Random effects in cumulative mortality models
Résumé
In toxicological experiments for biological pest control, experiments frequently involve the study of cumulative mor tality in a groups of insects measured at various time points. Samples o f different strains, or isolates, of the compound under stud y are used, typically with some replication. The example conside red here is from a study of a microbial control to insect damag e in sugar cane. Cumulative multinomial models provide an obv ious approach to the analysis of these data, however, the bas ic model needs to be extended to account for overdispersion. He re we consider various random effect models, including the Dirichlet-multinomial and models with random effects in th e linear predictor. For some simple time trend models, fittin g using a generalized estimating equation approach leads to a surpri singly simple modification of the multinomial fit and casts li ght on the behaviour in more complex models. Other approaches conside red include quadrature methods for normal random effects. W e also consider modelling isolates as a random effect, with a m ixture distribution to cluster isolates with similar actio n, together with other replicate random effects for overdispersion.