Predictive ability of covariate-dependent Markov models and classification tree for analyzing rainfall data in Bangladesh

This study attempts to make comparison between different parametric regressive models for the bivariate binary data with a machine learning technique. The data on sequential occurrence of rainfall in consecutive days is considered. The outcomes are classified as rainfall in both days, rainfall in one of the consecutive days, and no rainfall in both days. The occurrence of rainfall in consecutive days is analyzed by using statistical models with covariate dependence and classification tree for the period from 1980 to 2014. We have used relative humidity, minimum temperature, maximum temperature, sea level pressure, sunshine hour, and cloud cover in the model as covariates. The binary outcome variable is defined as the occurrence or non-occurrence of rainfall. Five regions of Bangladesh are considered in this study and one station from each region is selected on the basis of two criteria: (i) contains fewer missing values and (ii) representative of the regional characteristics geographically. Several measures are used to compare the models based on Markov chain and classification tree. It is found that for yearly data, both the Markov model and classification tree performed satisfactorily. However, the seasonal data show variation of rainfall. In some seasons, both models perform equally good such as monsoon, pre-monsoon, and post-monsoon, but in the winter season, the Markov model works poorly whereas classification tree fails to work. Additionally, we also observe that the Markov model performed consistently for each season and performs better compared with the classification tree. It has been demonstrated that the covariate-dependent Markov models can be used as classifiers alternative to the classification tree. It is revealed that the predictive ability of the covariate-dependent Markov model based on Markovian assumption performs either better or equally good compared with the classification tree. The joint models also consistently showed better predictive performance compared with regressive model for whole year data as well as for several seasonal data.