Confirmatory Factor Analysis:
measurement models
Psychology 588: Covariance structure and factor models
Feb 17, 2010

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Few things on measurement theory
2
•
Measurement may be defined as assigning numbers to
observational units (“subjects”) so as to indicate the magnitude
(and direction if bipolar) on an intended concept (construct,
latent variable)
•
A measurement model quantitatively defines the relationships
between observed phenomena (items, indicators, measures,
manifest variables) and unobservable concepts (factors, latent
variables)
¾
e.g., Spearman’s single factor model, 2-parameter logistic
model, graded response model, etc.
¾
We will only consider linear relationships in SEM (in the
classical form, while generalized SEM allows nonlinear
relationships)