Difference between revisions of "Performance measures"

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The [http://en.wikipedia.org/wiki/R-squared coefficient of determination] is the square of the Pearson's product-moment correlation coefficient. Note that the COD only evaluates linear relations between variables!
 
The [http://en.wikipedia.org/wiki/R-squared coefficient of determination] is the square of the Pearson's product-moment correlation coefficient. Note that the COD only evaluates linear relations between variables!
  
   COD <- cor(Qobs,Qsim, use="complete.obs")^2
+
   COD <- cor(Qobs, Qsim, use="complete.obs")^2
  
  
 
===Root mean squared error===
 
===Root mean squared error===
  
The [http://en.wikipedia.org/wiki/Root_mean_square_deviation root mean squared error] is the square root of the variance:
+
As the name suggests, the root mean squared error is the square root of the [http://en.wikipedia.org/wiki/Mean_squared_error mean squared error]:
  
   RMSE <- cov(Qobs,Qsim, use="complete.obs")^0.5
+
   RMSE <- (mean((Qobs - Qsim)^2))^0.5

Latest revision as of 15:08, 15 September 2008

Introduction

Here is a selection of measures you can use for assessing the performance of your model.


Nash-Sutcliffe efficiency

The Nash-Sutcliffe efficiency is a widely used performance measure based on the error variance. It is implemented as NSeff() in the topmodel package. It takes two vectors, containing the simulated (Qsim) and observed (Qobs) discharge:

  Eff <- NSeff(Qobs,Qsim)

The underlying code is very simple:

  NSeff <- function (Qobs, Qsim){
     Qsim <- Qsim[!is.na(Qobs)]
     Qobs <- Qobs[!is.na(Qobs)]
     Qobs <- Qobs[!is.na(Qsim)]
     Qsim <- Qsim[!is.na(Qsim)]
     NS <- 1 - (sum((Qobs - Qsim)^2)/sum((Qobs - mean(Qobs))^2))
     return(NS)
  }


Coefficient of determination

The coefficient of determination is the square of the Pearson's product-moment correlation coefficient. Note that the COD only evaluates linear relations between variables!

  COD <- cor(Qobs, Qsim, use="complete.obs")^2


Root mean squared error

As the name suggests, the root mean squared error is the square root of the mean squared error:

  RMSE <- (mean((Qobs - Qsim)^2))^0.5