Modelos lineares generalizados na agronomia: análise de dados binomiais e de contagem, zeros inflacionados e enfoque bayesiano.

Abstract

The validation of any scientific research requires a correct statistical background. Despite the knowledge that statistics is a key element for the integrity of a investigation, its misuse is common in the Agricultural Sciences. In the first chapter, a bibliographical research was carried out in the journal “Science and Agrotechnology”, to discuss the statistical methods and mistakes found, stimulating more appropriate approaches to agronomic data. Because of the negligence with the statistics, the aim of this thesis was to spread techniques for the analysis of agronomic data that are still being used in an incipient way by researchers. Meanwhile, the second chapter presented techniques to analyze binomial and counting data, as well as the adjustment of zero inflation with three agronomic examples: germination of Peltogyne confertiflora (binomial data); biological control of cotton aphid Aphis gossypii Glover (counting data); and control of weed plants (binomial data). In each example, models to correct the overdispersion were adjusted. For the excess of zeros in the data, zero inflated models were presented for the cotton aphid example. The thesis is finished with the third chapter, applying the Generalized Additive Models (GAMs) in an experiment that aims to evaluate the effect of abiotic factors on the population of the aphid Brevicoryne brassicae. This chapter approaches models to control zero inflation and adjusts the autocorrelation of measurements over time. Frequentist methodologies and Bayesian analysis were applied through Monte Carlo Markov Chain (MCMC) simulation. Results demonstrate the importance to correct overdispersion from the negative binomial family. The autocorrelation was solved with ARMA structure, and the Bayesian model was able to construct the proposed model, with the only setback that data simulation consumed longer analysis time in detriment to other techniques. Fortunately, with the advancement of computer software, the results have been exhibited in less time: B. brassicae incidence, for example, showed that abiotic factors can be easily modeled and analyzed by GAMs.