Agriculture Reference
In-Depth Information
on different scales such as the estimated logistic rate, maximum disease and
AUDPC.
PCA was applied to various epidemic variables in order to select the best subset
of variables with the highest explanatory capacity to describe observed 60 disease
progress curves of papaya ringspot (papaya ringspot virus type P [PRSV-P])
incidence on papaya (Mora-Aguilera
et al.
, 1996). Standardised area under disease
progress curve, shape parameter of the Weibull distribution function, and time
between transplant date and first symptoms were selected as the most important
variables and represented 83.5% of the overall variance. These selected variables
were then used in cluster analysis. In analysing the effects of sowing date on
Fusarium
wilt of chickpea, PCA was applied to a set of epidemic variables,
including final disease intensity, AUDPC and parameters from the fitted Richards
model over 108 epidemics (Navas-Cortes
et al.
, 1998). Three components,
accounting for c. 98% of the total variance, were retained and they provided
plausible epidemiological interpretations: representing a temporal positional factor,
the AUDPC/final disease and the uniqueness of the estimated value for the point of
inflection, respectively. PCA scores for the retained components can also be used as
independent variables in regression analysis.
8.4.2 Factor analysis
The goal of factor analysis (FA) is to reproduce the correlation matrix of the original
data set with a few factors. In general, the PCA and FA share the specific goal of
summarising observed correlation patterns to a small number of components or
factors. PCA analyses variance whereas FA analyses covariance. PCA is a unique
mathematical solution whereas most forms of FA are not unique. In factor analysis,
the variation in the original data set is assumed to arise from a set of common
unknown explanatory variables (factors); these unknown factors are often called
latent variables. Each original variable is a linear combination of these unknown
factors. In general, if there are
p
variables, the relations between the
p
measured
(and/or derived) variables on disease development,
y
1
,
y
2
,…,
y
p
and the
n
factors (
f
1
,
f
2
,…,
f
n
) are
y
=
w
f
+
w
f
+
…
+
w
f
+
e
1
11
1
12
2
1
n
n
1
…
y
=
w
f
+
w
f
+
+
w
f
+
e
(8.11)
2
21
1
22
2
2
n
n
2
…
y
=
w
f
+
w
f
+
+
w
f
+
e
p
p
1
1
p
2
2
pn
n
p
The term
e
i
is an unexplained component (sometimes called unique component). The
underlying theory for FA is that the observed variables are correlated because they
are constructed from common factors. The greater the contribution from the
common factor, the higher will be the correlation between observed variables. It is
the correlation matrix of the original data that provides the information from which
the number of common factors and the weighting (
w
ij
) are determined. Unlike PCA,
