767 research outputs found
Gaussian Process Structural Equation Models with Latent Variables
In a variety of disciplines such as social sciences, psychology, medicine and
economics, the recorded data are considered to be noisy measurements of latent
variables connected by some causal structure. This corresponds to a family of
graphical models known as the structural equation model with latent variables.
While linear non-Gaussian variants have been well-studied, inference in
nonparametric structural equation models is still underdeveloped. We introduce
a sparse Gaussian process parameterization that defines a non-linear structure
connecting latent variables, unlike common formulations of Gaussian process
latent variable models. The sparse parameterization is given a full Bayesian
treatment without compromising Markov chain Monte Carlo efficiency. We compare
the stability of the sampling procedure and the predictive ability of the model
against the current practice.Comment: 12 pages, 6 figure
Identifying Causal Effects Using Instrumental Variables from the Auxiliary Population
Instrumental variable approaches have gained popularity for estimating causal
effects in the presence of unmeasured confounding. However, the availability of
instrumental variables in the primary population is often challenged due to
stringent and untestable assumptions. This paper presents a novel method to
identify and estimate causal effects in the primary population by utilizing
instrumental variables from the auxiliary population, incorporating a
structural equation model, even in scenarios with nonlinear treatment effects.
Our approach involves using two datasets: one from the primary population with
joint observations of treatment and outcome, and another from the auxiliary
population providing information about the instrument and treatment. Our
strategy differs from most existing methods by not depending on the
simultaneous measurements of instrument and outcome. The central idea for
identifying causal effects is to establish a valid substitute through the
auxiliary population, addressing unmeasured confounding. This is achieved by
developing a control function and projecting it onto the function space spanned
by the treatment variable. We then propose a three-step estimator for
estimating causal effects and derive its asymptotic results. We illustrate the
proposed estimator through simulation studies, and the results demonstrate
favorable performance. We also conduct a real data analysis to evaluate the
causal effect between vitamin D status and BMI.Comment: 19 page
Resurgence of the Endogeneity-Backed Instrumental Variable Methods
This paper investigates the nature of the IV method for tackling endogeneity. By tracing the rise and fall of the method in macroeconometrics and its subsequent revival in microeconometrics, it pins the method down to an implicit model respecification device—breaking the circular causality of simultaneous relations by redefining it as an asymmetric one conditioning on a non-optimal conditional expectation of the assumed endogenous explanatory variable, thus rejecting that variable as a valid conditional variable. The revealed nature explains why the IV route is popular for models where endogeneity is superfluous whereas measurement errors are of the key concern
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