Zero-inflated proportion data models applied to a biological control assay

Abstract

Biological control of pests is an important branch of entomology, providing environmentally friendly forms of crop protection. Bioassays are used to find the optimal conditions for the production of parasites and strategies for application in the field. In some of these assays, proportions are measured and, often, these data have an inflated number of zeros. In this work, six models will be applied to data sets obtained from biological control assays for Diatraea saccharalis , a common pest in sugar cane production. A natural choice for modelling proportion data is the binomial model. The second model will be an overdispersed version of the binomial model, estimated by a quasi-likelihood method. This model was initially built to model overdispersion generated by individual variability in the probability of success. When interest is only in the positive proportion data, a model can be based on the truncated binomial distribution and in its overdispersed version. The last two models include the zero proportions and are based on a finite mixture model with the binomial distribution or its overdispersed version for the positive data. Here, we will present the models, discuss their estimation and compare the results.

Annual indices of Atlantic bluefin tuna (Thunnus thynnus) larvae in the Gulf of Mexico developed using delta-lognormal and multivariate models

“…Recently, in many fields, it has become popular to model such data using regression models based on an assumption that the response is generated by a mixture of a standard count distribution (e.g. binomial, Poisson, or negative binomial) with a degenerate distribution with point mass of one at zero, creating a zero-inflated distribution (Hall 2000;Vieira et al 2000). As mentioned earlier, Martin et al (2005) reports that there are currently no reported models in the literature for data with zero-inflation due to both true and false zeros, and the use of mixture models based ZIP or ZINB distributional assumptions may not account for "false zeros" when modeling the data.…”

Limited foraging flexibility: increased foraging effort by a marine predator does not buffer against scarce prey

“…Proportional data were modeled with a binomial distribution and logit link function. Overdispersion, which is common with proportional data in binomial models and can lead to underestimates of standard error, was corrected with the addition of a dispersion parameter ø that is equal to Pearson χ 2 / df estimated from the global model (Vieira et al 2000). In our global model, Pearson χ 2 / df = 4.346, suggesting overdispersed data; therefore, 4.346 was used as an estimate of ø in all models and ĉ for quasi-likelihood adjusted Akaike's information criteria (QAIC c ) calculations.…”

Spatio-temporal modelling of coffee berry borer infestation patterns accounting for inflation of zeroes and missing values

“…A literature review and a discussion on a general methodology to model zero inflated count data is presented in Ridout et al (1998), with emphasis in applications in horticulture. Some models for zero inflated data of proportions with applications to biological control assays are also presented in Vieira et al (2000). Other recent applications of non spatial Poisson and binomial zero inflated models can be found for instance in Hall (2000) and in a Bayesian context in Angers & Biswas (2003); Rodrigues (2003) and Ghosh et al (2006).…”