Score-based tests of measurement invariance: use in practice

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Measurement invariance is crucial for comparing latent constructs across groups or conditions.
• Existing methods often require pre-specified subgroups, limiting flexibility.
• Score-based tests offer a powerful alternative for assessing measurement invariance.

Purpose of the Study:

• To introduce and explain a family of score-based measurement invariance tests.
• To demonstrate their utility with continuous and ordinal auxiliary variables.
• To guide researchers on applying these tests and interpreting results for model parameter violations.

Main Methods:

• Utilizing a family of score-based measurement invariance tests.
• Applying tests to continuous auxiliary variables without subgroup pre-specification.
• Adapting tests for ordinal auxiliary variables, sensitive to monotonic violations.
• Illustrating applications using R packages (lavaan, strucchange).
• Conducting novel simulations to evaluate practical performance.

Main Results:

• The score-based tests effectively assess measurement invariance with continuous auxiliary variables.
• Tests adapted for ordinal variables show sensitivity to monotonic invariance violations.
• Simulations confirm the practical utility and accuracy of the tests in identifying parameter violations.
• The R packages provide accessible tools for implementing these analyses.

Conclusions:

• This paper equips researchers with practical tools and knowledge for applying advanced measurement invariance tests.
• The score-based approach offers flexibility for continuous and ordinal auxiliary variables.
• These methods enhance the rigor of cross-group or cross-condition comparisons in various research fields.