ABSTRACT
The factorial invariance refers to replicating factors across systematic variations in the selection of variables or subjects. The fact that the samples are assumed to be from differing populations distinguishes factorial invariance from factorial replication; refers to the finding of the same factors across random samples. Factorial invariance across systematic variations of the samples is distinct from replication across random samples. The analytic rotation procedures are invariant to provide approximate solutions or it may be that even minor selection produces enough distortion in the configuration to affect invariance. The invariance of a factor solution across changes in the selection of variables or individuals is defined in terms of the loadings for a variable included in all of the analyses. An implication of the conditions for factor pattern invariance is that the selection of variables is a crucial and time-consuming step in a factor analysis.
