e goodness-of-fit measures are correlation, RMSE, MARNE, and R2 measures. Definitions are below.
Denote an observed response j (species) at sample i, \(i=1,...,n\), as \(y_{ij}\), and predicted value as \(\hat y_{ij}\).</p>
<p>$$RMSE(\boldsymbol{y_{j}}, \boldsymbol{\hat y_{j}}) =  \sqrt{\frac{1}{n}\Sigma_{i=1}^{n} {(y_{ij} - \hat y_{ij})^2}} $$</p>
<p>$$MAE(\boldsymbol{y_{j}}, \boldsymbol{\hat y_{j}}) =  \frac{1}{n}\Sigma_{i=1}^{n} |y_{ij} - \hat y_{ij}| $$</p>
<p>$$MARNE(\boldsymbol{y_{j}}, \boldsymbol{\ha