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Confirmatory Measurement Model Comparisons Using Latent Means.

R E Millsap, H Everson

    Multivariate Behavioral Research
    |January 19, 2016
    PubMed
    Summary

    Confirmatory Factor Analysis (CFA) can verify classical test theory models using mean structures. This study extends CFA to include nonzero latent means for a broader application in measurement model testing.

    Area of Science:

    • Psychometrics
    • Statistical Modeling
    • Measurement Theory

    Background:

    • Confirmatory Factor Analysis (CFA) traditionally verifies measurement models using covariance/correlation matrices.
    • Observed mean structures are often ignored in traditional CFA applications.
    • Classical test theory encompasses parallel, tau-equivalent, and congeneric test models.

    Purpose of the Study:

    • To extend Confirmatory Factor Analysis (CFA) to incorporate nonzero observed and latent means.
    • To test six measurement models derived from classical test theory using extended CFA.
    • To address three previously unexamined models within the context of CFA.

    Main Methods:

    • Application of Confirmatory Factor Analysis (CFA) to observed mean and covariance structures.

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  • Extension of CFA to include nonzero latent means.
  • Testing of six classical measurement models, including three novel applications.

    • Main Results:

    • The implications of six classical measurement models for observed mean and covariance structures are fully described.
    • Three examples demonstrate the use of CFA with nonzero latent means for model testing.
    • The study provides a comprehensive framework for applying CFA to a wider range of measurement models.

    Conclusions:

    • CFA with nonzero latent means offers an extended approach to verifying classical measurement models.
    • This extended CFA approach has implications for understanding both mean and covariance structures.
    • Advantages and limitations of using extended CFA for classical measurement models are discussed.