Measurement invariance (MI) is one of the main psychometric requirements for analyses that focus on potentially heterogeneous populations. MI allows researchers to compare latent factor scores across persons from different subgroups, whereas if a measure is not invariant across all items and persons then such comparisons may be misleading. If full MI does not hold further testing may identify problematic items showing differential item functioning (DIF). Most methods developed to test DIF focused on simple scenarios often with comparisons across two groups. In practical applications, this is an oversimplification if many grouping variables (e.g., gender, race) or continuous covariates (e.g., age) exist that might influence the measurement properties of items; these variables are often correlated, making traditional tests that consider each variable separately less useful. Here, we propose the application of Bayesian Moderated Nonlinear Factor Analysis to overcome limitations of traditional approaches to detect DIF. We investigate how modern Bayesian shrinkage priors can be used to identify DIF items in situations with many groups and continuous covariates. We compare the performance of lasso-type, spike-and-slab, and global-local shrinkage priors (e.g., horseshoe) to standard normal and small variance priors. Results indicate that spike-and-slab and lasso priors outperform the other priors. Horseshoe priors provide slightly lower power compared to lasso and spike-and-slab priors. Small variance priors result in very low power to detect DIF with sample sizes below 800, and normal priors may produce severely inflated type I error rates. We illustrate the approach with data from the PISA 2018 study. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

---

在调节非线性因素分析中评估测量不变性的贝叶斯惩罚方法。

测量不变性 (MI) 是针对潜在异质人群的分析的主要心理测量要求之一。MI 允许研究人员比较来自不同子组的人的潜在因素分数，而如果一个度量在所有项目和人之间不是不变的，那么这种比较可能会产生误导。如果完整的 MI 不支持进一步测试，可能会发现有问题的项目显示差异项目功能 (DIF)。为测试 DIF 而开发的大多数方法都侧重于简单的场景，通常会在两组之间进行比较。在实际应用中，如果存在许多可能影响项目测量属性的分组变量（例如，性别、种族）或连续协变量（例如，年龄），这就过于简单化了；这些变量通常是相关的，使单独考虑每个变量的传统测试变得不那么有用。在这里，我们建议应用贝叶斯调制非线性因子分析来克服传统方法检测 DIF 的局限性。我们研究了现代贝叶斯收缩先验如何用于在具有许多组和连续协变量的情况下识别 DIF 项目。我们将套索类型、尖峰和平板以及全局-局部收缩先验（例如，马蹄铁）的性能与标准正态和小方差先验进行了比较。结果表明 spike-and-slab 和 lasso 先验优于其他先验。与 lasso 和 spike-and-slab priors 相比，Horseshoe priors 提供的功率略低。小方差先验导致检测样本量低于 800 的 DIF 的能力非常低，而正常先验可能会产生严重膨胀的 I 类错误率。我们使用 PISA 2018 研究的数据来说明该方法。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。