Bert is correct. In addition, you are using prcomp() for your principal components analysis so the initial principal component loadings are called "rotation" in contrast to princomp() where they are called "loadings." So you do not have "rotated" components in the traditional sense of the word. If you compare the results, you will see that the two agree (with reflection of the first four components). To rotate the results you would need to use varimax() or another function (e.g. principal() in package psych) that provides more rotation methods.
Also stored in the output from prcomp() is an object called "x." These are the principal component scores for each component. They are uncorrelated and could be used as explanatory variables in a regression analysis. But ------------------------------------- David L Carlson Department of Anthropology Texas A&M University College Station, TX 77840-4352 -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Bert Gunter Sent: Friday, November 22, 2013 11:36 AM To: Chris Wilkinson Cc: r-help@r-project.org Subject: Re: [R] Principal Components in a Linear Model 1. Probably not, depending on what you expect to gain from this. R's numerical procedures can almost certainly handle the correlations. 2. Search on "R package for principal components regression" instead of rolling your own.There are several (e.g. "chemometrics", "pls", etc.) -- Bert On Fri, Nov 22, 2013 at 8:47 AM, Chris Wilkinson <kins...@verizon.net> wrote: > My data has correlations between predictors so I think it would be > advantageous to rotate the axes with prcomp(). > >> census <- > read.table(paste("http://www.stat.wisc.edu/~rich/JWMULT02dat","T 8-5.DAT",sep > ="/"),header=F) >> census > V1 V2 V3 V4 V5 > 1 5.935 14.2 2.265 2.27 2.91 > 2 1.523 13.1 0.597 0.75 2.62 > 3 2.599 12.7 1.237 1.11 1.72 > 4 4.009 15.2 1.649 0.81 3.02 > 5 4.687 14.7 2.312 2.50 2.22 > 6 8.044 15.6 3.641 4.51 2.36 > 7 2.766 13.3 1.244 1.03 1.97 > 8 6.538 17.0 2.618 2.39 1.85 > 9 6.451 12.9 3.147 5.52 2.01 > 10 3.314 12.2 1.606 2.18 1.82 > 11 3.777 13.0 2.119 2.83 1.80 > 12 1.530 13.8 0.798 0.84 4.25 > 13 2.768 13.6 1.336 1.75 2.64 > 14 6.585 14.9 2.763 1.91 3.17 > >> pca1 <- prcomp(census) >> summary(pca1) > Importance of components: > PC1 PC2 PC3 PC4 PC5 > Standard deviation 2.6327 1.3361 0.62422 0.47909 0.11897 > Proportion of Variance 0.7413 0.1909 0.04168 0.02455 0.00151 > Cumulative Proportion 0.7413 0.9323 0.97394 0.99849 1.00000 > >> pca1$rotation # eigenvectors > PC1 PC2 PC3 PC4 PC5 > V1 -0.78120807 0.07087183 -0.003656607 0.54171007 0.302039670 > V2 -0.30564856 0.76387277 0.161817438 -0.54479937 0.009279632 > V3 -0.33444840 -0.08290788 -0.014841008 0.05101636 -0.937255367 > V4 -0.42600795 -0.57945799 -0.220453468 -0.63601254 0.172145212 > V5 0.05435431 0.26235528 -0.961759720 0.05127599 -0.024583093 > > I'd like to create a linear model based on the rotated axes. > >> linmod <- lm(y~a+b+....) > > Could someone be kind enough to suggest how to code a, b...? > > Chris > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Bert Gunter Genentech Nonclinical Biostatistics (650) 467-7374 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
