Measurement invariance in multiple-group latent class analysis and latent transition analysis


Masyn, K. (2018). Measurement invariance in multiple-group latent class analysis and latent transition analysis. American Educational Research Association. New York, NY.


Compared to the vast and ever-growing psychometric research corpus regarding measurement invariance (MI) and differential item functioning (DIF) in the SEM and IRT spheres, there is a relative scarcity of work addressing these issues in finite mixture modeling (cf., Masyn, 2017). The majority of the scant existing work on measurement invariance in latent class and latent profile analysis has been done in the context of multiple-group models. Collins and Lanza (2013) describe a general procedure for invariance testing within an LCA, which involves first determining that the number and general pattern of item endorsements is similar; this is generally done by conducting separate LCAs by group and using standard fit indices (e.g., BIC, AIC, likelihood ratio test) to determine the optimal configuration of classes within each group. After this initial step, testing generally proceeds as in the continuous latent variable case, by successively testing constraints in a multiple-group LCA. There is some evidence (Finch, 2015) that, within this general procedure, comparisons to the baseline model should be made using a fit index which makes minimal assumptions, such as the bootstrap likelihood ratio test (BLRT). However, there is little evidence as to which choices yield optimal detection of non-invariance in the multiple-group approach. This paper presents the parameterization of measurement non-invariance in multiple-group latent class analysis (MGLCA). I discuss the translation of the standard levels of measurement invariance from the traditional multiple-group confirmatory factor analysis (MGCFA; a la Meredith, 1993)—configural, weak, strong, and strict—to the MGLCA setting and explore the meaning of “partial invariance” at these different levels in the case of a latent class measurement model. I demonstrate my recommended MGLCA measurement invariance testing procedure with a data from Wave 1 (1994-1995) of the National Longitudinal Study of Adolescent Health (Add Health; Harris, 2013). Following the Collins and Lanza (2013) empirical example of latent class analysis of adolescent delinquency, I use six dichotomized student questionnaire items about past-year delinquent behavior as indicators of a 4-class latent multinomial variable. Student sex (binary) was considered as the grouping variable of interest. The MGLCA parameterization of measurement non-invariance is then extended to the latent transition analysis (LTA) framework for the evaluation of longitudinal invariance. I demonstrate my recommended LTA measurement invariance testing procedure using the Add Health data from Waves 1-4 with the same LCA measurement model at each wave as was used for the MGLCA illustration. For both the MGLCA and LTA examples, empirical comparisons are made to demonstrate the potential consequences of failing to account for measurement non-invariance, including bias in structural parameters estimates and standard errors. I close with a discussion of future directions, including the adaptation of these procedures for the testing of approximate measurement invariance or measurement equivalence using Bayesian estimation.


Reference Type

Conference proceeding

Book Title

American Educational Research Association


Masyn, K.

Year Published


City of Publication

New York, NY

Reference ID