Navigating the Ever-Changing Landscape of Distals in Mixture Models: A Road Map of Current Approaches

• In Event: Recent Developments in Multiple-Group, Multilevel, and Longitudinal Mixture Modeling

Abstract

Applications of mixture models are often interested in understanding about the individuals that comprise each of the latent classes by using auxiliary variables such as predictors, covariates, distal outcomes. The model building process regarding how to include these auxiliary variables in mixture models is an active area of research and new methods continue to emerge. As such, best practices for the application of these emergent methods in real data settings are still not well established. This paper focuses on distal outcomes, or consequences of latent class membership, and provides an overview of three best of the many available methods currently available for estimating the effects of latent class membership on distal outcomes. We will briefly discuss other methods and why they are not currently recommended.
In the application for this paper, we use a growth mixture model (GMM) with Math outcome scores from grades 7-10, from the national dataset, the Longitudinal Study of American Youth (LSAY; Miller, 1987-1994, 2007). After choosing the optimal unconditional model, two binary distal outcomes – entry into a STEMM major and entry into a STEMM career – were included using each of the three approaches. Gender was included as a covariate in all approaches. We compare the distal outcome results across approaches.
The first approach, distal-as-indicator, includes the distal outcomes as indicators of the latent growth classes. Thus, they directly contributed to the enumeration of the classes and this can result in undesirable shifts in the latent classes. The second approach, the manual 3-step approach (e.g., Vermunt, 2010) estimates an unconditional model as the first step. Second, classification error resulting from nonperfect assignment of individuals to latent classes is included in the model to reduce latent class shifting. Once classification error is included in the model, class-specific means of the distal outcomes are estimated as the third step. The third approach, the BCH method (Bolck, Croon, & Hagenaars, 2004) is similar to the three-step approach. However, instead of calculating the average classification error in the second step, classification errors for each individual are computed, and the inverse logits of those individual-level error rates are used as weights in the third step rather than using the modal class assignment as imperfect latent class indicator.
Results of the unconditional GMM showed a seven-class model was optimal. Across distal approaches, class 6 had the greatest probability of entering into a STEMM major and this was significantly greater than all other classes. Though point estimates varied, the patterns of statistical significance were similar across the three approaches. This was not the case for STEMM career. The distal-as-indicator approach provided patterns of statistical significance that differed from the other two approaches. Additionally, standard errors of the distal outcome estimates were greater for the distal-as-indicator approach.
This paper demonstrates the different approaches for including distal outcomes and highlights strengths and weakness of each methods. We will not provide recommendations for which one is best. However, we suggest researchers understand the range of options for including distal outcomes to understand differences across approaches.

Authors

• Ryan Grimm, University of California - Davis

• Karen L. Nylund-Gibson, University of California - Santa Barbara

• Katherine E. Masyn, Georgia State University