Methods Commentary: Uncovering Unobserved Data Patterns With Latent Variable Mixture Modeling

In a recent article in the Journal of Pediatric Psychology entitled “Latent Profiles of Physical Activity and Sedentary Behavior in Elementary School-Age Youth: Associations With Health-Related Quality of Life,” Mitchell and Steele (2017) used latent variable mixture modeling (LVMM) to empirically uncover three patterns of physical activity and sedentary behavior (SB) based on accelerometer data. These three patterns, also known as latent classes, were subgroups of youth who were classified as Active, Moderate, or Inactive in terms of their physical activity and SB. More specifically, these patterns were based on the average proportion of time in moderate-to-vigorous physical activity (MVPA) and SB and average proportion of time in MVPA and SB bouts over the course of 3 weekdays and 2 weekend days. Male gender and younger age were found to increase the odds of being a member of the active profile (relative to the moderate and inactive profiles), which in turn was associated with higher psychosocial health-related quality of life (HRQOL), above and beyond the direct effects of gender and age on this outcome. Why isLVMMused? While there are many uses of LVMM, the most typical is to find two or more relatively homogenous subgroups of individuals from a larger, more heterogeneous group based on patterns of data (Berlin, Parra, & Williams, 2014; Berlin, Williams, & Parra, 2014). It is a person-centered technique that focuses on classifying people into subgroups based on similarities and differences rather than relations among variables. The term “mixture” refers to what researchers are able to observe: the “mixture” of these subpopulations’ variable distributions; however, it is unknown who belongs to which subgroup and the extent to which members may belong to multiple subgroups. As individuals’ memberships in these subgroups or classes are unknown and unobserved, it is considered “latent,” and these memberships must be inferred from the observed data. LVMM uses modeling-based methods to quantify the extent to which individuals probabilistically belong (or are classified in) to each class, and as such latent classes are also considered to be “free” of measurement error, as the technique can adjust for imprecise classification. Most generally, these latent classes differ on (or are “defined” by) conceptually important variables. The basic idea is that unobserved latent memberships give rise to observed indicators and/or model parameters. These class-specific parameters are typically means and/or proportions in latent profile and latent class analyses, respectively; however, there are nearly limitless ways in which we can “define” these classes. In addition to classes differing in their means and proportions, they can differ in the correlations among variables, variances/covariances, intercepts, direct and indirect effects/regression coefficients, survival times, latent variable means, multilevel random effects, and longitudinal growth among many other types of parameters (Muthén & Muthén, 1998–2017). Why was LVMM used in Mitchell and Steele? An LVMM approach is well suited for research examining patterns of physical activity and SB as risk factors for obesity (Berlin et al., 2017). Obesity is a complex problem associated with a number of various lifestyle risk factors (Agras, Hammer, McNicholas, & Kraemer, 2004; Davison & Birch, 2001), and a person-centered approach allows researchers to look at patterns among a constellation of variables across subgroups of individuals (Berlin, Parra, et al., 2014; Berlin, Williams, et al., 2014). While Mitchell and Steele were justified in using daily averages as class indicators (given the research questions and sample size), it is important to note that quantitative techniques are available to integrate mixture and multilevel (random effect) models to analyze daily temporal data (Vermunt, 2008). Regardless of the statistical approach, identifying subgroups of individuals at varying risk for developing obesity or psychosocial consequences of obesity (e.g., lower health-related quality of life) may facilitate the development of more targeted interventions. How is LVMM conducted? LVMM proceeds in a series of steps that are ideally guided by both theory and past research while balancing model parsimony, complexity, and sample size (Bauer & Curran, 2003; Ram & Grimm, 2009). Problem Definition is the first step in which authors hypothesize how to define their classes (e.g., what are the class indicators vs. covariates vs. predictors vs. outcome) and how many classes they anticipate. This is followed by Model Specification, in which researchers determine what aspects (i.e., model parameters) of their classes will be the same or different across the classes. The next step is Model Estimation, in which researchers specify different numbers of latent classes and ensure computationally trustworthy models that yield a variety of information, indices, and tests to be used in the next step. In Model Selection and Interpretation, researchers’ major task is to choose the most optimal number of classes based on the research question, fit indices, statistical tests, smallest class sizes, the substantive meaning of each solution, parsimony, and/or theory. For some research questions, this could be the stopping point; however, an additional step is often necessary. A step we call Model Elaboration and Extension is useful when researchers are interested in predicting class membership and/or determining whether class membership predicts outcomes. Essentially, the final model selected in the previous step is used to explore an “auxiliary” or secondary model in which class memberships are retained (Asparouhov & Muthén, 2014). This allows for latent class memberships to be used in a variety of models that explore direct, indirect, and moderation effects, as well as many others strategies and their combinations (Bauer & Shanahan, 2007; Berlin, Karazsia, & Klages, 2018; Karazsia, Berlin, Armstrong, Janicke, & Darling, 2014; Muthén, 2008). What are the benefits of LVMM? LVMM affords researchers tremendous flexibility in the types of research questions that can be explored, largely because it is part of the broader latent variable modeling framework (Muthén, 2001), which also includes structure equation modeling and multilevel structural equation modeling (Kline, 2016). As such, variable- and person-centered analyses can be fully integrated. A practical benefit of LVVM is that it can take into account the precision of how accurately individuals were classified as to decrease bias when these classes are described, predicted, and/or used as predictors of important outcomes (Asparouhov & Muthén, 2014; McLachlan & Peel, 2000). WhatarethecaveatsandlimitationsofLVMM? LVMM is largely an exploratory approach, and as such evidence of validity and replication is important to avoid reifying latent classes. Conducting power analyses for LVMM is complicated and requires researchers to make numerous (and often arbitrary) assumptions, which almost uniformly suggest that the larger the sample size the better (Gudicha, Tekle, & Vermunt, 2016; Nylund, Asparouhov, & Muthén, 2007). There are also numerous potential pitfalls at every step in the LVMM process. For example, distinguishing between latent class indicators and covariates can be conceptually challenging in the Problem Definition and Model Specification steps. During the Model Estimation step, untrustworthy solutions are common. Choosing the final number of latent classes in the Model Selection and Interpretation step is often hampered by conflicting fit indices, and some of the “best” statistical options for helping to choose a model are noninformative in practice (i.e., always suggest that more classes are better than fewer) (Nylund et al., 2007). Furthermore, models are often selected in this step without utilization of consensus methods to minimize confirmation and other biases (Jones & Hunter, 1995; Nickerson, 1998; Waggoner, Carline, & Durning, 2016). Finally, in the Model Elaboration and Extension step, great care must be taken to rule out potential confounds. In the context of LVMM, this typically occurs when researchers find significant predictors of class that may also relate to outcomes (e.g., child age predicted both class membership and psychosocial HRQOL in Mitchell and Steel). In these circumstances, it is vital to model or “control” for these confounders (as did Mitchell and Steel) when exploring the effect of class on outcomes (Berlin et al., 2018; VanderWeele & Shpitser, 2013). What are thealternativesto LVMM? Researchers have many analytical options when seeking to determine if patterns of data exist and the extent to which these patterns relate to important variables. Most notable are cluster analyses and random forest models. Cluster analyses, as a group of methods, have the goal of classifying individuals into groups based on a set of observed variables. While LVMM is considered a model-based technique for clustering, it can be contrasted to cluster analyses, which are considered nonmodel-based, such as k-means clustering (Pastor, 2010). While both techniques have the same goal, nonmodel-based techniques are not considered inferential statistics (Pastor, 2010). One beneficial element of nonmodel-based techniques is their ready availability in the popular statistics software SPSS and SAS, whereas LVMM requires a more specialized software for computation. A drawback of nonmodel-based methods is the result of homogenous group membership, where each participant is assigned membership to a single cluster (Pastor, 2010). LVMM, as described above, allows for classification uncertainty, allowing participants to have partially belong to many groups via fractional memberships (Berlin, Williams, et al., 2014). Random forest models, models made up of a set of individual classification trees, have the goal of making accurate predictions for classification and regression (Breiman, 2001). These models predict outcomes by passing individual participants “through” the trees to determine the most likely outcome (Strobl, Malley, & Tutz, 2009). Two benefits of random forest models are the ability to incorporate large numbers of indicator variables (p) for a small number of participants (small n, large p) and the ability to assign participants to proportional probabilities on the outcome variable (e.g., certain combinations of variables may have a 15 vs. 60% chance of producing a “yes” outcome) (Strobl et al., 2009). Given the complex nature of interpreting indicator variables in random forest models, they do not offer the same type of model interpretation as LVMM, where latent classes can be qualitatively interpreted for subgroups of participants (e.g., the inactive subgroup). Where can I learn more aboutLVMM? Those seeking additional guidance on the use of LVMM are encouraged to review two recent introductory articles within in the Journal of Pediatric Psychology. The first provides a general overview of LVMM and the cross-sectional techniques of Latent Class and Latent Profile analyses (Berlin, Williams, et al., 2014). The second article is an introduction Longitudinal LVMM, including Latent Class Growth Analysis and Growth Mixture Models (Berlin, Parra, et al., 2014). Additional resources include online training videos at the Mplus software developer’s Web page (http://statmodel.com/) as well as the Mplus message boards. Conflicts of interest: None declared.