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Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach.

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  • 1Department of Psychology, Beihang University, Beijing, 100191, China.

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Summary
This summary is machine-generated.

This study introduces a novel approach for multi-group structural equation modeling, enabling latent variable mean comparisons without strict intercept equality assumptions. The new method enhances data analysis by offering a validity index for mean differences.

Keywords:
bootstrapchi-square-difference statisticcommon scoremeasurement invariancespecific factorwald statistic

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Area of Science:

  • Psychometrics
  • Quantitative Psychology
  • Statistical Modeling

Background:

  • Conventional multi-group structural equation modeling (SEM) necessitates strict cross-group equality of intercepts for latent variable mean comparisons.
  • This prerequisite often complicates or prevents meaningful mean difference analyses.

Purpose of the Study:

  • To propose a new SEM setup that bypasses the need for estimating mean structural models and cross-group intercept equality.
  • To enable direct mean comparison of latent variables, including common and specific factors.
  • To introduce a validity index for assessing the proportion of mean differences attributable to common factors.

Main Methods:

  • A novel projection method is employed to decompose observed sample means into common and specific factor spaces.
  • The approach allows for independent testing of cross-group mean differences for common and specific factors.
  • A validity index is defined as the ratio of squared common score mean differences to total squared observed mean differences.

Main Results:

  • The proposed setup successfully identifies and estimates means of common and specific factors without requiring cross-group intercept equality.
  • Independent testing of mean differences for common and specific factors is achieved, simplifying the analysis.
  • A real-data analysis with two groups demonstrated that the new setup provides richer insights compared to conventional methods.

Conclusions:

  • The new multi-group SEM setup offers a more flexible and informative alternative for latent variable mean comparisons.
  • It eliminates restrictive assumptions of the conventional approach, facilitating broader application.
  • The introduced validity index offers a quantifiable measure of the meaningfulness of observed mean differences.