Assessing the Accuracy of Bootstrap-Based Standard Errors in Regression Models with Unobserved Heterogeneity

When the data at hand are suspected to stem from several latent subpopulations, Statisticians commonly speak of “unobserved heterogeneity”. While the presence and importance of this phenomenon is commonly acknowledged, there is relatively little guidance on how to carry out correct inferences under unobserved heterogeneities, even in relatively simple scenarios such as the linear regression model. In this work, bootstrap algorithms for the computation of standard errors are investigated in the context of a mixture-based regression approach which accounts for the clustered nature of the data. Of interest is both the accuracy of the standard errors (evidenced by confidence interval coverage rates) and the relative reduction in standard errors achieved in comparison to a naïve linear model fit. Simulations and a real data example are provided.