Integrative Data Analysis With Mixture Models: Person-Centered Approaches With Pooled Data

• In Event: Issues of Measurement Invariance in Mixture Models for Educational Data

Abstract

Finite mixture models are often labeled as “person-centered” approaches designed to characterized overall population heterogeneity in the form of a mixture of qualitatively distinct subgroups (i.e., latent classes), wherein total population variability is parameterized by a combination of within- and between-group variability. Individuals within each subgroup manifest similar response patterns to a set of observable variables, while the qualitative differences across subgroups based on their defining response typologies cannot be organized along a linear continuum. Unlike variable-centered approaches such as factor analysis, mixture models cannot be estimated using summary level data such as means, variances, and covariance—person-centered approaches rely on individual-level data.
Meta-analytic techniques have advanced substantially in recent years and have provided educational researchers with powerful statistical tools to combine the results of multiple studies, overcoming small sample sizes of individual studies and increasing the precision in estimating effects However, one of the key limitations of meta-analysis is the reliance on summary statistics derived from completed studies as the unit of analysis (Brown et al., 2018), rendering this approach wholly inappropriate for person-centered analysis of pooled data. Furthermore, meta-analysis is also limited by heterogeneity, meaning the degree of dissimilarity in the results of individual studies—higher degrees of heterogeneity can neutralize the rationale for pooling effect estimates (Esterhuizen & Thabane, 2016).
Integrative data analysis (IDA; Brown et al., 2018; Curran & Hussong, 2009) provides an alternate framework for pooled data analysis that can maintain the person-centered orientation of individual studies. IDA provides clear advantages for mixture analyses as its data pooling is based on raw data from individual participants (Hussong et al. 2013). For one, it is rare that the 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.
However, as clearly described by Curran et al. (2008), there is a central challenge of IDA in how to appropriately pool measures of key constructs across independent studies. Curran et al. (2008) engage the techniques of item response theory (IRT) to harmonize and link continuous latent factors across time and across independent studies as well as to account for multiple sources of study differences. In this paper, we utilize the emerging techniques related to measurement invariance and differential item functioning for latent class measurement models to develop a similar approach to IDA with finite mixture models.
We illustrate our proposed IDA approach to LPA using a pooled dataset (N = 5486) of participant-level data from seven different studies (Bravo et al., 2016, 2018; Pearson et al., 2015), all utilizing the Five Facet Mindfulness Questionnaire (Baer et al., 2006) to link the latent profiles from the separate studies and to explore the effects of profile membership in the pooled dataset on mindfulness treatment outcomes.

Authors

• Katherine E. Masyn, Georgia State University

• Adrian Bravo, William & Mary

• Matthew R Pearson, University of New Mexico