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A Solution to Modeling Multilevel Confirmatory Factor Analysis with Data Obtained from Complex Survey Sampling to

Jiun-Yu Wu1, John J H Lin2, Mei-Wen Nian1

  • 1Institute of Education, National Chiao Tung UniversityHsinchu, Taiwan.

Frontiers in Psychology
|October 12, 2017
PubMed
Summary
This summary is machine-generated.

Maximum models effectively handle unequal factor loadings in multilevel analyses, providing robust parameter estimates. Design-based and miss-specified models yield unreliable results, making maximum models preferable for complex survey data.

Keywords:
complex survey samplingdesign-based approachlevel-varying factor loadingsmaximum modelmeasurementmodel-based approachmultilevel confirmatory factor analysis

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Educational Measurement

Background:

  • Ensuring equality in between- and within-level structures is crucial for accurate Multilevel Confirmatory Factor Analysis (MCFA) parameter estimates and inferences.
  • A frequent challenge is unequal factor loadings within consistent level-varying structures, potentially biasing results.
  • This study addresses the robustness of different statistical models when faced with level-varying factor loadings in complex survey data.

Purpose of the Study:

  • To compare the robustness of five statistical models (two model-based, one design-based, two maximum models) under conditions of unequal factor loadings in MCFA.
  • To evaluate model performance in analyzing complex survey data with level-varying factor loadings.

Main Methods:

  • Mathematical investigation and Monte Carlo simulation were employed.
  • Empirical data from 120 3rd graders' perceived competence scale (nested within classrooms) were modeled using MCFA.
  • Parameter estimates from the empirical data served as true parameters for the simulation study.

Main Results:

  • Maximum models demonstrated robustness when dealing with unequal factor loadings.
  • Design-based and miss-specified model-based approaches resulted in conflated findings and spurious statistical inferences.
  • The full rank estimation of the variance-covariance matrix in maximum models proved effective.

Conclusions:

  • Maximum models are recommended when researchers have limited information regarding factor loading patterns and measurement structures in multilevel data.
  • The findings are generalizable to multilevel Structural Equation Modeling (SEM) and Confirmatory Factor Analysis (CFA) due to the foundational role of measurement models.
  • Mplus code is provided for implementing maximum and other analytical models.