Principal Component Analysis - Selecting components? + right choice?
Dear R gurus, I have some climatic data for a region of the world. They are monthly averages 1950 -2000 of precipitation (12 months), minimum temperature (12 months), maximum temperature (12 months). I have scaled them to 2 km x 2km cells, and I have around 75,000 cells. I need to feed them into a statistical model as co-variates, to use them to predict a response variable. The climatic data are obviously correlated: precipitation for January is correlated to precipitation for February and so on .... even precipitation and temperature are heavily correlated. I did some correlation analysis and they are all strongly correlated. I though of running PCA on them, in order to reduce the number of co-variates I feed into the model. I run the PCA using prcomp, quite successfully. Now I need to use a criteria to select the right number of PC. (that is: is it 1,2,3,4?) What criteria would you suggest? At the moment, I am using a criteria based on threshold, but that is highly subjective, even if there are some rules of thumb (Jolliffe,Principal Component Analysis, II Edition, Springer Verlag,2002). Could you suggest something more rigorous? By the way, do you think I would have been better off by using something different from PCA? Best,
Corrado Topi Global Climate Change & Biodiversity Indicators Area 18,Department of Biology University of York, York, YO10 5YW, UK Phone: + 44 (0) 1904 328645, E-mail: ct529 at york.ac.uk