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Measurement invariance (MI) in the latent class (LCA) context has a number of unique challenges both in application and conceptualization (Kankaras, Moors, & Vermut, 2011). This is in contrast to the factor analytic context which is well established and applied (Vandenberg & Lance, 2000). For example, LCA models typically have a large number of parameters to be tested for invariance, making ‘full measurement invariance’ less likely to be supported or practically meaningful. Further, it is unclear how violations of full measurement invariance (e.g., partial MI) would translate to bias when making substantive group comparisons.
The current paper illustrates an application of measurement invariance in the multigroup context with analyses conducted using Mplus 8.3 (Muthén & Muthén, 1998-2017). The sample consists of two groups of 10th grade students: 1) students who are perceived to have disabilities (POD) and 2) those who are not (non-POD). Here the research focus is on understanding how academic expectations of these students vary based on their perceived disability status.
The first step in invariance (configural) is tested by conducting the enumeration process separately for each group to determine if the endorsed model results in equal numbers of classes. Given this prerequisite is satisfied, structural invariance is tested using multigroup LCA by constraining the thresholds to be equivalent across POD and non-POD groups. The current study focuses on the substantive implications of structural invariance in an applied context. Although discussed in Morin, Meyer, Creusier, Bietry (2016), equality of class proportions (i.e., distributional invariance) are not considered in the illustrative example given that such constraints do not correspond with theoretical expectations nor are necessary for making group comparisons. In summary, measurement invariance is used to investigate the following research question: whether academic expectation patterns reported by parents, teachers and the focal student vary based on perceived disability status.
Before comparisons can be made of the emergent latent classes, an important analytic decision is choosing the comparison sample for the focal POD group. To determine the comparison sample (i.e., non-POD), two methods of sample selection were used, k-fold cross-validation (Kohavi, 1995) and propensity score matching (Sekhon, 2008). Once the comparison sample is selected, the steps of invariance will be presented in sequential order. The study illustrates measurement invariance across the POD and non-POD samples, focusing on practical significance of the differences across groups.
The current paper addresses the following two questions: 1) What are the patterns of academic ecological expectations found for 10th grade students perceived to have disabilities and those who are not? 2) How are these patterns similar or different across groups? Invariance methods developed in the latent variable literature have only superficially been extended to the context of mixture models. Procedures and best practices are largely left unspecified leaving this an open and developing area of research.