dual.spls (version 0.1.4)

d.spls.metric: Computes predictions criterias

Description

This function computes evaluation metrics commonly used in modelling. It provides the values of the root mean square error (RMSE), the mean absolute error (MAE) and the Rsquared.

Usage

d.spls.metric(hat.y,real.y)

Value

A list of the following attributes

RMSE

the vector of the root mean square error values for each component.

MAE

the vector of the mean absolute error values for each component.

Rsquared

the vector of the Rsquared values for each component.

Arguments

hat.y

a numeric vector. It represents the fitted response variable for each observation using a Dual-SPLS method.

real.y

a numeric vector. It represents the response variable for each observation.

Author

Louna Alsouki François Wahl

Details

The Root Mean Square Error (RMSE) is the standard deviation of the residuals. It is computed as follows: $$RMSE=\sqrt{\sum_{i=1}^n \frac{(y_{fi}-y_{ri})^2}{n}}.$$

The Mean Absolute Error measures the average magnitude of the errors in a set of predictions, without considering their direction. It is computed as follows: $$MAE=\frac{1}{n}\sum_{i=1}^n |y_{fi}-y_{ri}|.$$

The Rsquared represents the proportion of the variance for a dependent variable that's explained by an independent variable in a regresison. It is computed as follows:

$$R2=\frac{\sum_{i=1}^n (y_{fi}-\bar{y})^2}{\sum_{i=1}^n (y_{ri}-\bar{y})^2}.$$ Where \(\bar{y}=\frac{1}{n}\sum_{i=1}^n y_{fi}\). Note that \(y_f\) are the fitted values and \(y_r\) are the real ones.

Examples

### load dual.spls library
library(dual.spls)
### constructing the simulated example
n <- 100
p <- 50
nondes <- 20
sigmaondes <- 0.5
data=d.spls.simulate(n=n,p=p,nondes=nondes,sigmaondes=sigmaondes)

X <- data$X
y <- data$y

#fitting the Dual-SPLS lasso model

ncomplasso <- d.spls.cv(X=X,Y=y,ncomp=10,dspls="lasso",ppnu=0.9,nrepcv=20,pctcv=75)
mod.dspls.lasso <- d.spls.lasso(X=X,y=y,ncp=ncomplasso,ppnu=0.9,verbose=TRUE)

predmetric= d.spls.metric(mod.dspls.lasso$fitted.values,y)

#Error plots
plot(1:ncomplasso,predmetric$RMSE,
main=("Root mean squares error values"),xlab='Number of components',ylab='Errors',col='blue',pch=19)
lines(1:ncomplasso,predmetric$RMSE,col='blue')
points(1:ncomplasso,predmetric$MAE,col='red',pch=19)
lines(1:ncomplasso,predmetric$MAE,col='red')
points(1:ncomplasso,predmetric$R2,col='green',pch=19)
lines(1:ncomplasso,predmetric$R2,col='green')
legend("topright", legend = c("RMSE", "MAE", "R2"), bty = "n",
 cex = 0.8, col = c("blue", "red","green"), lty = c(1,1,1))