A Comparison of Label Switching Algorithms in the Context of Growth Mixture Models

Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth mixture model is used in this simulation study, and the design crosses three manipulated variables-number of latent classes, latent class probabilities, and class separation, yielding a total of 18 conditions. Within each of these conditions, the accuracy of a priori identifiability constraints, a priori training of the algorithm, and four post hoc algorithms developed by Tueller et al.; Cho; Stephens; and Rodriguez and Walker are tested to determine their classification accuracy. Findings reveal that, of all a priori methods, training of the algorithm leads to the most accurate classification under all conditions. In a case where an a priori algorithm is not selected, Rodriguez and Walker's algorithm is an excellent choice if interested specifically in aggregating class output without consideration as to whether the classes are accurately ordered. Using any of the post hoc algorithms tested yields improvement over baseline accuracy and is most effective under two-class models when class separation is high. This study found that if the class constraint algorithm was used a priori, it should be combined with a post hoc algorithm for accurate classification.

Improving convergence in growth mixture models without covariance structure constraints

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

Covariance pattern mixture models: Eliminating random effects to improve convergence and performance

Growth mixture models (GMMs) are prevalent for modeling unknown population heterogeneity via distinct latent classes. However, GMMs are riddled with convergence issues, often requiring researchers to atheoretically alter the model with cross-class constraints simply to obtain convergence. We discuss how within-class random effects in GMMs exacerbate convergence issues, even though these random effects rarely help answer typical research questions. That is, latent classes provide a discretization of continuous random effects, so including additional random effects within latent classes can unnecessarily complicate the model. These random effects are commonly included in order to properly specify the marginal covariance; however, random effects are inefficient for patterning a covariance matrix, resulting in estimation issues. Such a goal can be achieved more simply through covariance pattern models, which we extend to the mixture model context in this article (covariance pattern mixture models, or CPMMs). We provide evidence from theory, simulation, and an empirical example showing that employing CPMMs (even if they are misspecified) instead of GMMs can circumvent the computational difficulties that can plague GMMs, without sacrificing the ability to answer the types of questions commonly asked in empirical studies. Our results show the advantages of CPMMs with respect to improved class enumeration and less biased class-specific growth trajectories, in addition to their vastly improved convergence rates. The results also show that constraining the covariance parameters across classes in order to bypass convergence issues with GMMs leads to poor results. An extensive software appendix is included to assist researchers in running CPMMs in Mplus.

Multilevel Latent Profile Analysis With Covariates

Latent profile analysis (LPA) is a person-centered method commonly used in organizational research to identify homogeneous subpopulations of employees within a heterogeneous population. However, in the case of nested data structures, such as employees nested in work departments, multilevel techniques are needed. Multilevel LPA (MLPA) enables adequate modeling of subpopulations in hierarchical data sets. MLPA enables investigation of variability in the proportions of Level 1 profiles across Level 2 units, and of Level 2 latent classes based on the proportions of Level 1 latent profiles and Level 1 ratings, and the extent to which covariates drawn from the different hierarchical levels of the data affect the probability of a membership of a particular profile. We demonstrate the use of MLPA by investigating job characteristics profiles based on the job-demand-control-support (JDCS) model using data from 1,958 university employees clustered in 78 work departments. The implications of the results for organizational research are discussed, together with several issues related to the potential of MLPA for wider application.

Extracting Spurious Latent Classes in Growth Mixture Modeling With Nonnormal Errors

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This can lead to the overextraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study are (1) to explore the performance of the Bayesian information criterion, sample-adjusted BIC, and bootstrap likelihood ratio test in growth mixture modeling analysis with nonnormal distributed outcome variables and (2) to examine the effects of nonnormal time invariant covariates in the estimation of the number of latent classes when outcome variables are normally distributed. For both of these goals, we will include nonnormal conditions not considered previously in the literature. Two simulation studies were conducted. Results show that spurious classes may be selected and optimal solutions obtained in the data analysis when the population departs from normality even when the nonnormality is only present in time invariant covariates.