calc_rsquared {mvrsquared}

Calculate R-Squared.

Description

Calculate R-Squared for univariate or multivariate outcomes.

Usage

calc_rsquared(y, yhat, ybar = NULL, return_ss_only = FALSE, threads = 1)

Arguments

y

The true outcome. This must be a numeric vector, numeric matrix, or coercible to a sparse matrix of class dgCMatrix. See 'Details' below for more information.

yhat

The predicted outcome or a list of two matrices whose dot product makes the predicted outcome. See 'Details' below for more information.

ybar

Numeric scalar or vector; the mean of y. Useful for parallel computation in batches.

return_ss_only

Logical. Do you want to forego calculating R-squared and only return the sums of squares?

threads

Integer number of threads for parallelism; defaults to 1.

Details

There is some flexibility in what you can pass as y and yhat. In general, y can be a numeric vector, numeric matrix, a sparse matrix of class dgCMatrix from the Matrix package, or any object that can be coerced into a dgCMatrix.

yhat can be a numeric vector, numeric matrix, or a list of two matrices whose dot product has the same dimensionality as y. If yhat is a list of two matrices you may optionally name them x and w indicating the order of multiplication (x left multiplies w). If unnamed or ambiguously named, then it is assumed that yhat[[1]] left multiplies yhat[[2]].

Value

If return_ss_only = FALSE, calc_rsqured returns a numeric scalar R-squared. If return_ss_only = TRUE, calc_rsqured returns a vector; the first element is the error sum of squares (SSE) and the second element is the total sum of squares (SST). R-squared may then be calculated as 1 - SSE / SST.

Note

On some Linux systems, setting threads greater than 1 for parallelism may introduce some imprecision in the calculation. As of this writing, the cause is still under investigation. In the meantime setting threads = 1 should fix the issue.

Setting return_ss_only to TRUE is useful for parallel or distributed computing for large data sets, particularly when y is a large matrix. However if you do parallel execution you MUST pre-calculate 'ybar' and pass it to the function. If you do not, SST will be calculated based on means of each batch independently. The resulting r-squared will be incorrect.

See example below for parallel computation with future_map from the furr package.

Examples

# standard r-squared with y and yhat as vectors
f <- stats::lm(mpg ~ cyl + disp + hp + wt, data = datasets::mtcars)

y <- f$model$mpg

yhat <- f$fitted.values

calc_rsquared(y = y, yhat = yhat)

# standard r-squared with y as a matrix and yhat containing 'x' and linear coefficients
s <- summary(f)

x <- cbind(1, as.matrix(f$model[, -1]))

w <- matrix(s$coefficients[, 1], ncol = 1)

calc_rsquared(y = matrix(y, ncol = 1), yhat = list(x, w))

# multivariate r-squared with y and yhat as matrices
calc_rsquared(y = cbind(y, y), yhat = cbind(yhat, yhat))

# multivariate r-squared with yhat as a linear reconstruction of two matrices
calc_rsquared(y = cbind(y, y), yhat = list(x, cbind(w,w)))