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A note on residual M-distances for identifying aberrant response patterns.

Christof Schuster1, Dirk Lubbe1

  • 1University of Giessen, Germany.

The British Journal of Mathematical and Statistical Psychology
|February 14, 2019
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This study introduces a new M-distance (d_si) for identifying unusual responses in statistical models. Derived from Thomson factor scores, it complements existing methods for psychometric analysis.

Keywords:
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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Individual Differences

Background:

  • Statistical models may not explain all individual responses in a sample.
  • M-distances offer a way to quantify how well an individual's response vector fits a psychometric model's covariance structure.
  • Existing M-distances include d_ri (based on Bartlett factor scores) and d_si.

Purpose of the Study:

  • To derive the d_si M-distance based on Thomson factor scores.
  • To provide an alternative method for assessing individual fit within a one-factor model.
  • To enhance the understanding of M-distances in psychometric analysis.

Main Methods:

  • Focus on the one-factor model in psychometric analysis.
  • Derivation of the d_si M-distance using Thomson factor scores.
  • Comparison with the existing d_ri M-distance derived from Bartlett factor scores.

Main Results:

  • The d_si M-distance was successfully derived based on Thomson factor scores.
  • This derivation provides a new tool for assessing individual response deviations.
  • The d_si M-distance is sensitive to different aspects of the factor model compared to d_ri.

Conclusions:

  • The d_si M-distance offers a valuable, alternative approach to identifying unusual individual responses.
  • This work extends the utility of M-distances in psychometric modeling.
  • Researchers can now utilize both d_ri and d_si for a more comprehensive assessment of model fit.