# Comparison of Multi-response Prediction Methods

## TL;DR

This paper compares various multi-response prediction methods, including new envelope techniques and established approaches like PLS and PCR, analyzing their performance on real and simulated data with different properties.

## Contribution

It provides a comparative analysis of multi-response prediction methods, highlighting their strengths and limitations under various data conditions.

## Key findings

- Envelope methods perform well with high multicollinearity.
- PLS and PCR are robust across different response correlations.
- Method performance varies with principal component relevance.

## 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.