We have been preparing predictive soil property (sand, Silt, Clay, pH and EC of the top soil) maps for an area (about 60 km2) using Digital soil mapping techniques in R with random forest in Southern Ethiopia. About 33 covariates were used. The results revealed that the R squared values for instance for clay fraction of the top soil is negative and very small (-0.12). Can R square values be negative? If so, what are the implications of such results?
Probably your model is poorly adjusted.
If you are running RF analysis with the randomForest or metaforest packages then a good explanation may be found elsewhere:
https://stats.stackexchange.com/a/144730/4950
http://developmentaldatascience.org/post/29-01-18_metaforest_no_effect/
@ Fekadu, R2 is not always the square of anything, so it can have a negative value without violating any rules of math. R2 is negative only when the chosen model does not follow the trend of the data, so fits worse than a horizontal line.
Negative R means the model prediction is worse than linear regression.
first of all, it is a pseudo R2, in random Forest it is computed as 1 - mse / Var(y). so yes it can be negative. Some package impute 0 to negative values before reporting them.
also, Duong Pham Luu Trung , that is not correct: you can have a negative R^2 if out-of-sample data are used to compute that statistic even for linear regression - what you say only holds in-sample.
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