ABSTRACT
Interest in the invariance of the factor model with respect to different populations of
individuals, different time periods, or even different variables from a domain appeared
early in the history of factor analysis. Thurstone (1947) studied how the factor structure
for a set of measured variables changes when additional variables are included in the set
being analyzed (Little, Lindenburger, & Nesselroade, 1999). Change in the factor
structure of a measure taken longitudinally has also been studied, but population
differences in factor structure have received the most attention. Technical developments
in methods for studying group differences in factor structure have now advanced to the
point where studies of invariance can be completed by anyone with a personal computer
and access to confirmatory factor-analytic software. As noted by McDonald (1999), the
factor model can even be applied to the study of group differences in the factor structure
of dichotomously scored items. However, these technical developments have not fully
resolved some conceptual or practical problems facing researchers who study factorial
invariance. This chapter focuses on four of these unresolved problems and the prospects
for their solutions. We begin with a review of definitions of factorial invariance and their
relation to broader notions of measurement invariance (Meredith & Millsap, 1992), and
follow with sections describing each problem in turn.
