Multi-item surveys are frequently used to study scores on latent factors, like human values, attitudes, and behavior. Such studies often include a comparison, between specific groups of individuals or residents of different countries, either at one or multiple points in time (i.e., a cross-sectional or a longitudinal comparison or both). If latent factor means are to be meaningfully compared, the measurement structures of the latent factor and their survey items should be stable, that is “invariant.” As proposed by Mellenbergh (1989), “measurement invariance” (MI) requires that the association between the items (or test scores) and the latent factors (or latent traits) of individuals should not depend on group membership or measurement occasion (i.e., time). In other words, if item scores are (approximately) multivariate normally distributed, conditional on the latent factor scores, the expected values, the covariances between items, and the unexplained variance unrelated to the latent factors should be equal across groups. Many studies examining MI of survey scales have shown that the MI assumption is very hard to meet. In particular, strict forms of MI rarely hold. With “strict” we refer to a situation in which measurement parameters are exactly the same across groups or measurement occasions, that is an enforcement of zero tolerance with respect to deviations between groups or measurement occasions. Often, researchers just ignore MI issues and compare latent factor means across groups or measurement occasions even though the psychometric basis for such a practice does not hold. However, when a strict form of MI is not established and one must conclude that respondents attach different meanings to survey items, this makes it impossible to make valid comparisons between latent factor means. As such, the potential bias caused by measurement non-invariance obstructs the comparison of latent factor means (if strict MI does not hold) or regression coefficients (if less strict forms of MI do not hold). Traditionally, MI is tested for in a multiple group confirmatory factor analysis (MGCFA) with groups defined by unordered categorical (i.e., nominal) between-subject variables. In MGCFA, MI is tested at each constraint of the latent factor model using a series of nested (latent) factor models. This traditional way of testing for MI originated with Joreskog (1971), who was the first scholar to thoroughly discuss the invariance of latent factor (or measurement) structures. Additionally, Sorbom (1974, 1978) pioneered the specification and estimation of latent factor means using a multi-group SEM approach in LISREL (Joreskog and Sorbom, 1996). Following these contributions the multi-group specification of latent factor structures has become widespread in all major SEM software programs (e.g., AMOS Arbuckle, 2006, EQS Bender and Wu, 1995, LAVAAN Rosseel, 2012, Mplus Muthen and Muthen, 2013, STATA STATA, 2015, and OpenMx Boker et al., 2011). Shortly thereafter, Byrne et al. (1989) introduced the distinction between full and partial MI. Although their introduction was of great value, the first formal treatment of different forms of MI and their consequences for the validity of multi-group/multi-time comparisons is attributable to Meredith (1993). So far, a tremendous amount of papers dealing with MI have been published. The literature on MI published in the 20th century is nicely summarized by Vandenberg and Lance (2000). Noteworthy is also the overview of applications in cross-cultural studies provided by Davidov et al. (2014), as well as a recent book by Millsap (2011) containing a general systematic treatment of the topic of MI. The traditional MGCFA approach to MI-testing is described by, for example, Byrne (2004), Chen et al. (2005), Gregorich (2006), van de Schoot et al. (2012), Vandenberg (2002) and Wicherts and Dolan (2010). Researchers entering the field of MI are recommended to first consult Meredith (1993) and Millsap (2011) before reading other valuable academic works. Recent developments in statistics have provided new analytical tools for assessing MI. The aim of this special issue is to provide a forum for a discussion of MI, covering some crucial “themes”: (1) ways to assess and deal with measurement non-invariance; (2) Bayesian and IRT methods employing the concept of approximate MI; and (3) new or adjusted approaches for testing MI to fit increasingly complex statistical models and specific characteristics of survey data.
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Open Access
Oct 15, 2023
Güler Yavuz Temel 
