Comparison of Multi-response Prediction Methods
KBMraju.rimal@nmbu.no KBM
trygve.almoy@nmbu.no NMBU
solve.sabo@nmbu.no
2019-04-29
Abstract
While data science is battling to extract information from the enormous explosion of data, many estimators and algorithms are being developed for better prediction. Researchers and data scientists often introduce new methods and evaluate them based on various aspects of data. However, studies on the impact of/on a model with multiple response variables are limited. This study compares some newly-developed (envelope) and well- established (PLS, PCR) prediction methods based on real data and simulated data specifically designed by varying properties such as multicollinearity, the correlation between multiple responses and position of relevant principal components of predictors. This study aims to give some insight into these methods and help the researcher to understand and use them in further studies.
Introduction
The prediction has been an essential component of modern data science, whether in the discipline of statistical analysis or machine learning. Modern technology has facilitated a massive explosion of data however, such data often contain irrelevant information that consequently makes prediction difficult. Researchers are devising new methods and algorithms in order to extract information to create robust predictive models. Such models mostly contain predictor variables that are directly or indirectly correlated with other predictor variables. In addition, studies often consist of many response variables correlated with each other. These interlinked relationships influence any study, whether it is predictive modelling or inference.
Modern inter-disciplinary research fields such as chemometrics, econometrics and bioinformatics handle multi-response models extensively. This paper attempts to compare some multivariate prediction methods based on their prediction performance on linear model data with specific properties. The properties include the correlation between response variables, the correlation between predictor variables, number of predictor variables and the position of relevant predictor components. These properties are discussed more in the Experimental Design section. Among others, Sæbø, Almøy, and Helland (2015) and Almøy (1996) have conducted a similar comparison in the single response setting. In addition, Rimal, Almøy, and Sæbø (2018) have also conducted a basic comparison of some prediction methods and their interaction with the data properties of a multi-response model. The main aim of this paper is to present a comprehensive comparison of contemporary prediction methods such as simultaneous envelope estimation (Senv) (Cook and Zhang 2015) and envelope estimation in predictor space (Xenv) (Cook, Li, and Chiaromonte 2010) with customary prediction methods such as Principal Component Regression (PCR), Partial Least Squares Regression (PLS) using simulated dataset with controlled properties. In the case of PLS, we have used PLS1 which fits individual response separately and PLS2 which fits all the responses together. Experimental design and the methods under comparison are discussed further, followed by a brief discussion of the strategy behind the data simulation.