# regressionMetrics: Calculate some standard regression evaluation metrics of... In performanceEstimation: An Infra-Structure for Performance Estimation of Predictive Models

## Description

This function is able to calculate a series of regression evaluation statistics given two vectors: one with the true target variable values, and the other with the predicted target variable values. Some of the metrics may require additional information to be given (see Details section).

## Usage

 `1` ```regressionMetrics(trues, preds, metrics = NULL, train.y = NULL) ```

## Arguments

 `trues` A numeric vector with the true values of the target variable. `preds` A numeric vector with the predicted values of the target variable. `metrics` A vector with the names of the evaluation statistics to calculate (see Details section). If none is indicated (default) it will calculate all available metrics of this function. `train.y` An optional numeric vector with the values of the target variable on the set of data used to obtain the model whose performance is being tested.

## Details

In the following description of the currently available metrics we denote the vector of true target variable values as t, the vector of predictions by p, while N denotes the size of these two vectors, i.e. the number of test cases.

The regression evaluation statistics calculated by this function belong to two different groups of measures: absolute and relative. In terms of absolute error metrics the function includes currently the following:

"mae": mean absolute error, which is calculated as sum(|t_i - p_i|)/N

"mse": mean squared error, which is calculated as sum( (t_i - p_i)^2 )/N

"rmse": root mean squared error that is calculated as sqrt(mse)

The remaining measures ("mape", "nmse", "nmae" and "theil") are relative measures, the three later comparing the performance of the model with a baseline. They are unit-less measures with values always greater than 0. In the case of "nmse", "nmae" and "theil" the values are expected to be in the interval [0,1] though occasionaly scores can overcome 1, which means that your model is performing worse than the baseline model. The baseline used in both "nmse" and "nmae" is a constant model that always predicts the average target variable value, estimated using the values of this variable on the training data (data used to obtain the model that generated the predictions), which should be provided in the parameter `train.y`. The "theil" metric is typically used in time series tasks and the used baseline is the last observed value of the target variable. The relative error measure "mape" does not require a baseline. It simply calculates the average percentage difference between the true values and the predictions.

These measures are calculated as follows:

"mape": sum(|(t_i - p_i) / t_i|)/N

"nmse": sum( (t_i - p_i)^2 ) / sum( (t_i - AVG(Y))^2 ), where AVG(Y) is the average of the values provided in vector `train.y`

"nmae": sum(|t_i - p_i|) / sum(|t_i - AVG(Y)|)

"theil": sum( (t_i - p_i)^2 ) / sum( (t_i - t_{i-1})^2 ), where t_{i-1} is the last observed value of the target variable

The user may also indicate the value "all" in the parameter `metrics`. In this case all possible metrics will be calculated. This will only include the "nmse", "nmae" and "theil" metrics if the value of the `train.y` parameter is set, otherwise only the other metrics will be returned.

## Value

A named vector with the calculated evaluation scores.

## Note

In case you require either "nmse", "nmae" or "theil" to be calculated you must supply a vector of numeric values through the parameter `train.y`, otherwise the function will return an error message. These values are required to obtain a fair baseline against which your model predictions will be compared to.

## Author(s)

Luis Torgo ltorgo@dcc.fc.up.pt

## References

Torgo, L. (2014) An Infra-Structure for Performance Estimation and Experimental Comparison of Predictive Models in R. arXiv:1412.0436 [cs.MS] http://arxiv.org/abs/1412.0436

`classificationMetrics`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## Not run: ## Calculating several statistics of a regression tree on the Swiss data data(swiss) idx <- sample(1:nrow(swiss),as.integer(0.7*nrow(swiss))) train <- swiss[idx,] test <- swiss[-idx,] library(rpart) model <- rpart(Infant.Mortality ~ .,train) preds <- predict(model,test) ## by default only mse is calculated regressionMetrics(test[,'Infant.Mortality'],preds) ## calculate mae and rmse regressionMetrics(test[,'Infant.Mortality'],preds,metrics=c('mae','rmse')) ## calculate all statistics regressionMetrics(test[,'Infant.Mortality'],preds,train.y=train[,'Infant.Mortality']) ## End(Not run) ```