Regularization and Model Selection for Item-on-Items Regression with Applications to Food Products' Survey Data

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 survey datasets on food products consisting of Likert-type items, we propose a strategy for smoothing and selection of ordinally scaled predictors in the cumulative logit model. First, the original group lasso is modified by use of difference penalties on neighbouring dummy coefficients, thus taking into account the predictors' ordinal structure. Second, a fused lasso type penalty is presented for fusion of predictor categories and factor selection. The performance of both approaches is evaluated in simulation studies, while our primary case study is a survey on the willingness to pay for luxury food products.