Abstract
In this paper we show how complete hierarchical multinomial marginal (HMM) models for categorical variables can be defined, estimated and tested using the R package hmmm. Models involving equality and inequality constraints on marginal parameters are needed to define hypotheses of conditional independence, stochastic dominance or notions of positive dependence, or when the parameters are allowed to depend on covariates. The hmmm package also serves the need of estimating and testing HMM models under equality and inequality constraints on marginal interactions.
Highlights
Marginal models are defined for categorical variables by imposing restrictions on marginal distributions of contingency tables, (Agresti 2013, Chapter 12)
A complete hierarchical multinomial marginal (HMM) model is specified by an ordered set of marginal distributions and a set of interactions defined within different marginal distributions according to the rules of hierarchy and completeness, see Bergsma and Rudas (2002) and Bartolucci, Colombi, and Forcina (2007)
In the Bergsma and Rudas models the components of η are log-linear parameters defined in marginal distributions, while in the Bartolucci et al (2007) parameterization all the previous logits can be used and η is called a vector of generalized marginal interactions which are more meaningful when the variables have an ordinal nature
Summary
Marginal models are defined for categorical variables by imposing restrictions on marginal distributions of contingency tables, (Agresti 2013, Chapter 12). We developed a new package hmmm for the R statistical programming environment (R Core Team 2014) for estimating and testing HMM models with equality and inequality conhmmm: Hierarchical Multinomial Marginal Models in R straints on marginal parameters. The marginal models (Bergsma and Rudas 2002) are HMM models where the interactions of log-linear type are defined in different marginal distributions. Bartolucci et al (2007) proposed an extension of the Bergsma and Rudas HMM models involving more general types of interactions, while multivariate logistic models (Glonek and McCullagh 1995) are HMM models which use all the marginal distributions and the parameters are the highest order interactions that can be defined within every marginal distribution.
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