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Measurement invariance versus selection invariance: is fair selection possible?

Denny Borsboom1, Jan-Willem Romeijn, Jelte M Wicherts

  • 1Department of Psychology, University of Amsterdam, Roetersstraat 15, Amsterdam, The Netherlands. d.borsboom@uva.nl

Psychological Methods
|June 19, 2008
PubMed
Summary

Measurement invariance often conflicts with selection invariance. This occurs because differing group characteristics can lead to unequal test performance metrics, impacting predictions, especially in minority groups.

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Social sciences

Background:

  • Measurement invariance is crucial for comparing groups using assessment tools.
  • Selection invariance, concerning equal test sensitivity and specificity across groups, is often assumed but may not hold.
  • Discrepancies between measurement and selection invariance can lead to biased predictions.

Purpose of the Study:

  • To investigate the inconsistency between measurement invariance and selection invariance.
  • To elucidate how group differences in latent distributions affect predictive values.
  • To explore the implications for differential prediction, particularly in minority groups.

Main Methods:

  • Theoretical analysis of measurement and selection invariance.
  • Examination of sensitivity, specificity, and predictive values under varying latent distribution parameters.
  • Simulation studies to assess the magnitude of the effect in realistic scenarios.
  • Connection to Simpson's paradox due to dichotomization of continuous scores.

Main Results:

  • Measurement and selection invariance are generally incompatible.
  • Group differences in latent means or variances lead to unequal sensitivity, specificity, and predictive values.
  • Higher latent means correlate with higher sensitivity and positive predictive value, while lower means correlate with higher specificity and negative predictive value.
  • The magnitude of these differences depends on both mean and variance disparities.

Conclusions:

  • The observed effect, a form of Simpson's paradox, can be substantial and may contribute to overprediction in minority groups.
  • Existing methods for ensuring measurement invariance may not guarantee selection invariance.
  • Methodological adjustments and careful consideration of social policy implications are necessary for equitable assessment and prediction.