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Collapsibility of Graphical CG‐Regression Models
Author(s) -
Didelez Vanessa,
Edwards David
Publication year - 2004
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2004.00405.x
Subject(s) - univariate , mathematics , graphical model , conditional independence , multivariate statistics , regression , statistics , property (philosophy) , graph , regression analysis , conditional expectation , independence (probability theory) , factor regression model , econometrics , bayesian multivariate linear regression , combinatorics , proper linear model , philosophy , epistemology
. CG‐regressions are multivariate regression models for mixed continuous and discrete responses that result from conditioning in the class of conditional Gaussian (CG) models. Their conditional independence structure can be read off a marked graph. The property of collapsibility, in this context, means that the multivariate CG‐regression can be decomposed into lower dimensional regressions that are still CG and are consistent with the corresponding subgraphs. We derive conditions for this property that can easily be checked on the graph, and indicate computational advantages of this kind of collapsibility. Further, a simple graphical condition is given for checking whether a decomposition into univariate regressions is possible.