Regression models with ordered multiple categorical predictors |
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Authors: | Haitao Tian Ching-Yu Cheng Liang Zhang |
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Institution: | 1. School of Mathematics, Southwest Jiaotong University, Chengdu, China;2. Singapore Eye Research Institute, Duke-NUS Medical School, Singapore;3. Singapore Eye Research Institute, Singapore |
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Abstract: | Ordered multiple categorical (MC) variable has been widely considered and studied as response variable, and few studies have carefully considered it as a predictor in linear regression. When doing this, the existence of some pseudo-categories may result in overfitting, and to detect those pseudo-categories by hypothesis test of all dummy variables might have low specificity. In this paper, we propose a transformation method of dummy variables for such ordered MC predictors, after which a model selection method combined with BIC will be elaborated. Theoretical consistency of our model selection method is established under some common assumptions. Both simulation studies and real data analysis of a medical survey indicate that our method provides good performance and is applicable to a wide range of biomedical research. |
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Keywords: | Dummy variables pseudo-categories transformation regression least squares BIC |
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