Invariance or Not Invariance

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Invariance or Not Invariance

• Keith Widaman
• University of California, Davis

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Little on Invariance

• Equivalence of measurement
• Measurement is given too little emphasis in
• Curriculum
• Technical writings on invariance
• Substantive applications
• SEM will save the day (!?)
• Turn sows ears into silk purses
• But, will it?

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Little on Invariance

• Testing Invariance
• Configural invariance
• Weak factorial invariance
• Strong factorial invariance
• Strict factorial invariance

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Millsap on Invariance

• Factorial invariance vs. invariance of prediction
  relations
• Factorial invariance does not ensure invariant
  predictive equations
• Reinforces need for high quality measurement
• Need guidelines for what high quality
  measurement means
• e.g., reliability

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Millsap on Invariance

• Should make us wary of using sows ears measures
  for any important decision
• Diagnosis of mental retardation
• Subnormal general intellectual functioning
• Deficits in adaptive behavior
• MR diagnosis in death penalty cases
• Flynn effects and its influence on diagnosis

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Ram on (Non)invariance

• Invariance in developmental contexts
• Invariance may be constraining but we need
  baseline to ensure that poor measurement is not
  the culprit
• Throw off the tired shibboleths of the prior
  generation
• Beware invalidity of the new shibboleths

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Ram on (Non)invariance

• Invariance in matrix of correlations/ covariances
  among factors
• How falsifiable is this representation?
• Falsifiability is a criterion of science (Popper,
  Lakatos)
• If non-falsifiable, then non-science

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Ram on (Non)invariance

• Resolving conflicts / contentions with this new
  framework
• Requires going beyond the idiosyncratic pattern
  matrices
• Need to adopt a more comprehensive investigation
  of construct validity
• Lets update Cronbach Meehl