[R] Comparing initial eigenvalues to broken stick results

dcarlson at tamu.edu dcarlson at tamu.edu
Mon Apr 14 17:23:19 CEST 2014

```It helps a great deal if you provide a small data set using
dput() and indicate what packages need to be loaded for the
functions you are using. This example uses random data so there
are no eigenvalues above the initial broken stick values:

> set.seed(42)
> x <- matrix(rnorm(200), 20, 10)
> require(vegan)
> bs <- rle(eigen(cor(x))\$values>bstick(10,tot.var=10))
> as.vector(ifelse(bs\$values[1]==TRUE, bs\$lengths[1], 0))
[1] 0

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

----Original Message-----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On Behalf Of Allyson
Combes
Sent: Sunday, April 13, 2014 11:01 PM
To: r-help at R-project.org
Subject: [R] Comparing initial eigenvalues to broken stick
results

I am trying to create a function that will allow me to determine
the number of components to retain based on the results of the
broken stick criterion.  In order to do so I know I need to
compare the initial eigen values to the broken stick eigen
values.  The initial eigen value which becomes lower than the
broken stick is the cutoff point so the cutoff for the number of
components to retain is the number of eigen values before this
cutoff points.

So far this is the syntax I have and what I get.

ev <- eigen(cor(EFAexample))
ev
bstick(24, tot.var=24)

> ev
\$values
[1] 7.2819381 2.3951299 1.8190170 1.6056666 0.9862474 0.9092235
0.8269931
[8] 0.7861644 0.6978157 0.6824547 0.6333925 0.5997783 0.5737571
0.5347758
[15] 0.4976710 0.4849214 0.4502025 0.4223273 0.3819080 0.3599697
0.3353226
[22] 0.3184069 0.2146300 0.2022866

> bstick(24, tot.var=24)
Stick1     Stick2     Stick3     Stick4     Stick5
Stick6     Stick7
3.77595818 2.77595818 2.27595818 1.94262484 1.69262484
1.49262484 1.32595818
Stick8     Stick9    Stick10    Stick11    Stick12
Stick13    Stick14
1.18310103 1.05810103 0.94698992 0.84698992 0.75608083
0.67274750 0.59582442
Stick15    Stick16    Stick17    Stick18    Stick19
Stick20    Stick21
0.52439585 0.45772918 0.39522918 0.33640566 0.28085010
0.22821852 0.17821852
Stick22    Stick23    Stick24
0.13059947 0.08514493 0.04166667

In this case the cutoff would be at stick 2 thus we would only
retain 1 component.  What syntax can I use to automatically make
this comparison instead of having to do it manually each time?

Also, am I using bstick correctly?  From what I understand I
should just have to enter the number of components and the total
variance which will be the total number of components.

Any help would be greatly appreciated.  Thanks!

Allyson
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