  Data augmentation (DA) turns seemingly intractable computational problems
into simple ones by augmenting latent missing data. In addition to
computational simplicity, it is now well-established that DA equipped with a
deterministic transformation can improve the convergence speed of iterative
algorithms such as an EM algorithm or Gibbs sampler. In this article, we
outline a framework for the transformation-based DA, which we call data
transforming augmentation (DTA), allowing augmented data to be a deterministic
function of latent and observed data, and unknown parameters. Under this
framework, we investigate a novel DTA scheme that turns heteroscedastic models
into homoscedastic ones to take advantage of simpler computations typically
available in homoscedastic cases. Applying this DTA scheme to fitting linear
mixed models, we demonstrate simpler computations and faster convergence rates
of resulting iterative algorithms, compared with those under a
non-transformation-based DA scheme. We also fit a Beta-Binomial model using the
proposed DTA scheme, which enables sampling approximate marginal posterior
distributions that are available only under homoscedasticity. An R package,
Rdta, is publicly available at CRAN.
