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

Central banks and information provided to the private sector

This paper examines the information provided to the private sector by central anks. By using the principal component analysis, we investigated the variance of the procedural rules followed by nine major central banks about information reatments. We investigate problems related to the information coming from the entral banks by focusing on the quantity and quality perspectives and highlight the methodological complexity of the investigation. We find that a synthetic uantitative index of transparency is not enough to represent the phenomenon ince it can result misleading in understanding the behavior of institutionally different central banks associated with the same index values.Central bank transparency, principal components, monetary policy.

Central Banks and Information Provided to the Private Sector

This paper examines the information provided to the private sector by central banks. By using the principal component analysis, we investigated the variance of the procedural rules followed by nine major central banks about information treatments. We investigate problems related to the information coming from the central banks by focusing on the quantity and quality perspectives and highlight the methodological complexity of the investigation. We find that a synthetic quantitative index of transparency is not enough to represent the phenomenon since it can result misleading in understanding the behavior of institutionally different central banks associated with the same index values.Central bank transparency, principal components, monetary policy

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