Agriculture Reference
In-Depth Information
it is possible to define a factor analysis model in which the unexplained components
are chance effects, which leads to a statistical test as to whether a proposed model
fits the data satisfactorily. Often, PCA is conducted first to suggest number of
factors for FA.
The basic presentation of results, the terms used, and the interpretation are the
same as in PCA. Similarly, the initial solutions are usually rotated to improve
interpretation. Factor loadings of original variables are critical to interpreting factors
biologically or epidemiologically. One useful outcome of FA is the factor score,
which is the estimate the score subjects would have received on each of the factors
had they been measured directly. Because there are normally fewer factors than the
original variables, there is not a unique solution for expressing each factor as a
function of original variables. In general, several options are offered in common
statistical packages on how to calculate the factor scores.
Kranz (1968) identified six factors from 13 variables describing disease progress
curves of 40 pathosystems. In a study of bean hypocotyl rot, four factors were
identified from eight variables describing disease progress curves of 100 epidemics
(Campbell
et al.
, 1980b). These four factors were all given plausible epidemio-
logical interpretations.
8.5 COMPARING EPIDEMICS
One of the main objectives in epidemiological research is to compare epidemics so
that key differences between epidemics can be established and attributed to
treatments such as a cultivar and fungicide programme, to uncontrollable natural
climatic factors, and to inherent biological/epidemiological differences between
pathosystems. Usually, new variables derived from the original temporal disease
assessment data using the methods described above are used as input for comparing
epidemics, although original data can also be included.
Understanding the relationship of statistics describing temporal epidemic
characteristics with underlying physical and biological factors is the key to the
success of comparative epidemiology. Several studies (Xu and Ridout, 1998, 2000a,
2001) have clearly shown that spatio-temporal statistics are influenced greatly by
sampling schemes, such as sampling quadrat size/shape and orientation in relation to
prevailing wind, initial epidemic conditions and strength of prevailing wind, as well
as by biological parameters. Thus, caution may also be needed in interpreting the
observed differences between statistics reported in different studies since these
differences may reflect, at least in part, differences in non-biological factors such as
sampling details, initial conditions and wind conditions.
8.5.1 Analysis of variance (ANOVA)
A simple and straightforward analysis to compare different epidemics is to conduct
either a univariate or multivariate analysis of variance. For example, if AUDPC is
used to summarise temporal disease data, appropriate univariate ANOVA should be
sufficient to illustrate whether disease development as described by AUDPC has
