Integrative Data Analysis With Mixture Models: Person-Centered Approaches With Individual Participant-Level Data Across Multiple Studies

• In Event: Interrogating Mixture Models in Pursuit of True Population Heterogeneity

Abstract

In 1976, Glass coined the term meta-analysis for the statistical analytic approach to combining the results of multiple studies. In 2000, Glass called for aggregated data (AD) meta-analysis to be replaced by individual participant-level data (IPD) meta-analysis (Cooper & Patall, 2009). Although AD meta-analytic techniques had advanced substantially in the interim—providing educational researchers with powerful statistical tools to combine the results of multiple studies, overcoming small sample sizes and increasing precision in estimating effects—those advances could not remove the reliance on summary statistics derived from completed studies (Brown et al., 2018) nor could they erase the constraints of heterogeneity across studies wherein higher degrees of heterogeneity can neutralize the rationale for pooling effect estimates (Esterhuizen & Thabane, 2016).

In contrast, capturing and explaining population heterogeneity is the rationale for person-centered approaches such as finite mixture models. The parameterization of population heterogeneity takes the form of a mixture of qualitatively distinct subgroups (i.e., latent classes). Individuals within each subgroup manifest similar response patterns to a set of observable variables, characterizing each class, while qualitative differences across subgroups based on their defining response typologies distinguish between the classes. Unlike variable-centered approaches such as factor analysis, mixture models cannot be estimated using summary statistics. Consequently, finite mixture modeling within a single study population seems incompatible with meta-analysis, at least the AD type.

However, the advent of modern IPD meta-analysis and the nearly simultaneous rise of integrative data analysis (IDA; Brown et al., 2018; Curran & Hussong, 2009), offers a reframing of pooled data analysis that can maintain the person-centered orientation of individual studies using mixture models. Considering mixture modeling in an IDA context may provide some clear advantages over singular study analyses. For one, it is rare that latent classes are uniformly distributed in the population; as such, in a single study, there may be under-representation of a potentially important latent subgroup in the population. By pooling participants across studies, not only could between-class comparisons be more precise, the external validity of the latent classes themselves could be increased.

The central challenge of any IDA is the need to establish measurement equivalence for the latent constructs across studies. Bauer and Hussong (2009) proposed a moderated nonlinear factor analysis (MNLFA) as a generalization of the linear factor analysis model and the 2-parameter logistic (2-PL) IRT model for evaluating measurement invariance. This MNFLA approach has been elaborated and extended in the IDA setting and beyond over the last 10 years (e.g., Bauer, 2017) but exclusively in the continuous latent variable domain.

This paper presents an adaptation of the MNLFA approach to evaluating the measurement equivalence of latent classes across multiple studies in a participant-level pooled data set. Our proposed moderated nonlinear latent class analysis (MNLCA) technique allows for a multivariable assessment of potential individual sources of measurement noninvariance interacting with study membership. We provide an empirical demonstration of our approach using an integrated data set of participant-level observations across six distinct, school-based, preventive intervention trials with extensive long-term follow-up.

Authors

• Katherine E. Masyn, Georgia State University
  Presenting Author

• Rashelle Musci
  Presenting Author