mvrsquared {mvrsquared}

mvrsquared

Description

Compute the Coefficient of Determination for Vector or Matrix Outcomes

Details

Welcome to the mvrsquared package! This package does one thing: calculate the coefficient of determination or "R-squared". However, this implementation is different from what you may be familiar with. In addition to the standard R-squared used frequently in linear regression, 'mvrsquared' calculates R-squared for multivariate outcomes. (This is why there is an 'mv' in mvrsquared).

mvrsquared implements R-squared based on a derivation in this paper (https://arxiv.org/abs/1911.11061). It's the same definition of R-squared you're probably familiar with, i.e. 1 - SSE/SST but generalized to n-dimensions.

In the standard case, your outcome and prediction are vectors. In other words, each observation is a single number. This is fine if you are predicting a single variable. But what if you are predicting multiple variables at once? In that case, your outcome and prediction are matrices. This situation occurs frequently in topic modeling or simultaneous equation modeling.