Abstract：In this paper， a functional cumulative Logistic regression model is constructed for the data whose response variable is an ordinal multi-classification index and covariables are functional index. Specific solution process is as follows： firstly， the relation between the ordinal response variable and functional covariables are connected through a latent variable. Meanwhile， the regression coefficient function and independent variable of regression are expanded by selected principal component basis function， and the error term is set to following a standard logistic distribution. Polya-Gamma transform then is used to solve the complexity of the likelihood function of the model， and the posterior distribution of the expansion coefficients is obtained to construct a Gibbs sampling algorithm. Finally， the proposed method is applied to the analysis of simulated data and an actual air quality index (AQI) data， and the results show that performance of new method are both better than traditional methods.
2023, Vol. 57 
