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Schedule:
Wednesday, May 28, 2014
Columbia Foyer (Hyatt Regency Washington)
* noted as presenting author
A primary reason for using regression mixture models is to understand the causes of heterogeneous effects. This is typically accomplished by including predictors of the latent class which represent heterogeneity in effects. However, there is debate in the literature about how and when to include covariates in these models. The current study uses simulations to investigate three different approaches to including predictors of latent classes: 1) including the covariate in a second model after identifying differential effects in an unconditional regression mixture; 2) including the effect of the covariate on the latent class only; and 3) including both direct and indirect effects of the covariate.
Data was generated under nine different realistic scenarios varying the direct and indirect effects of the covariate as well as the correlation of the covariate with the primary independent variable for a two-class model. Analyses were run for each of the three analytic approaches described above. Results indicate that including predictors of latent classes in the model as well as the direct effects on outcomes and the correlation with the primary exogenous variable results in no bias. This approach is not feasible, however, when many predictors of differential effects are included. Analyses that excluded the direct effect of the covariate when the path was non-zero lead to overestimation of the number of classes, as well as significant bias in parameter estimates which caused the beta weights to appear closer in value. In the most extreme simulation setting, excluding this effect caused differences between classes in the regression weights (differential effects) to go away completely. In contrast, excluding the covariate from the model entirely did not lead to class enumeration issues even in the worst case scenario. However, when the covariate relates to both the predictor and the outcome, bias was observed in the parameter estimates which were still not as severe as the bias in parameter estimates for the model excluding only the direct effect.
These results suggest a promising approach for understanding the driving forces of heterogeneity identified in regression mixtures: first, estimate the model without covariates to determine the number and nature of differential effects; second, include covariates to understand the variables responsible for differential effects. Future research will include a replication study of these misspecifications, in addition to the inclusion of scenarios with weaker correlations between the covariate and the predictor/outcome.