Hello everyone, I applied PCA in python by taking lagged climate indices and then used its resulted two principal components (showing maximum variance) with GLDAS satellite data precipitation values in multiple linear regression to predict monthly precipitation. My data was 38 years monthly data. The correlation between GLDAS and model's predicted precipitation on the training set was 0.50 and on the test set was 0.49.
I wanted to check the model's performance further so I took 22 years monthly TRMM data and calculated PCA on 22 years monthly lagged climate indices. I entered the obtained two PC values in the previous developed multiple linear regression equation and acquired the predicted monthly precipitation. The correlation was calculated between the TRMM and model predicted precipitation which was negative -0.45.
What is the reason that I got negative correlation and what this negative correlation shows?
Hi Asfandiyar Khan,
Based on your correlation coefficients, it seems that the PCs are of negative signs of each other for the GLDAS and the TRMM. The signs of PCs are arbitrary, as they are to be multiplied to the 'patterns (which will also have negative sign)' and the eigenvalues (always set to positive (non-negative) for correlation matrix).
Just check if two 1st PCs of each dataset are strongly negatively correlated (e.g., -0.99) to ensure that they are equivalent modes but of negative signs, and the just multiply -1 to the latter (as well as to the patterns if you are to reconstruct them).
The other point that I want to mention is, however, that your approach is little bit dangerous, as PCs are calculated from different datasets and they are not exactly equivalent. We just hope that the PCs are the projections of the population distribution which is again by the same dynamics, but they aren't.
Sometimes people use PC based regression (prediction) model in such a way that, you calculate PCs (and eigenvectors) from the reference dataset, and project it to the new dataset to obtain a PC-like projections. I guess details depend on your purpose though.
Hope it helps.
- WonMoo
TRMM shows the amount of condensed water in the atmosphere. Not all condensed water falls to the surface of the earth. Water does not always fall on the surface of the earth in the place where the satellite showed. Maybe this is the problem. What is the spatial scale of averaging? This may be important.
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