Some methods allowing for aggregated patterns of disease incidence in the analysis of data from designed experiments

Analysing disease incidence data from designed experiments by generalized linear mixed models

“…Hughes & Madden (1995) found that for the mildew data aggregation varied among treatments. Model (2) is readily modified to account for variable aggregation by assuming that the variance of e ijkl depends on treatment, i.e.…”

“…Parameter estimates based on both models are given in Table 4. For comparability, estimates of the same parameters as reported in Hughes & Madden (1995) are shown. Since the models are overparameterized, the restriction ␣ 1 ¼ 0 was used.…”

“…the beta-binomial model, William's (1982) models II and III, and extensions thereof as suggested by Moore (1987). These approaches, which are extensions of the usual GLM, have been nicely reviewed by Anderson (1988), Collett (1991), Hughes & Madden (1995) and Hinde & Demétrio (1998). Unfortunately, most of these methods are not easily extended to the case were there are several sources of random variation.…”

“…A real example is used for demonstrating the flexibility of the approach. Hughes & Madden (1995) report data from an experiment on the incidence of downy mildew (Plasmopara viticola) of grape (Vitis lambrusca). Six different disease control treatments were tested in a randomized complete block design with three replications.…”

“…Because of violation of the independence assumption, however, the variance of disease incidence data is frequently greater than expected under the binomial model. The independence assumption is often violated, because incidence of disease tends to be clustered or aggregated (Hughes & Madden, 1995). The resulting overdispersion needs to be allowed for in statistical analysis.…”