Title: On regularized regression of categorical responses on categorical predictors
Authors: Ko Sugiura - Keio University (Japan) [presenting]
Teruo Nakatsuma - Keio University (Japan)
Akiyoshi Shimura - Tokyo Medical University (Japan)
Abstract: Data analysis plays a great important role in healthcare. Data in the field of healthcare is usually collected through a set of questionnaires with categorical scaling. For example, the questionnaire for persons mental health is recorded with the ordinal coding scheme: 0 (no problem), 1 (mild problem), 2 (moderate problem), 3 (severe problem), and 4 (complete problem). Regression analysis for such data has been conducted by regarding the data as continuous on the basis of certain scoring rules for simplicity, because regression on categorical predictors tends to suffer from the high dimensionality of variables. However, such modification makes the meaning of resulting variables abstractive and sometimes ambiguous. For the sake of effective interpretation, one may wish to take the original categorical data into the model without any modification. To deal with the problem of the high dimensionality, we propose a version of the Lasso-type regularization, and demonstrate its effectiveness through an empirical study using the real data on mental stress.