A Comparison of Categorical and Continuous Latent Variable Models in a Moderation Framework

• In Event: 61.063 - Mixture Modeling in Practice

Abstract

Researchers using scales have a range of analytic models to choose from. Given a set of items, one can fit a series of models, such as confirmatory factor analysis (CFA) which assumes a continuous latent variable, a latent profile analysis (LPA) model which assumes a categorical latent variable, or their hybrid model: a factor mixture model (FMM). CFA and LPA are both subsets of FMM, where CFA is restricted to a one-class model, and LPA restricts all factor loadings to zero (Hallquist & Wright, 2013). This paper expands upon previous research comparing CFA, LPA and FMM models by incorporating the latent variable as a moderator in a structural model. Our goal is to determine if different treatments of the latent variable structure for the same items results in different conclusions in the regression framework.
The latent variable in this study is based on the Social Emotional Health Survey - Secondary (SEHS-S; You et al., 2013) which measures four domains of student social emotional health (α = .860). Social emotional distress (SEDS) is used as the predictor (α = .987; Dowdy, Furlong, Nylund-Gibson, Moore, & Moffa, 2018). A one-item measure of life satisfaction (LS) (1 = dissatisfied with life, 100 = satisfied with life) was included as the distal outcome (N = 10,591 secondary students). To compare fit across models, we used the BIC and AIC (Lubke et al., 2007). To compare within mixture models, we used the BIC and BLRT (Nylund, Asparouhov, & Muthén, 2007). Mixture moderation was done via the BCH method (Nylund-Gibson, Grimm, Quirk, & Furlong, 2014). All models were fit in Mplus (Muthén & Muthén, 1998-2017).
Results
The best fitting model for the CFA was a one-factor model, while the LPA and the FMM both enumerated a four-class model (Table 1). The FMM had the lowest AIC, BIC, and LL, indicating it fit the data best. Thus, social emotional health can best be categorized as four ordered but distinct classes with varying levels of severity across each.
Next, the latent variable for each model was entered into a structural regression model as a moderator between SEDS and LS (see Figure 1). SEHS was a significant moderator in all three models, although the interpretation differed. The factor model found a negative slope increasing in magnitude as emotional health decreased (Figure 2). The LPA and the FMM found that the slope was not significant in the lowest class of social emotional health, steepest in the middle two classes, and less steep in the highest class of emotional health (see Figures 3 and 4).
Significance
Lubke et al., (2007) concluded that when latent classes are ordered, they add no value and should instead be rejected as a viable solution and treated as continuous factor(s). Our research shows that the interpretation may not be as straight forward; ordered classes can result in different conclusions (in comparison to a continuous factor) when the latent variable is incorporated into a regression model.

Authors

• Melissa Gordon Wolf, University of California - Santa Barbara

• Karen L. Nylund-Gibson, University of California - Santa Barbara

• Erin Dowdy, University of California - Santa Barbara

• Michael James Furlong, University of California - Santa Barbara