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 Title
 Estimation for DyadicDependent Exponential Random Graph Models
 Creator
 Yang, Xiaolin, Rinaldo, Alessandro, Fienberg, Stephen E.
 Date
 2014, 20140430
 Description

Graphs are the primary mathematical representation for networks, with nodes or vertices corresponding to units (e.g., individuals) and edges...
Show moreGraphs are the primary mathematical representation for networks, with nodes or vertices corresponding to units (e.g., individuals) and edges corresponding to relationships. Exponential Random Graph Models (ERGMs) are widely used for describing network data because of their simple structure as an exponential function of a sum of parameters multiplied by their corresponding sufficient statistics. As with other exponential family settings the key computational difficulty is determining the normalizing constant for the likelihood function, a quantity that depends only on the data. In ERGMs for network data, the normalizing constant in the model often makes the parameter estimation intractable for large graphs, when the model involves dependence among dyads in the graph. One way to deal with this problem is to approximate the likelihood function by something tractable, e.g., by using the method of pseudolikelihood estimation suggested in the early literature. In this paper, we describe the family of ERGMs and explain the increasing complexity that arises from imposing different edge dependence and homogeneous parameter assumptions. We then compare maximum likelihood (ML) and maximum pseudolikelihood (MPL) estimation schemes with respect to existence and related degeneracy properties for ERGMs involving dependencies among dyads.
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 Journal of Algebraic Statistics
 Title
 A Family of Quasisymmetry Models
 Creator
 Kateri, Maria, Mohammadi, Fatemeh, Sturmfels, Bernd
 Date
 2015, 20150611
 Description

We present a oneparameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its...
Show moreWe present a oneparameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated with graphs. Our discussion of the statistical issues centers around maximum likelihood estimation.
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 Journal of Algebraic Statistics
 Title
 Maximum Likelihood Estimation of the Latent Class Model through Model Boundary Decomposition, Special Volume in honor of memory of S.E.Fienberg
 Creator
 Elizabeth S. Allman, BaĆ±os Cervantes, Hector, Evans, Robin, Hosten, Serkan, Kubjas, Kaie, Lemke, Daniel, Rhodes, John, Zwiernik, Piotr
 Date
 2019, 20190412
 Description

The ExpectationMaximization (EM) algorithm is routinely used for maximum likelihood estimation in latent class analysis. However, the EM...
Show moreThe ExpectationMaximization (EM) algorithm is routinely used for maximum likelihood estimation in latent class analysis. However, the EM algorithm comes with no global guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata and performance of the EM algorithm. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.
Show less  Collection
 Journal of Algebraic Statistics