11,590 research outputs found
Network Psychometrics
This chapter provides a general introduction of network modeling in
psychometrics. The chapter starts with an introduction to the statistical model
formulation of pairwise Markov random fields (PMRF), followed by an
introduction of the PMRF suitable for binary data: the Ising model. The Ising
model is a model used in ferromagnetism to explain phase transitions in a field
of particles. Following the description of the Ising model in statistical
physics, the chapter continues to show that the Ising model is closely related
to models used in psychometrics. The Ising model can be shown to be equivalent
to certain kinds of logistic regression models, loglinear models and
multi-dimensional item response theory (MIRT) models. The equivalence between
the Ising model and the MIRT model puts standard psychometrics in a new light
and leads to a strikingly different interpretation of well-known latent
variable models. The chapter gives an overview of methods that can be used to
estimate the Ising model, and concludes with a discussion on the interpretation
of latent variables given the equivalence between the Ising model and MIRT.Comment: In Irwing, P., Hughes, D., and Booth, T. (2018). The Wiley Handbook
of Psychometric Testing, 2 Volume Set: A Multidisciplinary Reference on
Survey, Scale and Test Development. New York: Wile
An Importance Sampling Algorithm for the Ising Model with Strong Couplings
We consider the problem of estimating the partition function of the
ferromagnetic Ising model in a consistent external magnetic field. The
estimation is done via importance sampling in the dual of the Forney factor
graph representing the model. Emphasis is on models at low temperature
(corresponding to models with strong couplings) and on models with a mixture of
strong and weak coupling parameters.Comment: Proc. 2016 Int. Zurich Seminar on Communications (IZS), Zurich,
Switzerland, March 2-4, 2016, pp. 180-18
The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods
The inverse Ising problem consists in inferring the coupling constants of an
Ising model given the correlation matrix. The fastest methods for solving this
problem are based on mean-field approximations, but which one performs better
in the general case is still not completely clear. In the first part of this
work, I summarize the formulas for several mean- field approximations and I
derive new analytical expressions for the Bethe approximation, which allow to
solve the inverse Ising problem without running the Susceptibility Propagation
algorithm (thus avoiding the lack of convergence). In the second part, I
compare the accuracy of different mean field approximations on several models
(diluted ferromagnets and spin glasses) defined on random graphs and regular
lattices, showing which one is in general more effective. A simple improvement
over these approximations is proposed. Also a fundamental limitation is found
in using methods based on TAP and Bethe approximations in presence of an
external field.Comment: v3: strongly revised version with new methods and results, 25 pages,
21 figure
High-dimensional Ising model selection using -regularized logistic regression
We consider the problem of estimating the graph associated with a binary
Ising Markov random field. We describe a method based on -regularized
logistic regression, in which the neighborhood of any given node is estimated
by performing logistic regression subject to an -constraint. The method
is analyzed under high-dimensional scaling in which both the number of nodes
and maximum neighborhood size are allowed to grow as a function of the
number of observations . Our main results provide sufficient conditions on
the triple and the model parameters for the method to succeed in
consistently estimating the neighborhood of every node in the graph
simultaneously. With coherence conditions imposed on the population Fisher
information matrix, we prove that consistent neighborhood selection can be
obtained for sample sizes with exponentially decaying
error. When these same conditions are imposed directly on the sample matrices,
we show that a reduced sample size of suffices for the
method to estimate neighborhoods consistently. Although this paper focuses on
the binary graphical models, we indicate how a generalization of the method of
the paper would apply to general discrete Markov random fields.Comment: Published in at http://dx.doi.org/10.1214/09-AOS691 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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