Improving inference of Gaussian mixtures using auxiliary variables

Authors: 
Andrea Mercatanti, Fan Li, Fabrizia Mealli
Bank of Italy, Duke University, University of Florence

May 7 2014

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting
back is often beneficial. This article rigorously investigates this perspective in the context of
finite mixture models, namely how to improve inference for mixture models by using auxiliary
variables. Despite the large literature in mixture models and several empirical examples, there
is no previous work that gives general theoretical justification for including auxiliary variables
in mixture models, even for special cases. We provide a theoretical basis for comparing inference
for mixture multivariate models with the corresponding inference for marginal univariate
mixture models. Analytical results for several special cases are established. We show that the
probability of correctly allocating mixture memberships and the information number for the
means of the primary outcome in a bivariate model with two Gaussian mixtures are generally
larger than those in each univariate model. Simulations under a range of scenarios, including
misspecified models, are conducted to examine the improvement. The method is illustrated by
two real applications in ecology and causal inference.

Keywords: 

bivariate, Hessian, information matrix, mixture model, score

Manuscript: 

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