Dimension reduction in functional regression with categorical predictor

In the present paper, we consider dimension reduction methods for functional regression with a scalar response and the predictors including a random curve and a categorical random variable. To deal with the categorical random variable, we propose three potential dimension reduction methods: partial functional sliced inverse regression, marginal functional sliced inverse regression and conditional functional sliced inverse regression. Furthermore, we investigate the relationships among the three methods. In addition, a new modified BIC criterion for determining the dimension of the effective dimension reduction space is developed. Real and simulation data examples are then presented to show the effectiveness of the proposed methods.