ASA Connect

Dear all, please i am soliciting for clarification on principal component regression aanlysis(PCRA). I have four climatic parameters( rainfall, relative humidity, sunshine and temperature) and yearly cassava production in Benue state Nigeria. Cassava data is my dependent variable while the climate data are my independent variables. Firstly, i want to run a PCA to know among the climate data which one(s) contribute most to the total variation observed. I am using R programming language. Right now i have done the PCA but dont know how to proceed to PCRA. Pease your input will be highly appreciated. Thanks.

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Ikenna Nnabue
Research Officer
National Root Crops Research Institute.
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The proc PCR seems to do what you want. 
https://27411.compute.dtu.dk/filemanager/uploads/27411/eNotepdfs/eNote4-PCRinR.pdf

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Chauncey Dayton
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Don't do it (especially with just 4 predictors).  PCA deals only with the predictor variables in complete isolation of what one wants to predict.  So why would messing around with the predictor variables give one a better predictor no matter what the response variable might be?  The smallest principal component might very well be the best predictor.  (Admittedly, that last sentence won't be true too often as you've chosen predictors that are likely to have some predictive value.)

Now after fitting using all variables (and after thought about what interactions might exist that you want to include in the model) looking at principal components to discern some structure among the predictors is fine.  But if hope for good predictions is what you're after, PCA won't buy you anything.  (If you've got tens or hundred of predictors, then maybe one might be forced to reduce the number of predictors and PCA might be an option.)

Some will say that PCA results in more numerically stable estimates of the coefficients.  That is true.  But those are coefficients that might not have any meaning and predictions won't improve.

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Jim Baldwin
Retired
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I recommend use of R-package RXshrink. Principal components regression is an (extreme) special case of "generalized" ridge regression. The statistics and graphics produced by RXshrink functions help researchers select the best (normal-theory maximum likelihood) choices for both the "Q"-shape (curvature) of the shrinkage path and also the best extent, M, of shrinkage along that path. Q = -5 is essentially principal components regression. With P=4 predictors, 0 <= M <= 4 is the approximate rank-deficiency in your predictor data. "Good" choices for Q and M enable shrinkage to correct wrong-signs problems and reduce MSE risk in estimation of the true Beta coefficient vector. My advice is to be conservative (and get better predictions) by doing somewhat less shrinkage than what appears optimal for estimating Betas.

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Bob Obenchain
Principal Consultant
Risk Benefit Statistics LLC
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Ridge regression or multiple linear regression would be my choice of method unless some of your predictors are not continuous.  In the latter case, PC maybe helpful.  The multiple linear regression techniques will automatically tell you the independent variables that may or may not be important based on F-to-in and F-to-out (where F is your F-statistic with associated degrees of freedom).  BMDP/SAS/SYSSTAT/SPSS/MINITAB/R-routines all have such facilities.

Ajit K. Thakur, Ph.D.
Retired Statistician

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Ajit K. Thakur, Ph.D.
Retired Statistician
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Dear Bob, thank you immensely for the response. I want to effect a trail on the R package. Could you please help me the R script (command) for the analysis? When I produce the result, I will surely get back to you for more clarification on the output.,
Best,
Nnabue Ikenna


------Original Message------

Dear all, please i am soliciting for clarification on principal component regression aanlysis(PCRA). I have four climatic parameters( rainfall, relative humidity, sunshine and temperature) and yearly cassava production in Benue state Nigeria. Cassava data is my dependent variable while the climate data are my independent variables. Firstly, i want to run a PCA to know among the climate data which one(s) contribute most to the total variation observed. I am using R programming language. Right now i have done the PCA but dont know how to proceed to PCRA. Pease your input will be highly appreciated. Thanks.

------------------------------
Ikenna Nnabue
Research Officer
National Root Crops Research Institute.
------------------------------