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Does strict invariance matter? Valid group mean comparisons with ordered-categorical items.

Winnie Wing-Yee Tse1, Mark H C Lai2, Yichi Zhang1

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Psychological Measurement

Background:

  • Measurement invariance (MI) is essential for valid group comparisons of constructs measured by psychometric scales.
  • Scalar invariance (loadings and intercepts) is generally accepted for comparing means with continuous items.
  • The applicability of scalar invariance to ordered-categorical items (polytomous and dichotomous) requires further examination.

Purpose of the Study:

  • To investigate the conditions under which scalar invariance permits valid mean comparisons for ordered-categorical items.
  • To determine the level of invariance required for accurate observed and factor mean comparisons with ordered-categorical data.
  • To highlight the impact of unique factor variance noninvariance on mean difference estimations.

Main Methods:

  • A Monte Carlo simulation study was employed to assess measurement invariance.
  • The study examined scalar invariance and strict invariance models with ordered-categorical items.
  • Simulations evaluated the effects of unique factor noninvariance on parameter estimation and statistical inference.

Main Results:

  • Scalar invariance adequately supports factor mean comparisons for ordered-polytomous items but not for dichotomous items.
  • Strict invariance (including thresholds and unique factor variances) is necessary for valid observed mean comparisons with both ordered-polytomous and dichotomous items.
  • Unique factor noninvariance significantly biased observed and factor mean differences, particularly for dichotomous items, leading to inflated Type I error rates.

Conclusions:

  • The assumption that scalar invariance suffices for mean comparisons with ordered-categorical items is only partially correct.
  • Strict invariance testing is recommended before comparing observed means with ordered-categorical data.
  • When strict invariance is violated, adjustments for partial invariance are suggested for factor mean comparisons.