-------- Original Message --------
Subject: Re: PGLS troubles
Date: Mon, 25 Feb 2008 10:56:10 -0800 (PST)
From: Philipp Mitteroecker <[EMAIL PROTECTED]>
To: [email protected]
References: <[EMAIL PROTECTED]>
Unlike canonical correlation analysis and multiple regression, there is
no big problem with sample size in PLS (no matrices need to be
inverted). Nevertheless, the observed covariances (the singular values)
or correlations increase when the sample size decreases relative to the
number of variables (see Mitteroecker & Bookstein 2007).
It seems that you only have one common factor in your data that drives
the PLS as the first dimension explains 94% of squared singular values
(and is nearly significant). The values do not add up to 1 because a 6th
dimension does exist. The number of extracted dimensions is min(p_1,
p_2, n-1), where p_1 and p_2 are the number of variables in block 1 and
2, respectively, and n is sample size.
Given your small sample size, a statistical test is probably meaningless.
Anyway, if the first dimension is not significant, it makes no sense to
interpret p-values of subsequent dimensions. There should be used a
different permutation approach for dimension 2 and higher than for the
first one (see Appendix in Mitteroecker & Bookstein 2008).
The different results of the two programs for the last few dimensions
could be due to rounding error. They seem to represent small spherical
noise that is uncorrelated between the two blocks.
Mitteroecker P, Bookstein FL (2007) The Conceptual and Statistical
Relationship between Modularity and Morphological Integration.
Systematic Biology 56 (5), 818–836.
Mitteroecker P, Bookstein FL (2008) The Evolutionary Role of Modularity
and Integration in the Hominoid Cranium. Evolution, in press, DOI:
10.1111/j.1558-5646.2008.00321
I hope this helps,
Philipp
--
Dr. Philipp Mitteröcker
Konrad Lorenz Institute for Evolution and Cognition Research, Austria
Department of Anthropology, University of Vienna, Austria
http://www.virtual-anthropology.com/Members/philippm
On Mo, 25.02.2008, 17:34, morphmet wrote:
-------- Original Message --------
Subject: PGLS troubles
Date: Sun, 24 Feb 2008 17:01:55 +0100
From: [EMAIL PROTECTED]
To: morphmet <[EMAIL PROTECTED]>
Dear morphometrician,
I am Carlo Meloro and I am conducting a research on macroevolutionary
integration in two portions of mammalian carnivore mandible (the
corpus mandibulae and the ascending ramus).
I am wondering if you could give me some suggestions on Partial Least
Square that I am using to validate the possible co-variation between
the two mandible portions.
I have several problems with the results obtained on the same landmark
dataset (separeted in two Blocks: Block 1 = shape variables after GPA
from 9 landmark configurations; Block 2 = shape variables after GPA
from 5 landmark configurations) independently on tpsPLS and Ntsys ver
2.20 N.
There are several discrepancies after the permutation test. Below I
report the output obtained for the same dataset of landmark data for
only 7 specimens. I suppose that there should be a problem of sample
size: do you know any problem associated to sample size in Partial
Least Square analysis?
I appreciate any help to understand this kind of results.
Thank you very much in advance,
Carlo Meloro
Below is the example with a small dataset of 7 specimens:
Results for 7 specimens (Block 1 = 9lnd, Block 2 = 5 lnd) with tpsPLs:
"
Number and percent of squared singular values >= observed
(Expressed as a proportion of the total.)
Dim. Observed Count Percent
1 0.939037 58 5.80%
2 0.049432 921 92.10%
3 0.007188 876 87.60%
4 0.003313 698 69.80%
5 0.000905 549 54.90%
Number and percent of cumulative squared singular values >= observed
(Expressed as a proportion of the total.)
Dim. Observed Count Percent
1 0.939037 58 5.80%
2 0.988470 137 13.70%
3 0.995657 309 30.90%
4 0.998970 422 42.20%
5 0.999876 367 36.70%
HERE THE CUMULATIVE PERCENTAGE DOES NOT APPROACH 100%
Number and percent of correlations >= observed
Dim. Observed Count Percent
1 0.780128 225 22.50%
2 0.479620 873 87.30%
3 0.770183 288 28.80%
4 0.663578 563 56.30%
5 0.615494 683 68.30%
6 0.589321 840 84.00%
"
From this report no correlation between Singular Axis is significant.
[Hide Quoted Text]
Same Results of permutation test from Ntsys:
"
(Note: counts include observed and small percentages imply "significance")
Number and percent of squared singular values >= observed
(Expressed as a proportion of the total.)
Dim. Observed Count Percent
1 0.939037 56 5.60%
2 0.049432 920 92.00%
3 0.007188 837 83.70%
4 0.000905 796 79.60%
5 0.000124 905 90.50%
Number and percent of cumulative squared singular values >= observed
(Expressed as a proportion of the total.)
Dim. Observed Count Percent
1 0.939037 56 5.60%
2 0.988470 130 13.00%
3 0.995657 279 27.90%
4 0.996563 722 72.20%
5 0.996687 801 80.10%
Number and percent of correlations >= observed:
Dim. Observed Count Percent
1 0.780128 51 5.10%
2 0.479620 81 8.10%
3 0.770183 12 1.20%
4 0.615494 92 9.20%
5 0.589321 62 6.20%
6 0.663578 26 2.60%
From this report the correlation obtained for Dimensions 3 and 6 are
significant. The first Dimension approaches significance at 0.05 level
(5.10 %).
Note that there is a large discrepancy in Number and percent of
correlations >= observed from tpsPLS and Ntsys output.
--
Replies will be sent to the list.
For more information visit http://www.morphometrics.org
--
Dr. Philipp Mitteröcker
Konrad Lorenz Institute for Evolution and Cognition Research, Austria
Department of Anthropology, University of Vienna, Austria
http://www.virtual-anthropology.com/Members/philippm
--
Replies will be sent to the list.
For more information visit http://www.morphometrics.org
