21,757 research outputs found
Robust Modeling Using Non-Elliptically Contoured Multivariate t Distributions
Models based on multivariate t distributions are widely applied to analyze
data with heavy tails. However, all the marginal distributions of the
multivariate t distributions are restricted to have the same degrees of
freedom, making these models unable to describe different marginal
heavy-tailedness. We generalize the traditional multivariate t distributions to
non-elliptically contoured multivariate t distributions, allowing for different
marginal degrees of freedom. We apply the non-elliptically contoured
multivariate t distributions to three widely-used models: the Heckman selection
model with different degrees of freedom for selection and outcome equations,
the multivariate Robit model with different degrees of freedom for marginal
responses, and the linear mixed-effects model with different degrees of freedom
for random effects and within-subject errors. Based on the Normal mixture
representation of our t distribution, we propose efficient Bayesian inferential
procedures for the model parameters based on data augmentation and parameter
expansion. We show via simulation studies and real examples that the
conclusions are sensitive to the existence of different marginal
heavy-tailedness
Combining multiple observational data sources to estimate causal effects
The era of big data has witnessed an increasing availability of multiple data
sources for statistical analyses. We consider estimation of causal effects
combining big main data with unmeasured confounders and smaller validation data
with supplementary information on these confounders. Under the unconfoundedness
assumption with completely observed confounders, the smaller validation data
allow for constructing consistent estimators for causal effects, but the big
main data can only give error-prone estimators in general. However, by
leveraging the information in the big main data in a principled way, we can
improve the estimation efficiencies yet preserve the consistencies of the
initial estimators based solely on the validation data. Our framework applies
to asymptotically normal estimators, including the commonly-used regression
imputation, weighting, and matching estimators, and does not require a correct
specification of the model relating the unmeasured confounders to the observed
variables. We also propose appropriate bootstrap procedures, which makes our
method straightforward to implement using software routines for existing
estimators
To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias
"M-Bias," as it is called in the epidemiologic literature, is the bias
introduced by conditioning on a pretreatment covariate due to a particular
"M-Structure" between two latent factors, an observed treatment, an outcome,
and a "collider." This potential source of bias, which can occur even when the
treatment and the outcome are not confounded, has been a source of considerable
controversy. We here present formulae for identifying under which circumstances
biases are inflated or reduced. In particular, we show that the magnitude of
M-Bias in linear structural equation models tends to be relatively small
compared to confounding bias, suggesting that it is generally not a serious
concern in many applied settings. These theoretical results are consistent with
recent empirical findings from simulation studies. We also generalize the
M-Bias setting (1) to allow for the correlation between the latent factors to
be nonzero, and (2) to allow for the collider to be a confounder between the
treatment and the outcome. These results demonstrate that mild deviations from
the M-Structure tend to increase confounding bias more rapidly than M-Bias,
suggesting that choosing to condition on any given covariate is generally the
superior choice. As an application, we re-examine a controversial example
between Professors Donald Rubin and Judea Pearl.Comment: Journal of Causal Inference 201
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