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Understanding Composite-Based Structural Equation Modeling Methods From the Perspective of Regression Component

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Summary
This summary is machine-generated.

Regression Component Analysis (RCA) offers determinate scores, unlike traditional factor analysis. RCA parameter estimates align with regression-weighted Partial Least Squares (PLS) and Generalized Structured Component Analysis (GSCA) when factor models are accurate.

Keywords:
Structural equation modelingcomposite-based methodsgeneralized structured component analysispartial least squaresregression component analysis

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Area of Science:

  • Multivariate statistics
  • Psychometrics
  • Data analysis methodology

Background:

  • Traditional factor analysis yields indeterminate factor scores, limiting direct interpretation and application.
  • Existing methods like Partial Least Squares (PLS) and Generalized Structured Component Analysis (GSCA) offer alternative approaches to component modeling.
  • The relationship between factor analysis and component-based methods, particularly concerning score determinacy, requires clarification.

Purpose of the Study:

  • To introduce and define Regression Component Analysis (RCA) as a method for obtaining determinate component scores.
  • To establish the analytical equivalence between RCA and regression-weighted factor scores.
  • To demonstrate the consistency of RCA with regression-weighted PLS and GSCA under specific conditions.

Main Methods:

  • Regression Component Analysis (RCA) is proposed, utilizing weighted composites of observed variables.
  • The weight matrix for RCA is derived from factor model parameter estimates.
  • Analytical comparisons are made between RCA, factor analysis, PLS, and GSCA, using a consistent symbolic framework and R syntax.

Main Results:

  • RCA produces determinate component scores, contrasting with the indeterminate scores from standard factor analysis.
  • Under conditions of a correct population factor model and standardized composites, RCA parameter estimates match those from regression-weighted PLS and GSCA.
  • RCA demonstrates the ability to replicate both correlation and regression weight versions of PLS and GSCA, especially with parallel measurement.

Conclusions:

  • Regression Component Analysis (RCA) provides a consistent framework for modeling data that adheres to a factor model, yielding determinate scores.
  • RCA, regression-weighted PLS, and GSCA are shown to be consistent modeling approaches when applied to factor-model-conforming data.
  • The findings unify these analytical methods under the concept of modeling with regression method factor scores.