Variance Explained in Distal Outcome(s) From Mixture Models

• In Event: 61.063 - Mixture Modeling in Practice

Abstract

This paper provides a framework to calculate the variance explained, or ΔR2, in the context of a mixture mediation model. This ΔR2 provides a way to quantify the variance explained in distal outcomes by the addition of a categorical latent mediator (e.g., a latent class variable) above and beyond other variables in the model (e.g., covariates). Mclarnon & O’Neill (2018) provide a modeling context where a covariate (X) and distal (Y) and the latent class variable can be specified to be a mediation model. Currently, it is possible to compute distal outcome differences based on a given fitted model, but there is no framework that directly calculates the added value in predicting the distal outcome from the latent class variable, above and beyond the covariate. Using an applied example that examines depression we illustrate a new method, demonstrate the calculations, provide syntax, and interpret how the method can be used for any mixture model.
To illustrate the method, we use a sample of 1st generation (n = 558) university student Latino/as. Sample characteristics are provided in Table 1. The mediator was the Patient Health Questionnaire (PHQ-8), an 8-item depression inventory (Spitzer, Kroenke & Williams, 1999), the covariates were gender (male=0 and female=1) and Family Cohesion (COH, Calix, 2013), a 9-item instrument that measures emotional bonding between family members, and the distal outcome was Quality of Life (QOL) (Zimmerman et al., 2006), a single-item survey that measures quality of life.
Latent class analysis (LCA) was used for class enumeration of the PHQ-8 and the manual 3-step approach was used for including auxiliary variables in the model (see figure 1). The variance explained in the distal outcome via C was calculated by utilizing a difference in Cox and Snell pseudo R2 ‘s (ΔR2CS). ΔR2CS was calculated by taking the difference of the model 1 R2CS (intercept and regression model) and the model 2 R2CS (intercept and full model) to obtain the ΔR2CS.
Results
The means and standard deviations for QOL, Gender, and COH can be found in Table 2. Results for the PHQ-8 LCA’s indicated a 3-class model (see Table 3). Item probability plots for the LCA (see Figure 2) reflected low, moderate, and high depression classes. Results indicated significance every relationship between the covariates and C and for all comparison of QOL between the classes. The ΔR2CS reflected that the added value of C in the equation was ΔR2CS = .075 suggesting that heterogeneity in depression scores explained 7.5% of the variance in QOL for 1st generation Latino/as. This research is useful for researchers as it provides a context to understand how much the heterogeneity can explain in the outcome variable. Further implications are discussed.

Authors

• Delwin Carter, University of California - Santa Barbara

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