Identifying Model-Implied Instrumental Variables in Structural Equation Models using Graphical Criteria
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2019-08-05
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en
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Abstract
Structural Equation Models (SEMs) are widely used in observational studies
in fields like econometrics, psychology, and education research. A crucial
step in SE modeling is to fit the model to the data. This is most commonly
done using the Maximum Likelihood (ML) estimator, which is an iterative,
global estimator that fits all model parameters simultaneously. This can
sometimes lead to practical issues in terms of computational costs, and
non-convergence when the model is not identifiable. In cases when some
parts of the model are misspecified, global estimation propagates the bias
to other parts of the model. Instrumental Variable (IV) estimation is a
non-iterative, local technique that addresses these practical issues of ML. But
to estimate any parameter using the IV estimator, IVs need to be identified
for it. Previously, algebraic algorithms have been proposed to find Model
Implied Instrumental Variables (MIIVs) from the model structure but these
are restricted to models of a certain form and are computationally ine cient.
In the field of Causal Bayesian Networks, graphical criteria for identifying
IVs have been proposed. Here, we show how graphical IV criteria can
be leveraged to identify MIIVs. This approach is computationally more
e cient and finds more IVs by extending the search to conditional IVs, which
allows us to (1) identify models much faster than before, rendering the
MIIV approach feasible for much larger models; (2) identify more models
than the algebraic MIIV approach; and (3) identify parameters with higher
precision. Our method is implemented in the pgmpy package in python.
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Faculteit der Sociale Wetenschappen