Estimation Method Of Linear Regression Model With Ordered Multiple Categorical Predictors And Its Applications

Studying categorical variables is a important topic in the research of regression models.When the response variable is categorical,many scholars have contributed to solve this problem.However,less work has been done concerning ordered multiple categorical predictors.suggested a simple procedure using ridge regression to incorporate the ordered multiple categorical predictors and obtain stable estimators.But we must know,the premise of this method is that the ordered multiple categorical variables are classified reasonably.If an ordered multiple categorical predictor has some pseudo-categories,ridge regression will 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.We call it TD-BIC,and theoretical consistency of our model selection method is established under some common assumptions.In simulation scenario,we generate variables with ordered multiple categorical predictors and random variables.In this way,the model used in the simulation is closer to the reality,and the results obtained are more general.When the sample size increasing,the frequency of correct fitting increases close to 1.This validates the asymptotic consistency result.The results show that TD-BIC method has a good performance in detecting pseudo categories.After eliminating the pseudo categories,the goodness of fit of the model has been improved and the model become simpler,which also shows that the TD-BIC method proposed in this paper is valuable to improve the goodness of fit of the model.this method can be applied to a wide range of biomedical researches,it also has the advantages of being convenient to understand and apply.