Compute the Coefficient of Determination for Vector or Matrix Outcomes

Compute the coefficient of determination for outcomes in n-dimensions. May be useful for multidimensional predictions (such as a multinomial model) or calculating goodness of fit from latent variable models such as probabilistic topic models like latent Dirichlet allocation or deterministic topic models like latent semantic analysis. Based on Jones (2019) .

mvrsquared

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. It's the same definition of R-squared you're probably familiar with (1 - SSE/SST) but generalized to n-dimensions.

In the standard case, your outcome y and prediction yhat 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, y and yhat are matrices. This situation occurs frequently in topic modeling or simultaneous equation modeling.

Installation

You can install from CRAN with

install.packages("mvrsquared")

You can get the development version with

install.packages("remotes")

remotes::install_github("tommyjones/mvrsquared")

Check out the vignette to see how to...

1. Calculate the regular R-squared we all know and love!
2. Calculate R-squared for multiple outcome variables at once (like a multinomial regression)!
3. Calculate R-squared for probabilistic (e.g. LDA) and non-probabilistic (e.g. LSA) topic models!
4. Split your BIG DATA into batches and calculate R-squared with a parallel/distributed map-reduce framework!