Modeling Overdispersion, Autocorrelation, and Zero-Inflated Count Data Via Generalized Additive Models and Bayesian Statistics in an Aphid Population Study.

Count variables are often positively skewed and may include many zero observations, requiring specific statistical approaches. Interpreting abiotic factor changes in insect populations of crop pests, under this condition, can be difficult. The analysis becomes even more complicated because of possible temporal or spatial correlation, irregularly spaced data, heterogeneity over time, and zero inflation. Generalized additive models (GAM) are important tools to evaluate abiotic factors. Moreover, Markov chain Monte Carlo (MCMC) techniques can be used to fit a model that contains a temporal correlation structure, based on Bayesian statistics (BGAM). We compared methods of modeling the effects of temperature, precipitation, and time for the Brevicoryne brassicae (L.) population in Uberlândia, Brasil. We applied the proposed BGAM to the data, comparing this to the GAM model with and without autocorrelation for time, using the statistical programming language R. Analysis of deviance identified significant effects of the smoothers for precipitation and time on the frequentist models. With BGAM, the problem in variance estimations for precipitation and temperature from the previous models was solved. Furthermore, trace and density plots for population-level effects for all parameters converged well. The estimated smoothing curves showed a linear effect with an increase of precipitation, where lower precipitation indicated no presence of the aphid. The average temperature did not affect the aphid incidence. Autocorrelation was solved with ARMA structures, and the excess of zero was solved with zero-inflation models. The example of B. brassicae incidence showed how well abiotic (and biotic) factors can be modeled and analyzed using BGAM.