Academic journal article Journal of Marriage and Family

Investigating Family Shared Realities with Factor Mixture Modeling

Academic journal article Journal of Marriage and Family

Investigating Family Shared Realities with Factor Mixture Modeling

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Statistical methods possess fascinating ways of describing relationships among variables. However, they are at their most powerful when they answer questions of deep practical and theoretical import. One method that has the potential to address such questions in family science is factor mixture modeling (FMM). Typical factor models examine unobservable parts of family life, providing information about their structure and function. FMM extends this by identifying how the underlying factor structures may vary in systematic ways. Furthermore, hypotheses regarding predictors and outcomes of these structures can be tested.

Because detailed statistical elaborations of FMMs can be found elsewhere (Lubke & Muthén, 2005; McLachlan & Peel, 2000), we do not present such in-depth information here. Instead, we explore the essential concepts of FMM and provide an illustrative example. Central to this example is our description of how FMMs allow for testing foundational hypotheses of family research-hypotheses that have often been overlooked. We suggest FMM can be a useful tool for identifying the degree of shared reality in families as well as modeling its predictors and outcomes.

FINITE MIXTURE MODELS

The use of finite mixture models (see McLachlan & Peel, 2000) has dramatically increased over the last few years. In general, the purpose of these models is to test whether a sample is a "mixture" of several populations, each with its own unique characteristics. Using these models, researchers identify groups of persons within a sample who are categorically different from one meaning of the underlying factor is similar or differs across classes.

FINITE MIXTURE MODELS

The use of finite mixturemodels (seeMcLachlan & Peel, 2000) has dramatically increased over the last few years. In general, the purpose of these models is to test whether a sample is a "mixture" of several populations, each with its own unique characteristics. Using these models, researchers identify groups of persons within a sample who are categorically different from one another. This is often referred to as a taxonomic approach to data analysis; that is, rather than assessing how individuals differ along a continuous range, finite mixturemodels examine a given population and identify groups that have categorically different model parameters.

Mixture regression (Wedel & DeSarbo, 2002) groups persons on the basis of variations in regression coefficients. For instance, in a multiple regression, Dyer, Pleck, and McBride (2012) used mixture regression to identify classes of persons who varied on the coefficient that represented the relationship between fathers' incarceration and child externalizing problems. For one class, the coefficient was nonsignificant, for two classes the coefficient was positive and significant, and for the fourth class the coefficient was negative and significant.

In the examples given above, general hypotheses were initially made about the existence of various classes. However, the classes were not defined a priori, as is done in multiple-group analyses. In multiple-group models, model parameters are identified for each of the predetermined groups. Differences across groups are then examined. In contrast, mixture modeling identifies latent groups that are not observed a priori but are identified on the basis of differences of certain model parameters (e.g., growth parameters, item means, regression parameters). These types of models have been referred to as person centered in that they focus on grouping persons with similar characteristics.

This is also analogous to the differences between mixture models and random effects models. In random effectsmodels, model parameters can vary across predefined levels (e.g., within and between person levels). In contrast, the mixture models identify a new, previously unidentified level on which individuals in the population differ (see Vermunt & Van Dijk, 2001, for additional details on the relationship between mixture and random effects models). …

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