Open AccessJournal Article
An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints
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In this article, the authors extend Bergsma and Rudas' hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continu- ation type which may be more suitable with ordinal data.Abstract:
We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continu- ation type which may be more suitable with ordinal data. We introduce a general definition of marginal interaction parameters and show that this parameterization constitutes a link function so that linear models defined by equality and inequality constraints may be fitted and tested by extending the methods of Colombi and Forcina (2001). Computation and asymptotic properties of maximum likelihood estimators are discussed, and the asymptotic distribution of the likelihood ratio test is derived.read more
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References
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Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Graphical models in R
TL;DR: This paper presents Graphical Models for Complex Stochastic Systems, a meta-modelling framework for graphical models of complex systems that combines Gaussian Graphical models, Mixed Interaction Models, and Log-Linear Models.
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Information and Exponential Families in Statistical Theory
TL;DR: In this article, the information and exponential families in statistical theory were studied. But they did not consider the exponential family in the context of exponential families. And they were not considered in this paper.