Agriculture Reference
In-Depth Information
affected by treatments. Essentially, this method fits nested models with a ranging
number of parameters to the data set and then uses ANOVA to determine whether a
model with common parameters results in similar goodness-of-fit as that by a more
complex model with separate parameters for each treatment. This analysis is
powerful in a sense that it can statistically assess which parameter(s) are
significantly affected by treatments while simultaneously considering other model
parameters. For example, suppose that logistic models fit all the observed temporal
data, then it is possible to establish which of the three parameters (rate, maximum
disease, and the time to the inflection point) is affected by treatments and if so by
which treatments. An important prior requirement for using this method is that the
same curve type can fit all (or nearly all) observed epidemics.
8.5.8 Canonical correlation
All the methods described so far are mainly concerned with describing and
understanding the characteristics of observed temporal patterns of epidemics in
relation to treatments. These treatment factors are usually qualitative variables, e.g.
cultivars, fungicide, management strategy or quantitative variables but set at pre-
defined levels, e.g. temperature and humidity set at different levels of constant
values. However, we are often interested in relating temporal patterns of disease
development to other non-controllable qualitative or quantitative variables, such as
variables related to climatic conditions and soil structure etc. If only one disease
variable, e.g. rate parameter and AUDPC, is used, then a regression analysis may be
sufficient enough to establish a quantitative relationship. However, ordinary
regression analysis cannot be used to establish a relationship of a set of more than
one disease-related variable (dependent variables - DV) with another set of more
than one variable (independent variables - IV), which can be approached by
canonical correlation analysis.
Canonical correlation analysis is based on the canonical correlation matrix,
which is a product of four correlation matrices, between DVs (inverted), between
IVs (inverted), and between DVs and IVs, i.e.
−
1
−
1
R
=
R
R
R
R
. The objective
is to redistribute the variance in the original variables into very few pairs of
canonical variates, each pair capturing a large share of variance and defined by
combinations of IVs on one side and DVs on the other. Linear combinations are
chosen to maximise the canonical correlation for each pair of canonical variates.
There are two potential problems in using canonical correlation analysis. First, a
procedure that maximises correlation does not necessarily maximise interpretation of
pairs of canonical variates. Therefore, canonical solutions are often mathematically
elegant but difficult to interpret biologically. Second, the procedure only maximises
the linear relationship between two sets of variables. Scholosser
et al.
(2000) applied
the canonical correlation analysis to characterise the relationship between plant
morphological characters and disease variables in rice blast.
yy
yx
xx
xy
