Biology Reference
In-Depth Information
configuration) or other reference. See also Consensus configuration, Procrustes superimposition, Reference
(Chapter 5).
Procrustes Size Preserving or Procrustes SP, is a Procrustes superimposition variant in which the superimposi-
tion is done using only translations and rotation, not scaling. Dryden and Mardia (1998) refer to this as the “size
and shape” of a configuration. It is possible to define a Procrustes SP distance as well. See also Procrustes Form
Space (Chapter 14).
Procrustes superimposition A superimposition of shapes that minimizes the Procrustes distances over the sam-
ple. The term is used whether the distance being minimized is the full or the partial Procrustes distance
(Chapter 4).
Red Book Bookstein, F.L., Chernoff, B., Elder, R.L. et al. (eds) (1985).
Morphometrics in Evolutionary Biology: The
Geometry of Size and Shape Change, with Examples from Fishes
. Academy of Natural Sciences of Philadelphia, Special
Publication No. 15. See also Black Book, Blue Book, Orange Book and White Book)
Reference, Reference form The shape to which all others are compared. It is the point of tangency between
Kendall's shape space and the tangent space. Because the linear approximation to Kendall's shape space may be
inaccurate when the point of tangency is far from the center of the distribution of specimens, the reference is usu-
ally chosen to minimize the distances between it and the other specimens
i.e. it is chosen to be the consensus
shape (Chapter 4).
Regression An analytic procedure for fitting a predictive model to data and assessing the validity of that model.
One variable is expressed as a function of the other, e.g.
Y
b
expresses
Y
as a linear function of
X
. The pre-
dictor variable(s) are the independent variable(s), and those variables predicted by the model are the dependent
variable(s). In the linear model above,
X
is the independent variable that predicts the dependent variable,
Y
. The
term “regression” comes from Francis Galton (1889), who concluded that offspring tend towards (regress
towards) the mean of the population. As stated by Galton in his law of universal regression, “each peculiarity in
a man is shared by his kinsman, but
on the average
, in a less degree”. Thus, the offspring of unusually tall fathers
regress towards the mean height of the population (Chapters 8, 9).
Relative warps Principal components of partial warp scores, sometimes weighted to emphasize components of
low or high bending energy (that weighting is done by setting the parameter
mX
5
1
α
to a value other than 0).
Originally, the term referred to an eigenanalysis of the variance
covariance matrix relative to the bending-energy
matrix, hence a new term was coined for these components (Bookstein, 1991). Currently, the term usually refers
to a conventional principal components analysis of partial warp scores. See also
Alpha
(
), Bending energy,
α
Partial warp scores, Principal components analysis (Chapter 5).
Repeated measurement error The level of variation that appears when a single specimen is repeatedly measured,
this quantity indicates the achievable level of precision in a particular approach to measurement. In landmark-
based methods, it is measured as the summed squared Procrustes distances of repeated measurements of a single
specimen about the mean of those measurements, or as the square root of this value, the RMS scatter.
Repeated median The median of medians, used in estimating the scaling factor and rotation angle by resistant-fit
superimposition methods such as RFTRA. The repeated median is more robust to large deviations than the
median or a least squares estimator. See also Resistant-fit superimposition, RFTRA (Chapter 4).
Resampling A method whereby a new data set is constructed by randomly selecting from the original data
(either values recorded on specimens or residuals from a model). Construction of a large series of resampled data
sets can be used to simulate either the distribution of measured values or the distribution of a test statistic under
the null model. Under some conditions, resampling can also be used to produce confidence intervals around the
statistic. This approach permits hypothesis tests when the data are expected to deviate from the distributional
assumptions of conventional analytic tests. Resampling may be done with replacement, meaning that each obser-
vation can appear more than once in a resampled data set; resampling without replacement means each observa-
tion appears only once in a set. See also Bootstrap test, Jackknife test, Permutation test (Chapters 8, 9).
Rescale Multiply or divide by a scalar value; used in geometric morphometrics to change the centroid size of a
configuration (Chapters 3, 4).
Residual Deviation of an observation from the expected value under a model. For example, a residual from a
regression is the deviation between the observed and expected values of the dependent variable at a given value
