从回归分析的角度理解基于复合的结构方程建模方法 组件分析
1Department of Marketing, Georgia State University.
Multivariate behavioral research
|April 9, 2024
概括
回归组件分析 (RCA) 与传统的因子分析不同,提供了确定的分数. 当因子模型准确时,RCA参数估计与回归加权的部分最小平方 (PLS) 和通用结构组件分析 (GSCA) 保持一致.
科学领域:
- 多变量统计的多变量统计.
- 心理测量 心理测量 心理测量
- 数据分析方法论数据分析方法论
背景情况:
- 传统的因子分析产生不确定的因子得分,限制了直接的解释和应用.
- 现有的方法,如部分最小平方 (PLS) 和通用结构组件分析 (GSCA),为组件建模提供了替代方法.
- 因子分析和基于组件的方法之间的关系,特别是关于得分的确定性,需要澄清.
研究的目的:
- 引入和定义回归组件分析 (RCA) 作为获得特定组件分数的方法.
- 为了确定RCA和回归加权因子得分之间的分析等价性.
- 在特定条件下证明RCA与回归加权PLS和GSCA的一致性.
主要方法:
- 建议进行回归组件分析 (RCA),利用观察到的变量的加权复合物.
- RCA 的权重矩阵是从因子模型参数估计得出的.
- 在RCA,因子分析,PLS和GSCA之间进行分析比较,使用一致的符号框架和R语法.
主要成果:
- RCA产生了确定组件分数,与标准因子分析的不确定分数形成鲜明对比.
- 在正确的人口因子模型和标准化复合材料的条件下,RCA参数估计与回归加权PLS和GSCA的估计相匹配.
- RCA证明了能够复制PLS和GSCA的相关性和回归重量版本的能力,特别是在并行测量时.
结论:
- 回归组件分析 (RCA) 为数据建模提供了一个一致的框架,它遵循一个因子模型,产生特定的分数.
- 当应用到符合因子模型数据时,RCA,回归加权PLS和GSCA被证明是一致的建模方法.
- 这些发现将这些分析方法统一在回归方法因子得分的建模概念下.
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