Agriculture Reference
In-Depth Information
variables to disease epidemic development. For example, Hennessy
et al.
(1990)
used discriminant function analysis to determine the relationship of climatic factors
with severity of sorghum leaf blight in South Africa.
Logistic regression analysis, which may be termed as logistic discriminant
analysis when used for classification, can be used where there are only two groups.
In contrast to the discriminant analysis approach, the logistic model treats the
classification variables (i.e. disease-related data) as predictors rather than response
variables. Hence there are no probabilistic assumptions made about the distribution
of these values. Consequently, the normality requirement of the discriminant model
does not apply to the logistic model. Under the logistic model, the random variable
is presumed to be the variable that indicates group membership. In addition, ordinal
and categorical variables can also be included as predictors in the logistic model.
8.5.6 Survival analysis
Often in plant disease epidemiology we are interested in when an event will occur
and how long it will take before it occurs. Examples of such an event may include
time to defoliation and time to ultimate plant death; these type of data usually
contain censored observation. In this sort of question, we are particularly interested
in whether the probability and the time-course for a specific event are related to the
amount of disease present. Several recent topics provide a more detailed statistical
treatment on analysis of survival data (Le, 1997; Kalbfleisch and Prentice, 2002) and
its application in plant disease epidemiology is provided by Scherm and Ojiamho
(2004). Weibull functions were derived for survivorship studies.
Principally, there are three applications of survival analysis in modelling
temporal epidemic data. First, it allows the estimation of survival time distributions
(e.g. survival and hazard function) for a group of individuals. Second, analysis can
be conducted to determine whether there are significant differences in survival time
distributions between groups. Finally, the effects of independent variables on the
survival variables can be quantified. Two main mathematical functions in survival
analysis are survival and hazard functions. The former is a cumulative distribution
function describing the probability that an individual will survive until time
t
; the
latter is the conditional probability density function describing the instantaneous risk
that an event will occur at time
t
. Scherm and Ojiamho (2004) provided an example
on how the survival analysis can be applied to plant disease epidemiology.
Specifically, they demonstrated how the analysis can be used to determine whether
Septoria
leaf spot on blueberry could result in greater defoliation of the diseased
leaves.
8.5.7 Fitting models with common parameters
Gilligan (1990) described a method for comparing epidemics by fitting common
parameters to growth models between treatments. He illustrated the power of the
method by constraining one or more common parameters to all treatments while
fitting the remaining parameters separately for identifying which parameter(s) are
