A General Method for Studying Differences in Factor Means and Factor Structure Between Groups

Abstract

A statistical model is developed for the study of similarities and differences in factor structure between several groups. The model assumes that the observed variables satisfy a factor analysis model in each group. A method of data analysis is presented which, in contrast to earlier work, makes use of information in the observed means as well as the observed variances and covariances to estimate the parameters in each group, i.e. factor means, factor loadings, factor variances and covariances and unique variances. Usually the units of measurement in the observed variables have no intrinsic meaning and therefore it is only meaningful to compare the relative magnitudes of the parameters for the different groups. The method estimates the parameters for all groups simultaneously and can take into account a priori information about factorial invariance of various degrees.

Changing attitudes toward immigration in Europe, 2002–2007: A dynamic group conflict theory approach

“…In order to assess scalar invariance, the data should thus be augmented with mean-structure information (often referred to as mean and covariance structure [MACS] modeling, see Sörbom, 1974). Scalar equivalence implies that the measurement scales do not only have the same intervals, but also share origins.…”

Measurement equivalence: A comparison of methods based on confirmatory factor analysis and item response theory.

“…Given this current uncertainty, only the equality of slopes or factor loadings is used as a condition for measurement equivalence in this presentation, while noting that it can easily be expanded to include the equality of intercepts as some have done (i.e., Chan, 2000). Readers interested in testing for differences in latent factor means are referred to Bollen (1989), Byrne (1998), McDonald (1999, Sörbom (1974), and Vandenberg and Lance (2000) for additional discussion and illustrated applications.…”

How Harmful are Survey Translations? A Test with Schwartz's Human Values Instrument

“…99-107) are not sufficiently adequate as they only deal with information on covariance structures but not with information on mean structures. However, MACS analysis (Sörbom, 1974(Sörbom, , 1978, as well as 'differential item functioning' approaches based on item response theory provide an adequate means to test for scalar equivalence of survey instruments across groups (Raju, Lafitte, & Byrne, 2002;Reise, Widaman, & Pugh, 1993;Stark, Chernyshenko, & Drasgow, 2006).…”