Multinomial logit PLS regression of compositional data

This paper studies the discriminant modeling method for the constrained data. We propose the multinomial logit partial least squares (ML-PLS) regression of compositional data by implementing the ML-PLS regression method on the centered logratio (clr) transformed data. And the model presents the following advantages: i) compared to the additive logratio (alr) transformation of the compositional data, the clr transformed variables are symmetrical to the components of the original compositional data, which is favorable in explaining the modeling results; ii) the PLS related technique is efficient in dealing with the clr transformed variables which have the problem of being completely correlated; iii) the ML-PLS regression can not only give the classification results but also calculate in what probabilities each sample belonging to the classes; iv) compared to the PLS logistic regression on compositional data which can only deal with binary or ordinal response, the ML-PLS regression on compositional data can also tackle the multiclass problem. To evaluate the model, experiments with simulated and real compositional data were performed and also compared with the results from the logcontrast PLS discriminant model of compositional data, respectively, which illustrate the validity and practicability of the model.