Biology Reference
In-Depth Information
Corti, 2000
). Another important difference is that the coefficients produced by a CCA are
interpreted like partial regression coefficients, meaning that (as discussed above), each
coefficient indicates the contribution made by an independent variable when all others are
held constant. In this way, CCA, like multiple regression, is not well-suited to analyses in
which the variables within a block are correlated. As discussed above, constructing axes
that are mutually uncorrelated with each other within each block by a preliminary PCA
need not yield the same axes as those constructed by maximizing the covariances between
the two blocks.
PLS compared to Canonical Variates/Discriminant Analysis
PLS might not seem comparable to a CVA because PLS examines the relationship
between two blocks of variables whereas CVA discriminates between groups. However,
canonical correlation analysis and canonical variates analysis are closely related techniques
and PLS is related to both. PLS has been used to discriminate between groups, such as
between types of dementia (
Gottfries et al., 1995
) and even between years of a vintage port
wine (
Ortiz et al., 1996
). When used for purposes of discrimination, one block of variables
consists of codes that indicate an individual's membership in a group. The resultant scores
can then be inspected to assess the separation between groups (
Barker and Rayens, 2003;
Mitteroecker and Bookstein, 2011
). The procedure for discrimination by PLS is equivalent
to the method introduced in the last chapter, the Between-group PCA, when shape is one
block and (normalized) codes for the groups are the other (
Mitteroecker and Bookstein,
2011
). This approach is particularly useful when the number of variables greatly exceeds
the number of individuals; under these conditions, the results of a CVA can be what looks
like very large differences between groups even when the “groups” are random samples
from a single population.
APPLICATIONS OF PLS
PLS can be used to address a large range of biological questions about the relationship
between shape and other variables. To exemplify some of these applications, we consider
two cases in which both blocks comprise shape data, but the questions asked about the
relationships between the blocks differ and some of the methodological details also differ.
We also consider several applications that relate shape to other variables, surveying sev-
eral studies to show the diversity (and treatment) of those non-shape variables.
Using PLS as an Exploratory Tool to Characterize a Population: The Anterior
Human Dentition
The forensic discipline of bitemark analysis has come under scrutiny (
Rothwell, 1995;
Pretty and Sweet, 2001; Bowers, 2006; Pretty, 2006
;
NAS, 2009
) due to a number of criminal
convictions based on bitemark analysis that were later overturned based on DNA evidence
(
Bowers, 2006
). Forensic identification of post-mortem victims based on the examination of
