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Using generalizability theory with continuous latent response variables.

Walter P Vispoel1, Carrie A Morris1, Murat Kilinc1

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Generalizability theory (G-theory) with continuous latent response variables (CLRV) and structural equation modeling (SEM) improves score reliability and validity. This approach quantifies measurement error, offering stable indices independent of scale coarseness.

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Categorization errors and unequal intervals in data collection can distort measurement.
  • Traditional methods may not adequately address these sources of measurement error.

Purpose of the Study:

  • To demonstrate the application of generalizability theory (G-theory) with continuous latent response variables (CLRV).
  • To address scale coarseness and transformation errors using structural equation modeling (SEM).
  • To provide stable indices of score consistency and validity.

Main Methods:

  • Utilized structural equation modeling (SEM) to derive variance components for G-theory analyses.
  • Applied G-theory to continuous latent response variables (CLRV) to quantify multiple error sources.
  • Illustrated with nested and non-nested designs, and disattenuation of correlation coefficients.

Main Results:

  • G-theory with CLRV effectively quantifies various measurement error sources.
  • Achieved stable indices of reliability and validity, robust to scale coarseness and interval unevenness.
  • Demonstrated effectiveness in norm- and criterion-referenced score interpretation.

Conclusions:

  • G-theory integrated with SEM offers a robust framework for psychometric analysis with CLRV.
  • This approach yields more accurate and stable reliability and validity estimates.
  • Recommendations provided for applying G-theory to raw score and CLRV metrics.