  Extending generalized estimating equations (GEE) to ordinal response data
requires a conversion of the ordinal response to a vector of binary category
indicators. That leads to a rather complicated association structure, and the
introduction of large matrices when the number of categories and dimension of
the cluster are large. To allow a richer specification of working correlation
assumptions, we adopt the weighted scores method which is essentially an
extension of the GEE approach, since it can also be applied to families that
are not in the GLM class. The weighted scores method stems from the lack of a
theoretically sound methodology for analyzing multivariate discrete data based
only on moments up to second order and it is robust to dependence and nearly as
efficient as maximum likelihood. There is no need to convert the ordinal
response to binary indicators, thus the weight matrices have smaller dimensions
and it is not necessary to guess the correlations of indicator variables for
different categories. We focus on important issues that would interest the data
analyst, such as choice of the structure of the correlation matrix and of
explanatory variables, comparison of results obtained from our methods versus
GEE, and insights provided by our method that would be missed with the GEE
method. Our modelling framework is implemented in the package weightedScores
within the open source statistical environment R.
