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\noindent Statistica Sinica {\bf 17}(2007), 691-711

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\centerline{\large\bf AN EXTENDED CLASS OF MARGINAL LINK FUNCTIONS}
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\centerline{\large\bf FOR MODELLING CONTINGENCY TABLES BY}
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\centerline{\large\bf EQUALITY AND INEQUALITY CONSTRAINTS}
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\author{Francesco Bartolucci$^1$,  Roberto Colombi$^2$ and  Antonio Forcina$^1$}
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\centerline{\it $^1$Universit\`a di Perugia and $^2$Universit\`a di Bergamo} %}
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\begin{quotation}
\noindent {\it Abstract:}
We extend Bergsma and Rudas (2002)'s hierarchical complete
marginal parameterization to allow for logits and higher order
effects of global and continuation type
%FB: invece "type global and continuation"
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,
%FB: inserita virgola
and the asymptotic distribution of the likelihood ratio test is
derived.\par
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\noindent {\it Key words and phrases:}
 Chi-bar-squared distribution,  likelihood inference,
marginal models, one-sided linear hypothesis. \par
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