  For the estimation of cumulative link models for ordinal data, the
bias-reducing adjusted score equations in \citet{firth:93} are obtained, whose
solution ensures an estimator with smaller asymptotic bias than the maximum
likelihood estimator. Their form suggests a parameter-dependent adjustment of
the multinomial counts, which, in turn suggests the solution of the adjusted
score equations through iterated maximum likelihood fits on adjusted counts,
greatly facilitating implementation. Like the maximum likelihood estimator, the
reduced-bias estimator is found to respect the invariance properties that make
cumulative link models a good choice for the analysis of categorical data. Its
additional finiteness and optimal frequentist properties, along with the
adequate behaviour of related asymptotic inferential procedures make the
reduced-bias estimator attractive as a default choice for practical
applications. Furthermore, the proposed estimator enjoys certain shrinkage
properties that are defensible from an experimental point of view relating to
the nature of ordinal data.
