Psychometrics, Measurement Invariance, and Latent Variable Modeling
Why Measurement Is Theory
Constructs and indicators
Psychological variables are often latent, meaning they are not directly observed but inferred from indicators. Good measurement requires a theory of the construct, an operationalization strategy, and evidence that scores behave as intended across time, groups, and contexts.
Measurement principle
If a construct cannot be measured validly, it cannot be manipulated, compared, or improved with confidence.
Classical and Modern Approaches
Measurement frameworks
Classical Test Theory
- Score = true score + error
- Simple and intuitive
- Limited item-level diagnostics
Item Response Theory
- Models item characteristics
- Supports adaptive testing
- Requires stronger modeling assumptions
What does measurement invariance test?
Measurement invariance assesses whether comparisons across groups or occasions are meaningful.
Correct answer: Whether a construct is measured equivalently across groups or time
Why is scalar invariance important?
Without scalar invariance, mean differences may reflect measurement artifacts rather than true differences.
Correct answer: It supports meaningful comparison of latent means across groups.
Frontier issues in psychometrics
Current work emphasizes network psychometrics, multilevel measurement, Bayesian estimation, fairness auditing, and digital phenotyping. A major open problem is whether many widely used scales remain valid in changing digital, multicultural, and longitudinal environments.
A key limitation of using a scale in a new culture without testing invariance is that
Cross-cultural comparisons require evidence that the scale functions equivalently.
Correct answer: score differences may reflect measurement bias rather than substantive differences
Name one modern psychometric method used for item-level analysis.
IRT models how item difficulty and discrimination relate to latent ability or trait levels.
Correct answer: Item response theory.