Canonical Correlation Analysis in R

Question

I have a dataset of temperature readings of different burner parts which determine the final temperature of the burner and time to set off burner

So my dataset looks like this:

Knob_reading_of_Coil_temperature(P1) Knob_reading_of_barrel_temperature(P2) Knob_reading_of_collar_temperature(P3)

Knob_reading_of_air_holes_temperature(P4)   Knob_reading_of_jet_temperature(P5) Knob_reading_of_base_temperature(P6)    Final_temperature_of_output_burner(I1)  Time_to_set_off_the_burner(I2)
11.23   89.12   65.32   97.12   96.4    56.7    67.7    10.2
41.12   86.7    76.76   78.65   91.2    78.24   55.42   21.67
75.65   83.79   82.65   82.43   90.6    87.45   81.13   5.89
78.13   82.57   59.34   92.56   89.8    67.72   75.08   6.65

I used CCA( Canonical Correlation Analysis ) to find which of the parameters are highly correlated.

But will CCA help me to find which of these parameters similarly affect the Final temperature of output burner or Time to set off the burner

Let me explain this better: What I want to find out is whether either of parameters (P1,P2,P3) affect the Final temperature of output burner similary. If yes, I could conclude that P1 P2 P3 affect the final temperature so instead of using all three parameters,i could use only one of them

Similarly , if P4 P5 P6 affect the time to setoff of burner similarly i could conclude that instead of using all three i could use either one as they affect the time to set of burner similarly.

Will CCA help me to find such an correlation ?

Or are there any algorithms that help me to find out how the parameters (P1-P5) affect the other set (I1-I2) ? ie to find if there a similarity in way (P1-P5) affect/ correlate the other set (I1-I2)?

Answer 1

I think this is fairly simple. For output burner, you want to compare 4 models: output to P1, output to P2, output to P3 and output to P1+P2+P3. You can compare these in the usual way by comparing the R-squared statistics or, more formally, doing an F test on the incremental model mean square. You want to compare the full model to each of the one variable models. Then do the same thing with P4, P5, P6 and time to burner setoff. If I have understood your question correctly, it has nothing to do with CCA.

So what would CCA give you in this situation?

Your CCA compares P1-P6, on the one hand, to (I1,I2), on the other. You will get two component pairs from the analysis. The first pair gives you a linear combination of P1-P6 and another linear combination of I1 and I2 ... think of it as a weighted sum of the P group and a weighted sum of the I1 group.

These scores answer the question, "What score from the P group has maximal correlation with what score from the I group?" The second score picks the second best pair, subject to being uncorrelated with the first.

Anyway, CCA packages give a lot of output, typically showing correlations between the scores and the component variables (like factor loadings in factor analysis). This output helps you to interpret your scores, but not in a way that will answer your question. For example, if P1, P2 and P3 all give similar information about I1, then the first score will probably pull out their average, while the score in I1 and I2 will load heavily on I1. CCA doesn't help you get rid of redundant information; on the contrary, it will pull in anything that helps boost the prediction. In fact, the first pair will probably be something close to the average of the P group and the average of the I group.

Since you are using R, I recommend the yacca package. The manual actually contains a detailed explanation of what the output means and how to interpret it. Package CCA has some nice plots, which can be helpful as well.