Factorial Invariance: Historical Trends and New Developments
Roger E. Millsap1 and William W. Meredith2
1Arizona State University, 2University of California, Berkeley

Factorial invariance concerns features of the factor structure that remain the same across different populations, time periods, or sets of variables. The history of this topic can be divided into three periods: an early period focusing on the influence of selection on invariance, a middle period concerned with rotational procedures for evaluating or imposing invariance, and the current period dominated by confirmatory factor analysis. Much technical progress has been made, but some questions remain, including problems of identification, the meaning of partial invariance, the use of ordinal measures, the implications of selection theory, and the role of invariance in the general question of measurement bias. We discuss these questions and some new developments.