4,617 research outputs found
On Modeling and Estimation for the Relative Risk and Risk Difference
A common problem in formulating models for the relative risk and risk
difference is the variation dependence between these parameters and the
baseline risk, which is a nuisance model. We address this problem by proposing
the conditional log odds-product as a preferred nuisance model. This novel
nuisance model facilitates maximum-likelihood estimation, but also permits
doubly-robust estimation for the parameters of interest. Our approach is
illustrated via simulations and a data analysis.Comment: To appear in Journal of the American Statistical Association: Theory
and Method
Congenial Causal Inference with Binary Structural Nested Mean Models
Structural nested mean models (SNMMs) are among the fundamental tools for
inferring causal effects of time-dependent exposures from longitudinal studies.
With binary outcomes, however, current methods for estimating multiplicative
and additive SNMM parameters suffer from variation dependence between the
causal SNMM parameters and the non-causal nuisance parameters. Estimating
methods for logistic SNMMs do not suffer from this dependence. Unfortunately,
in contrast with the multiplicative and additive models, unbiased estimation of
the causal parameters of a logistic SNMM rely on additional modeling
assumptions even when the treatment probabilities are known. These difficulties
have hindered the uptake of SNMMs in epidemiological practice, where binary
outcomes are common. We solve the variation dependence problem for the binary
multiplicative SNMM by a reparametrization of the non-causal nuisance
parameters. Our novel nuisance parameters are variation independent of the
causal parameters, and hence allows the fitting of a multiplicative SNMM by
unconstrained maximum likelihood. It also allows one to construct true (i.e.
congenial) doubly robust estimators of the causal parameters. Along the way, we
prove that an additive SNMM with binary outcomes does not admit a variation
independent parametrization, thus explaining why we restrict ourselves to the
multiplicative SNMM
Nested Markov Properties for Acyclic Directed Mixed Graphs
Directed acyclic graph (DAG) models may be characterized in at least four
different ways: via a factorization, the d-separation criterion, the
moralization criterion, and the local Markov property. As pointed out by Robins
(1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of
DAG models also imply equality constraints that are not conditional
independences. The well-known `Verma constraint' is an example. Constraints of
this type were used for testing edges (Shpitser et al., 2009), and an efficient
marginalization scheme via variable elimination (Shpitser et al., 2011).
We show that equality constraints like the `Verma constraint' can be viewed
as conditional independences in kernel objects obtained from joint
distributions via a fixing operation that generalizes conditioning and
marginalization. We use these constraints to define, via Markov properties and
a factorization, a graphical model associated with acyclic directed mixed
graphs (ADMGs). We show that marginal distributions of DAG models lie in this
model, prove that a characterization of these constraints given in (Tian and
Pearl, 2002b) gives an alternative definition of the model, and finally show
that the fixing operation we used to define the model can be used to give a
particularly simple characterization of identifiable causal effects in hidden
variable graphical causal models.Comment: 67 pages (not including appendix and references), 8 figure
Sparse Nested Markov models with Log-linear Parameters
Hidden variables are ubiquitous in practical data analysis, and therefore
modeling marginal densities and doing inference with the resulting models is an
important problem in statistics, machine learning, and causal inference.
Recently, a new type of graphical model, called the nested Markov model, was
developed which captures equality constraints found in marginals of directed
acyclic graph (DAG) models. Some of these constraints, such as the so called
`Verma constraint', strictly generalize conditional independence. To make
modeling and inference with nested Markov models practical, it is necessary to
limit the number of parameters in the model, while still correctly capturing
the constraints in the marginal of a DAG model. Placing such limits is similar
in spirit to sparsity methods for undirected graphical models, and regression
models. In this paper, we give a log-linear parameterization which allows
sparse modeling with nested Markov models. We illustrate the advantages of this
parameterization with a simulation study.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Economic Feasibility of Commercial Algae Oil Production in the United States
A Monte Carlo simulation model was constructed to analyze the economic feasibility of growing algae as a renewable fuel source. Increasing growth rates, pond water depth, oil content, and facility size are important for ensuring the economic viability of a commercial algae facility.algae, renewable, fuel, feedstock, microalgae, Agribusiness, Agricultural and Food Policy, Crop Production/Industries, Production Economics, Resource /Energy Economics and Policy, Risk and Uncertainty,
Potential Outcome and Decision Theoretic Foundations for Statistical Causality
In a recent paper published in the Journal of Causal Inference, Philip Dawid
has described a graphical causal model based on decision diagrams. This article
describes how single-world intervention graphs (SWIGs) relate to these
diagrams. In this way, a correspondence is established between Dawid's approach
and those based on potential outcomes such as Robins' Finest Fully Randomized
Causally Interpreted Structured Tree Graphs. In more detail, a reformulation of
Dawid's theory is given that is essentially equivalent to his proposal and
isomorphic to SWIGs.Comment: 54 pages, 7 Figures, 3 Tables. Some more minor edits and correction
Assumptions and Bounds in the Instrumental Variable Model
In this note we give proofs for results relating to the Instrumental Variable
(IV) model with binary response and binary treatment , but with an
instrument with states. These results were originally stated in
Richardson & Robins (2014), "ACE Bounds; SEMS with Equilibrium Conditions,"
arXiv:1410.0470.Comment: 27 pages, 1 figure, 1 table. Proofs of Theorems 1 and 2 stated in
Richardson and Robins (2014) [arXiv:1410.0470]. v2 improves the writing in a
few place
Effect of Concussion on Clinically Measured Reaction Time in 9 NCAA Division I Collegiate Athletes: A Preliminary Study
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147005/1/pmr2212.pd
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