[R] Extracting Factor Pattern Matrix Similar to Proc Factor

[David L Carlson]

The pattern matrix is easy to compute from the results of princomp(). First we need a reproducible example so we'll use the iris data set (use ?iris for details) that comes with R.

> data(iris)
> iris.pc <- princomp(iris[,-5], cor=TRUE)
> print(iris.pc$loadings, cutoff=0)

Loadings:
             Comp.1 Comp.2 Comp.3 Comp.4
Sepal.Length  0.521 -0.377  0.720  0.261
Sepal.Width  -0.269 -0.923 -0.244 -0.124
Petal.Length  0.580 -0.024 -0.142 -0.801
Petal.Width   0.565 -0.067 -0.634  0.524

               Comp.1 Comp.2 Comp.3 Comp.4
SS loadings      1.00   1.00   1.00   1.00
Proportion Var   0.25   0.25   0.25   0.25
Cumulative Var   0.25   0.50   0.75   1.00

The object iris.pc is a list with 7 elements. One of those, iris.pc$loadings contains the standardized loadings so that the sum of the squared values in each column is 1. The default print method suppresses the printing of small loadings (< .1) so I've set cutoff=0 so we see them all. 

To get the pattern matrix we just need to multiple each of the columns by iris.pc$sdev (the square roots of the eigenvalues):

> iris.pat <- sweep(iris.pc$loadings, 2, iris.pc$sdev, "*")
> print(iris.pat, cutoff=0)

Loadings:
             Comp.1 Comp.2 Comp.3 Comp.4
Sepal.Length  0.890 -0.361  0.276  0.038
Sepal.Width  -0.460 -0.883 -0.094 -0.018
Petal.Length  0.992 -0.023 -0.054 -0.115
Petal.Width   0.965 -0.064 -0.243  0.075

               Comp.1 Comp.2 Comp.3 Comp.4
SS loadings     2.918  0.914  0.147  0.021
Proportion Var  0.730  0.229  0.037  0.005
Cumulative Var  0.730  0.958  0.995  1.000
> iris.pc$sdev^2
    Comp.1     Comp.2     Comp.3     Comp.4 
2.91849782 0.91403047 0.14675688 0.02071484

The sweep() function multiplies each column by its standard deviation. Now the sums of the squared values in each column sum to the eigenvalue. 

Alternatively, you can install the "psych" package which computes the pattern (structure) matrix directly:

> library(psych)
> iris.pca <- principal(iris[,-5], nfactors=4, rotate="none")
> print(iris.pca$Structure, cutoff=0)

-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352

-----Original Message-----
From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Scott Colwell
Sent: Monday, February 23, 2015 12:15 PM
To: r-help at r-project.org
Subject: [R] Extracting Factor Pattern Matrix Similar to Proc Factor

Hello,

I am fairly new to R and coming from SAS IML. I am rewriting one of my MC
simulations in R and am stuck on extracting a factor pattern matrix as would
be done in IML using Proc Factor.  

I have found the princomp() command and read through the manual but can't
seem to figure out how to save the factor pattern matrix.  I am waiting for
the R for SAS Users book to arrive. What I would use in SAS IML to get at
what I am looking for is:

PROC FACTOR Data=MODELCOV15(TYPE=COV) NOBS=10000 N=16 CORR
OUTSTAT=FAC.FACOUT15;
RUN;

DATA FAC.PATTERN15; SET FAC.FACOUT15;
IF _TYPE_='PATTERN';
DROP _TYPE_ _NAME_;
RUN;

Would any SAS IML to R converts be able to help me with this?

Thanks,

Scott Colwell, PhD




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