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A correlated traits correlated (methods - 1) multitrait-multimethod model for augmented round-robin data.

David Jendryczko1, Fridtjof W Nussbeck1

  • 1Department of Psychology, University of Konstanz, Konstanz, Germany.

The British Journal of Mathematical and Statistical Psychology
|October 16, 2023
PubMed
Summary

This study introduces a new statistical model for analyzing dyadic round-robin data, enhancing multitrait-multimethod analyses. The model accurately estimates parameters and detects model fit, even with reciprocity in augmented designs.

Keywords:
dyadic datamultitrait-multimethodround-robinstructural equation modelling

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Area of Science:

  • Psychometrics
  • Social Network Analysis
  • Statistical Modeling

Background:

  • Multitrait-multimethod (MTMM) models are crucial for assessing construct validity.
  • Dyadic round-robin designs capture complex social interactions.
  • Existing models may not fully account for dependencies in augmented round-robin data.

Purpose of the Study:

  • To derive and present a correlated traits correlated (methods - 1) [CTC(M - 1)] multitrait-multimethod (MTMM) model for augmented dyadic round-robin data.
  • To extend the CTC(M - 1) model to handle dependencies between raters and targets.
  • To provide methods for evaluating model fit and interpreting results.

Main Methods:

  • Development of a structural equation model for augmented dyadic round-robin data.
  • Inclusion of reciprocity covariance parameters to account for interdependencies.
  • Variance decomposition, consistency, and reliability coefficient presentation.
  • Simulation study to evaluate parameter estimation and model fit detection.

Main Results:

  • The proposed CTC(M - 1) model accurately estimates parameters and detects model fit using established indices.
  • Satisfactory parameter estimation bias and coverage rates were observed even with small groups.
  • Larger group sizes are recommended for minimizing parameter estimation inaccuracy.
  • Neglecting reciprocity covariance did not severely bias other parameter estimates.

Conclusions:

  • The derived CTC(M - 1) model offers a robust framework for analyzing augmented dyadic round-robin data.
  • The model provides valuable insights into consistency and reliability in complex social data.
  • The findings support the accurate application of this model in psychometric research.