  Bivariate observations of binary and ordinal data arise frequently and
require a bivariate modelling approach in cases where one is interested in
aspects of the marginal distributions as separate outcomes along with the
association between the two. We consider methods for constructing such
bivariate models with logistic marginals and propose a model based on the
Ali-Mikhail-Haq bivariate logistic distribution. We motivate the model as an
extension of that based on the Gumbel type 2 distribution as considered by
other authors and as a bivariate extension of the logistic distribution which
preserves certain natural characteristics. Basic properties of the obtained
model are studied and the proposed methods are illustrated through analysis of
two data sets, one describing the trekking habits of Norwegian hikers, the
other stemming from a cognitive experiment of visual recognition and awareness.
