Data analysis of flea beetle (Psylliodes chrysocephala L.): comparing three (3) distribution families of Generalized Linear Model

Abstract

Generalized linear models (GLMs) are used when the variance is not constant, and when the errors are not normally distributed. Some ecological and entomological response variables invariably suffer from these two standard assumptions, and GLMs are excellent at dealing with them. Three distribution families of GLM: (1) Linear, (2) Poisson and (3) Gamma, were fitted to the null, reduced and full models with the log link function. The data used was derived from a study on the cabbage flea beetle (Psylliodes chrysocephala L.). According to the residual deviance (Goodness of Fit) and Akaike information criterion (AIC) as an estimator of model quality, it was confirmed that Gamma GLM is the best fit for the data set. Both the AIC and deviance were low in the Gamma model, while high values were noted for Poisson and Linear GLMs. Our study confirms that severe skewness often exists in data sets pertaining to parasitology and entomology. The Gamma distribution provided a better and more robust alternative estimator than Poisson and Linear models. Poisson distribution is mostly used to model the count of events occurring within a given time interval. Poisson and linear GLMs did not fit well with the data set, which was evident by their high scaled deviance (G2).