Premium
High‐dimensional regression with ordered multiple categorical predictors
Author(s) -
Huang Lei,
Hang Weiqiang,
Chao Yue
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8400
Subject(s) - categorical variable , regression analysis , consistency (knowledge bases) , regression diagnostic , computer science , feature selection , regression , transformation (genetics) , linear regression , variable (mathematics) , statistics , data transformation , econometrics , data mining , mathematics , artificial intelligence , machine learning , bayesian multivariate linear regression , mathematical analysis , biochemistry , chemistry , data warehouse , gene
Models for the ordered multiple categorical (OMC) response variable have already been extensively established and widely applied, but few studies have investigated linear regression problems with OMC predictors, especially in high‐dimensional situations. In such settings, the pseudocategories of the discrete variable and other irrelevant explanatory variables need to be automatically selected. This paper introduces a transformation method of dummy variables for such OMC predictors, an L 1 penalty regression method is proposed based on the transformation. Model selection consistency of the proposed method is derived under some common assumptions for high‐dimensional situation. Both simulation studies and real data analysis present good performance of this method, showing its wide applicability in relevant regression analysis.