Abstract

Different from traditional practice that considers factor analysis as either exploratory or confirmatory, different amounts of substantive information can be available in between the confirmatory and exploratory extremes under the partially confirmatory approach. Based on Bayesian Lasso methods, three models were recently proposed for various types of data under the new approach: the partially confirmatory factor analysis (PCFA), generalized PCFA, and partially confirmatory item response model. All models with related variants can be implemented in the R package LAWBL, which is available free of charge. This article introduces the theoretical and statistical foundation of the three models in a unified framework, including model formulation, identification, variants, and Bayesian inference and estimation with regularizations. Didactic examples covering different scenarios are employed to illustrate the implementation of the models and their variants in LAWBL step by step. Guidelines and suggestions are given to researchers and practitioners in a discussion.

摘要

与将因子分析视为探索性或验证性的传统做法不同，在部分验证性方法下，在验证性和探索性极端之间可以获得不同数量的实质性信息。基于贝叶斯套索方法，最近针对新方法下的各类数据提出了三种模型：部分验证性因子分析（PCFA）、广义PCFA和部分验证性项目响应模型。所有具有相关变体的模型都可以在免费提供的 R 包 LAWBL 中实现。本文在一个统一的框架中介绍了三个模型的理论和统计基础，包括模型制定、识别、变体以及贝叶斯推理和正则化估计。涵盖不同场景的教学示例用于逐步说明模型及其变体在 LAWBL 中的实施。在讨论中向研究人员和从业者提供指导和建议。