Independencies Induced from a Graphical Markov Model After Marginalization and Conditioning: The R Package ggm

We describe some functions in the R package ggm to derive from a given Markov model, represented by a directed acyclic graph, different types of graphs induced after marginalizing over and conditioning on some of the variables. The package has a few basic functions that find the essential graph, the induced concentration and covariance graphs, and several types of chain graphs implied by the directed acyclic graph (DAG) after grouping and reordering the variables. These functions can be useful to explore the impact of latent variables or of selection effects on a chosen data generating model.

Matrix representations and independencies in directed acyclic graphs

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.Comment: Published in at http://dx.doi.org/10.1214/08-AOS594 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chain graph models of multivariate regression type for categorical data

We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to those of a chain graph model recently defined in the literature. Next we provide a parametrization based on a sequence of generalized linear models with a multivariate logistic link function that captures all independence constraints in any chain graph model of this kind.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ300 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Star graphs induce tetrad correlations: for Gaussian as well as for binary variables

Tetrad correlations were obtained historically for Gaussian distributions when tasks are designed to measure an ability or attitude so that a single unobserved variable may generate the observed, linearly increasing dependences among the tasks. We connect such generating processes to a particular type of directed graph, the star graph, and to the notion of traceable regressions. Tetrad correlation conditions for the existence of a single latent variable are derived. These are needed for positive dependences not only in joint Gaussian but also in joint binary distributions. Three applications with binary items are given.Comment: 21 pages, 2 figures, 5 table

Independencies Induced from a Graphical Markov Model After Marginalization and Conditioning: The R Package ggm

We describe some functions in the R package ggm to derive from a given Markov model, represented by a directed acyclic graph, different types of graphs induced after marginalizing over and conditioning on some of the variables. The package has a few basic functions that find the essential graph, the induced concentration and covariance graphs, and several types of chain graphs implied by the directed acyclic graph (DAG) after grouping and reordering the variables. These functions can be useful to explore the impact of latent variables or of selection effects on a chosen data generating model

The Brown and Payne model of voter transition revisited

Abstract We attempt a critical assessment of the assumptions, in terms of voting behavior, underlying the Goodman (1953) and the Brown and Payne (1986) models of voting transitions. We argue that the first model is only a slightly simpler version of the second which, however, is fitted in a rather inefficient way. We also provide a critical assessment of the approach inspired b

Endometrial Cancer Risk Prediction According to Indication of Diagnostic Hysteroscopy in Post-Menopausal Women

We conducted a prospective observational study investigating the clinical relevance of endometrial thickness (ET) and abnormal uterine bleeding (AUB) on endometrial cancer (EC) risk in a cohort of postmenopausal patients undergoing diagnostic hysteroscopy and endometrial biopsy. Patients were divided into two groups according to the indication of diagnostic hysteroscopy: ET_Group (asymptomatic patients with endometrial thickness 4 mm) and AUB_Group (patients with a history of abnormal uterine bleeding). We further divided the AUB_Group into two subgroups based on endometrial thickness (AUB_Subgroup1: ET < 4 mm; AUB_Subgroup2: ET 4 mm). The primary outcome was the risk of endometrial cancer and atypical hyperplasia according to the indications of diagnostic hysteroscopy (AUB, ET 4 mm or both). The secondary outcome was to determine the best cut-o value of endometrial thickness to predict endometrial cancer in asymptomatic postmenopausal women. The prevalence of endometrial cancer and atypical hyperplasia in AUB_Group and ET_Group was 21% and 6.7% respectively. As well as for EC alone, higher prevalence of both conditions was observed in AUB_Subgroup2 (29.3%) in comparison to AUB_Subgroup1 (10.6%; p < 0.001). In asymptomatic patients the cut-o of endometrial thickness that showed the best sensitivity and specificity to diagnose endometrial cancer (100% and 80% respectively) was 11 mm (AUC of 91.4%; Exp : 1067; CI 95%). In conclusion, considering the high risk of neoplasia, diagnostic hysteroscopy with endometrial biopsy should be mandatory in cases of abnormal uterine bleeding in postmenopausal patients. Moreover, we want to emphasize the need for further evidence stating the clinical relevance of endometrial thickness value in asymptomatic patients and the impact of individual risk factors on endometrial cancer development