斯版本的对齐优化在估计小样本和低可靠性条件下的潜在均值和方差方面表现最佳。