Measurement Invariance in Multiple-Group and Longitudinal Mixture Models

• In Event: 1-155 - Mixture Modeling in Applied Developmental Research: Challenges and Opportunities

Integrative Statement

Longitudinal measurement invariance (MI) is critical to valid inference in developmental research when analyzing stability and change in one or more latent constructs over time. Additional challenges for evaluating measurement invariance emerge when latent variable indicators themselves are altered over time—a necessary practice in studies with wider timespans to ensure the use of developmentally-appropriate construct measures. As a result, noninvariance may present as items functioning differently over time or as different items being used to measure the same construct over time.

Compared to the vast and ever-growing psychometric research corpus regarding MI and differential item functioning (DIF) in the factor analysis 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 to determine the optimal configuration of classes within each group. 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. 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 (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 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. Student sex (binary) was considered as the grouping variable of interest.

The MGLCA is then extended to the latent transition analysis (LTA) framework for the evaluation of longitudinal invariance. The LTA measurement invariance testing procedure is explored using the Add Health data from Waves 1-4. This illustration presents with the added complication that some of the measures of adolescent delinquency were excluded in the adulthood Waves 3-4 while some adult-only measures were introduced. I discuss how the LTA measurement invariance model can be used to equate latent classes across time, even with changing indicators, so that all available indicators can be used at all time points rather than limiting the analysis to only the subset of indicators available at all four waves.

Author

• Katherine Masyn, Georgia State University
  Presenting Author