Selection of influential variables in ordinal data with preponderance of zeros

Presence of excess zero in ordinal data is pervasive in areas like medical and social sciences. Unfortunately, analysis of such kind of data has so far hardly been looked into, perhaps for the reason that the underlying model that fits such data, is not a generalized linear model. Obviously some methodological developments and intensive computations are required. The current investigation is concerned with the selection of variables in such models. In many occasions where the number of predictors is quite large and some of them are not useful, the maximum likelihood approach is not the automatic choice. As, apart from the messy calculations involved, this approach fails to provide efficient estimates of the underlying parameters. The proposed penalized approach includes ℓ1 penalty (LASSO) and the mixture of ℓ1 and ℓ2 penalties (elastic net). We propose a coordinate descent algorithm to fit a wide class of ordinal regression models and select useful variables appearing in both the ordinal regression and the logistic regression based mixing component. A rigorous discussion on the selection of predictors has been made through a simulation study. The proposed method is illustrated by analyzing the severity of driver injury from Michigan upper peninsula road accidents.