Moderated nonlinear factor analysis (MNLFA) has emerged as an important and flexible data analysis tool, particularly in integrative data analysis setting and psychometric studies of measurement invariance and differential item functioning. Substantive applications abound in the literature and span a broad range of disciplines. MNLFA unifies item response theory, multiple group, and multiple indicator multiple cause modeling traditions, and it extends these frameworks by conceptualizing latent variable heterogeneity as a source of differential item functioning. The purpose of this article was to illustrate a flexible Markov chain Monte Carlo-based approach to MNLFA that offers statistical and practical enhancements to likelihood-based estimation while remaining plug and play with established analytic practices. Among other things, these enhancements include (a) missing data handling functionality for incomplete moderators, (b) multiply imputed factor score estimates that integrate into existing multiple imputation inferential methods, (c) support for common data types, including normal/continuous, nonnormal/continuous, binary, ordinal, multicategorical nominal, count, and two-part constructions for floor and ceiling effects, (d) novel residual diagnostics for identifying potential sources of differential item function, (e) manifest-by-latent variable interaction effects that replace complex moderation function constraints, and (f) integration with familiar regression modeling strategies, including graphical diagnostics. A real data analysis example using the Blimp software application illustrates these features. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

---

使用马尔可夫链蒙特卡洛估计构建更简单的调节非线性因子分析模型。


调节非线性因子分析 （MNLFA） 已成为一种重要且灵活的数据分析工具，特别是在综合数据分析设置和测量不变性和差异项目功能的心理测量研究中。实质性的应用在文献中比比皆是，跨越广泛的学科。MNLFA 统一了项目反应理论、多组和多指标多原因建模传统，并通过将潜在变量异质性概念化为差异项目功能的来源来扩展这些框架。本文的目的是说明一种灵活的基于马尔可夫链蒙特卡洛的 MNLFA 方法，该方法为基于似然的估计提供统计和实践增强，同时保持对已建立分析实践的即插即用。除其他外，这些增强功能包括 （a） 缺少不完全调节因子的数据处理功能，（b） 集成到现有多重插补推理方法中的乘法插补因子分数估计值，（c） 支持常见数据类型，包括正态/连续、非正态/连续、二进制、有序、多分类名义、计数以及下限和上限效应的两部分结构，（d） 用于识别潜在来源的新型残差诊断差分项目函数，（e） 替代复杂调节函数约束的潜在变量交互效应，以及 （f） 与熟悉的回归建模策略集成，包括图形诊断。使用 Blimp 软件应用程序的真实数据分析示例说明了这些功能。（PsycInfo 数据库记录 （c） 2024 APA，保留所有权利）。