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Collapsibility of marginal models for categorical data. (arXiv:1711.00680v2 [math.ST] UPDATED)
来源于:arXiv
We consider marginal log-linear models for parameterizing distributions on
multidimensional contingency tables. These models generalize ordinary
log-linear and multivariate logistic models, besides several others. First, we
obtain some characteristic properties of marginal log-linear parameters. Then
we define collapsibility and strict collapsibility of these parameters in a
general sense. Several necessary and sufficient conditions for collapsibility
and strict collapsibility are derived using the technique of M\"{o}bius
inversion. These include results for an arbitrary set of marginal log-linear
parameters having some common effects. The connections of collapsibility and
strict collapsibility to various forms of independence of the variables are
discussed. Finally, we establish a result on the relationship between
parameters with the same effect but different margins, and use it to
demonstrate smoothness of marginal log-linear models under collapsibility
conditions thereby obtaining 查看全文>>