  This study deals with the problem of outliers in ordinal response model,
which is a regression on ordered categorical data as the response variable.
``Outlier" means that the combination of ordered categorical data and its
covariates is heterogeneous compared to other pairs. Although the ordinal
response model is important for data analysis in various fields such as
medicine and social sciences, it is known that the maximum likelihood method
with probit, logit, log-log and complementary log-log link functions, which are
often used, is strongly affected by outliers, and statistical analysts are
forced to limit their analysis when there may be outliers in the data. To solve
this problem, this paper provides inference methods with two robust divergences
(the density-power and $\gamma$-divergences). We also derive influence
functions for the proposed methods and show conditions on the link function for
them to be bounded and to redescendence. Since the commonly used link functions
satisfy these conditions, the analyst can perform robust and flexible analysis
with our methods. In addition, and this is a result that further highlights our
contributions, we show that the influence function in the maximum likelihood
method does not have redescendence for any link function in the ordinal
response model. Through numerical experiments using artificial and two real
data, we show that the proposed methods perform better than the maximum
likelihood method with and without outliers in the data for various link
functions.
