In restricted factor analysis each of the elements in
the matrices (of factor loadings, factor correlations,
and unique variances and covariances) can be fixed,
free to be estimated, or constrained. In this paper it is
argued that the common practice of constraining some
parameters at 0 often is not psychologically meaningful.
Alternative procedures for constraining parameters
are presented and illustrated using data based on the
Luria model. Index terms: Constrained parameters,
Factor analysis, Factor correlations, Factor
loadings, Factor uniqueness.