Agriculture Reference
In-Depth Information
been significantly affected by treatments. This approach is commonly used in many
experimental or theoretical research investigations. AUDPC values revealed marked
differences between fungicides with different properties (protectant, eradicant and
curative) against leaf diseases in wheat (Hims and Cook, 1992). In a simulation
study on the use of cultivar mixtures to control race-specific and non race-specific
pathogens, the logistic rate parameter and AUDPC values were found to be
satisfactory in describing the differences in development of simulated epidemics (Xu
and Ridout, 2000b; see also Chapter 10).
If more than one variable is used to describe disease progress data, such as
principal components/factors and growth curve parameters, multivariate analysis of
variance can be conducted. Various test statistics may be employed to test the
significance of treatment effects on epidemic development. However, existence of
correlation between variables may reduce the power of MANOVA (Hair et al. ,
1998). Analysis of variance of multivariate but correlated data should be analysed
by the residual maximum likelihood (REML) method. This is particularly the case if
original temporal disease assessment data (i.e., not derived variables) are used.
8.5.2 Residual (restricted) maximum likelihood (REML)
REML was introduced by Patterson and Thompson (1971). REML is used for
analysis of linear mixed models (i.e., a linear model with both fixed and random
effects), estimation of variance components and modelling of covariance structures.
It has many applications, particularly in obtaining information on sources and sizes
of variability in data sets. In the context of analysing disease epidemiological data,
in addition to its use in analysing designed epidemiological experiments with more
than one source of variation (Piepho, 1999; Madden et al. , 2002), it can be used to
analyse temporal disease data as a design of repeated measurements.
The repeated measurement design is similar to split-plot designs. One of the
main objectives is to measure the within-subject effect in addition to the usual
objective of evaluating differences between subjects. In the epidemiological context,
the subject is the group of plants receiving the same treatment, while disease
assessed over time is the repeated measurement. In repeated measurements,
variables are no longer independent but correlated with each other, i.e. disease
measured on the same treatment at time t is expected to correlate with the disease at
time t-1 . One option of analysing repeated measurement data is to use univariate
repeated-measures analysis of variance using the split-plot design. However, high
temporal correlation between disease measurements may lead to overestimating the
effects involving time.
In addition to the expected correlation between successive disease assessments,
we also expect correlation to decrease with the interval between the two
assessments. Hence, correlation between assessments at time t and t+1 is likely to be
greater than between t and t+2 . This variable correlation structure in repeated
measurements can be accommodated in REML. REML has another advantage of
being able to provide efficient estimates of treatment effects in unbalanced designs
with more than one source of error.
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