PCR vs. PLS (part 7)

We have used PLS with tis data set in the posts series "Analyzing Soy Meal in transmittance", so I just want to add in these coming posts a comparison between the regresiones developed in PLS and in PCR.

 

The best way to do it is comparing some plots and in this post I show the comparison of the PCR and PLS regression with the same number of terms and with the same calibration set (odd samples), and the same validation during the development of the model (Cross Validation).

 

The plot shows how (as expected), the first terms are more correlated for the constituent of interest (protein in this case) for the PLS terms than for the PCR, so the RMS are better, but as soon as more terms are added are almost the same (a little bit better for the PLS).

## add extra space to right margin of plot within frame
par(mar=c(5, 4, 4, 6) + 0.1)
plot(Xodd_pcr3,"validation",estimate="CV",ylim=c(0.5,2.0),

     xlim=c(1,10),col="blue",lwd=2,
     main=" Corr & RMSEP PCR vs PLS")
par(new=TRUE)
plot(Xodd_pls3,"validation", estimate="CV",

ylim=c(0.5,2.0),xlim=c(1,10),col="red",lwd=2,
     main="")
## Plot the second plot and put axis scale on right
par(new=TRUE)
plot(terms,Xodd_pls3_cor,  xlab="", ylab="", ylim=c(0,1),
     axes=FALSE, type="l",lty=4,lwd=2, col="red")
par(new=TRUE)
plot(terms,Xodd_pcr3_cor,  xlab="", ylab="", ylim=c(0,1),
     axes=FALSE,type="l",lty=4,lwd=2, col="blue")
## a little farther out (line=4) to make room for labels
mtext("Correlation",side=4,col="black",line=3)
axis(4, ylim=c(0,1), col="black",col.axis="black",las=1)
legend("bottomright",legend=c("RMSEP PLS", "RMSEP PCR",

       "Corr PLS","Corr PCR"),
       col=c("red","blue","red","blue"),

       lty=c(1,1,4,4),lwd=2)

 A reason for the improvement in the PLS can be seen in the regression coefficients (with 5 terms), where the PLS (in red), are more sharp, and can give better estimations ( we try to analyze this in coming posts)