Multi-Target Tobit Models for Completing Water Quality Data

TL;DR

This paper introduces a multi-target Tobit model to accurately estimate multiple censored water quality variables simultaneously, improving the analysis of microbiological data critical for public health.

Contribution

The paper presents a novel extension of the Tobit model for handling multiple censored variables jointly, with a stable optimization algorithm for better estimation accuracy.

Findings

Joint estimation outperforms separate estimation in real datasets

The model effectively handles multiple censored water quality measurements

Numerical stability is achieved through the proposed optimization algorithm

Abstract

Monitoring microbiological behaviors in water is crucial to manage public health risk from waterborne pathogens, although quantifying the concentrations of microbiological organisms in water is still challenging because concentrations of many pathogens in water samples may often be below the quantification limit, producing censoring data. To enable statistical analysis based on quantitative values, the true values of non-detected measurements are required to be estimated with high precision. Tobit model is a well-known linear regression model for analyzing censored data. One drawback of the Tobit model is that only the target variable is allowed to be censored. In this study, we devised a novel extension of the classical Tobit model, called the \emph{multi-target Tobit model}, to handle multiple censored variables simultaneously by introducing multiple target variables. For fitting the new model, a numerical stable optimization algorithm was developed based on elaborate theories. Experiments conducted using several real-world water quality datasets provided an evidence that estimating multiple columns jointly gains a great advantage over estimating them separately.