  Ordinal data are quite common in applied statistics. Although some model
selection and regularization techniques for categorical predictors and ordinal
response models have been developed over the past few years, less work has been
done concerning ordinal-on-ordinal regression. Motivated by a consumer test and
a survey on the willingness to pay for luxury food products consisting of
Likert-type items, we propose a strategy for smoothing and selecting ordinally
scaled predictors in the cumulative logit model. First, the group lasso is
modified by the use of difference penalties on neighboring dummy coefficients,
thus taking into account the predictors' ordinal structure. Second, a fused
lasso-type penalty is presented for the fusion of predictor categories and
factor selection. The performance of both approaches is evaluated in simulation
studies and on real-world data.
