[Linear factor analytic models for reliability analysis of composite variables]

Confirmatory factor analysis allows testing whether a composite variable may be considered as a reliable measure of a psychological attribute which is defined within a population.

Models for parallel, tau equivalent and congeneric measurements are presented along with their reliability coefficients.

When the variables are not tau equivalent, the averaged inter-item correlation should be preferred to coefficient alpha, which is not an estimator of the reliability of the corresponding data. As a rule, interpretation of a coefficient as a reliability coefficient requires that the corresponding structural model of the composite be known. Beyond unidimensionality, simultaneous analysis of several congeneric variables through the use of cross-sectional or longitudinal hierarchical models entails fragmenting the theoretical variables.

Interpreting a composite variable whose theoretical structure is corroborated by a hierarchical model may raise some difficulties because of its multidimensionality. Reliability formulae which account for this fragmentation are detailed.