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Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models.

Andrea Hildebrandt1, Oliver Lüdtke2,3, Alexander Robitzsch2,3

  • 1a Department of Psychology , Ernst-Moritz-Arndt-Universität Greifswald.

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Summary
This summary is machine-generated.

This study compares three methods for analyzing how factor model parameters change with continuous variables like age. Local structural equation modeling (LSEM) is highlighted for its accuracy, especially when compared to multiple-group mean and covariance structure (MGMCS) analyses.

Keywords:
Local structural equation modelWJ-III tests of cognitive abilitiesage differentiation of cognitive abilitiesmoderated factor analysismultiple-group mean and covariance structures

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Area of Science:

  • Psychometrics
  • Quantitative Psychology
  • Structural Equation Modeling

Background:

  • Investigating how factor model parameters vary across continuous variables (e.g., age, socioeconomic status) is crucial for understanding developmental and individual differences.
  • Existing methods like multiple-group mean and covariance structure (MGMCS) analyses can yield distorted estimates under certain conditions, necessitating alternative approaches.
  • Local structural equation modeling (LSEM) offers a formalized framework for examining parameter variation, but its properties and implementation require further clarification.

Purpose of the Study:

  • To investigate and compare three statistical modeling approaches—MGMCS, LSEM, and moderated factor analysis (MFA)—for studying variations in factor model parameters across continuous moderators.
  • To formalize and detail the LSEM approach, investigate its statistical properties through analytical derivation and simulation, and provide implementation code.
  • To examine factor loading variations across age using cognitive ability data to test the age differentiation hypothesis.

Main Methods:

  • Empirical analysis using cross-sectional cognitive ability data from individuals aged 4 to 23 years.
  • Application and comparison of multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA).
  • Analytical derivation and simulation study to assess the statistical properties of the LSEM approach.

Main Results:

  • Local structural equation modeling (LSEM) and moderated factor analysis (MFA) yielded convergent conclusions regarding variations in factor loadings across age.
  • Multiple-group mean and covariance structure (MGMCS) analyses produced distorted parameter estimates when groups had broad age ranges and varying indicator-factor relationships.
  • The study provides evidence supporting the age differentiation hypothesis, showing variations in factor loadings across the examined age range.

Conclusions:

  • Local structural equation modeling (LSEM) is a robust method for investigating moderation in factor model parameters, offering advantages over traditional MGMCS analyses.
  • MFA and LSEM are complementary approaches, both effective in capturing parameter variations across continuous moderators.
  • The findings underscore the importance of selecting appropriate statistical methods to accurately model developmental changes in psychological constructs.