It is well-known that a conditional independence statement for discrete variables is equivalent to constraining to zero a suitable set of log–linear interactions. In this paper we show that this is also equivalent to zero constraints on suitable sets of marginal log–linear interactions, that can be formulated within a class of smooth marginal log–linear models. This result allows much more flexibility than known until now in combining several conditional independencies into a smooth marginal model. This result is the basis for a procedure that can search for such a marginal parameterization, so that, if one exists, the model is smooth.
Marginal parameterizations of discrete models defined by a set of conditional independencies. J. of Multivariate Analysis, doi:10.1016/j.jmva.2010.07.001 / A.Forcina; M.Lupparelli; G.M.Marchetti. - In: JOURNAL OF MULTIVARIATE ANALYSIS. - ISSN 0047-259X. - STAMPA. - 101:(2010), pp. 2519-2527. [10.1016/j.jmva.2010.07.001]
Marginal parameterizations of discrete models defined by a set of conditional independencies. J. of Multivariate Analysis, doi:10.1016/j.jmva.2010.07.001.
M. Lupparelli;MARCHETTI, GIOVANNI MARIA
2010
Abstract
It is well-known that a conditional independence statement for discrete variables is equivalent to constraining to zero a suitable set of log–linear interactions. In this paper we show that this is also equivalent to zero constraints on suitable sets of marginal log–linear interactions, that can be formulated within a class of smooth marginal log–linear models. This result allows much more flexibility than known until now in combining several conditional independencies into a smooth marginal model. This result is the basis for a procedure that can search for such a marginal parameterization, so that, if one exists, the model is smooth.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.