Applying and Interpreting Mixture Distribution Latent State-Trait Models

Abstract

Latent state-trait (LST) models are commonly applied to determine the extent to which observed variables reflect trait-like versus state-like constructs. Mixture distribution LST (M-LST) models relax the assumption of population homogeneity made in traditional LST models, allowing researchers to identify subpopulations (latent classes) with differing trait- and state-like attributes. Applications of M-LST models are scarce, presumably because of the analysis complexity. We present a step-by-step tutorial for evaluating M-LST models based on an application to mother, father, and teacher reports of children’s inattention (n = 811). In the application, we found three latent classes for mother and father reports and four classes for teacher reports. All reporter solutions contained classes with very low, low, and moderate levels of inattention. The teacher solution also contained a class with high inattention. Comparable mother and father (but not teacher) classes exhibited similar levels of trait and state variance.

Keywords:

• Latent state-trait
• mixture distribution modeling
• consistency
• occasion-specificity
• longitudinal modeling
• latent classes

Notes

¹ Kenny and Zautra (1995) presented a single-indicator LST model. In principle, the M-LST approach that we illustrate in this article could also be applied to Kenny and Zautra’s model. In this article, we focus on multiple-indicator LST models, as these have been shown to result in fewer estimation problems compared to the Kenny and Zautra approach (Cole et al., 2005).

² LST models have been developed to account for polytomous indicators (Eid, 1996). These models have not yet been applied to a mixture distribution framework.

³ In cases in which constructs show mean change across time, an extended model with a trait-change component would have to be specified in some or all classes. Such hybrid models are beyond the scope of the present tutorial, but have been presented, for example, by Eid and Hoffmann (1998); Geiser et al. (2017); and Steyer et al. (2015) for the single-class case.

⁴ Father and teacher models will be discussed in Step 3.

⁵ It is possible that a single parameter (e.g., one trait mean or one error variance) differs across classes in the M-LST approach. Further, partial measurement invariance (e.g., Byrne, Shavelson, & Muthén, 1989; Lubke & Neal, 2008) is possible with the M-LST approach. We have not presented a step to examine differences of a single parameter across classes nor a step to examine partial measurement invariance, but it is possible to examine such differences using the present approach. We recommend examining such models only if there is a theoretical or practical reason to do so.

⁶ For additional classification diagnostics that could be reported using a mixture modeling approach, see Masyn (2013).

Additional information

Funding

Two Ministry of Economy and Competitiveness Grants, PSI2011-23254 and PSI2014-52605-R (Spanish Government), and a predoctoral fellowship co-financed by the European Social Fund and the Balearic Islands Government (FPI/1451/2012) in part supported this research.