Agriculture Reference
In-Depth Information
ARMA model can be further extended to describe periodic (seasonal, cyclic)
patterns. Analysis of spore trapping data of apple powdery mildew over five years
revealed that the temporal pattern of the number of airborne conidia was similar in
all five years (Xu
et al.
, 1995).
TF models are an extension of ordinary regression models; they recognise
temporal dependence within both the dependent and independent variables. In a
TF model, the current value of the dependent variable can be related to the current
and previous values of an independent variable. There may be a time lag before an
independent variable affects the dependent variable. An important difference
between TF models and ordinary regression models is in the assumption
concerning the random component {e
t
}. In ordinary regression, successive values
of {e
t
} are assumed to be independent, whereas in TF models these values are
assumed to follow an ARIMA model. It is also straightforward to model the
persistent effect of an independent variable, for example, the long-lasting effects
of a rain event on sporulation and dispersal. Results from TF analysis can be very
useful in developing ordinary regression models for predicting spores. For
example, a regression model was developed on the basis of TF analysis and this
model satisfactorily predicted the temporal pattern of conidium numbers for apple
powdery mildew (Xu
et al.
, 1995).
8.4 REDUCING DATA DIMENSION
All the methods described so far can be applied to original temporal disease
assessment data for each individual epidemic, first with a view to understanding the
epidemic pattern by summarising the observed pattern in a few parameters or
statistics. These derived variables can then be used in a second stage analysis if
necessary, where the emphasis is on evaluating treatment effects and comparing
characteristics of different epidemics. For this second stage, the fewer variables
describing observed epidemic patterns will result in easier analysis and
interpretation of the results. Since a single method is not likely to describe an
observed epidemic pattern completely, the derived statistics from more than one
method can be included in the second stage analysis. Furthermore, in addition to
these derived statistics as described above, researchers may also include other
variables related to disease development or crop loss due to disease injuries, such as
the level of initial inoculum and disease incidence/severity at a particular host
growth stage. Since these variables describe the same epidemics, high correlations
among them are expected. Given the high correlation, we may be able to describe
key features with fewer variables. Then one can use these newly derived variables
for further analysis. There are several methods that are designed for the purpose of
reducing data dimensions while maintaining the key features in the original data
sets. Here, only principal component and factor analyses are briefly described. For a
more thorough understanding of these and other related methods, the reader is
referred to many excellent topics, such as Hair
et al.
(1998) and Tabachnick and
Fidell (2000).
