STA 290 Seminar Series
DATE: Thursday, April 27th 2017, 4:10pm
LOCATION: MSB 1147, Colloquium Room. Refreshments at 3:30pm in MSB 4110
SPEAKER: Avi Feller, University of California, Berkeley
TITLE: “Principal stratification in the Twilight Zone: Weakly separated components in finite mixture models”
ABSTRACT: Principal stratification is a widely used framework for addressing post-randomization complications in a principled way. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to estimate these quantities. Unfortunately, standard estimators of the mixture parameters, like the MLE, are known to exhibit pathological behavior. We study this behavior in a simple but fundamental example: a two-component Gaussian mixture model in which only the component means are unknown. Even though the MLE is asymptotically efficient, we show through extensive simulations that the MLE has undesirable properties in practice. In particular, when mixture components are only weakly separated, we observe "pile up", in which the MLE estimates the component means to be equal, even though they are not. We first show that parametric convergence can break down in certain situations. We then derive a simple moment estimator that displays key features of the MLE and use this estimator to approximate the finite sample behavior of the MLE. Finally, we propose a method to generate valid confidence sets via inverting a sequence of tests, and explore the case in which the component variances are unknown. Throughout, we illustrate the main ideas through an application of principal stratification to the evaluation of JOBS II, a job training program.