Comparison between normal and binomial distributions for modelling presence of ectoparasites in goats

Generalized Linear Model (GLM) allows choosing the distribution according to the dependent variable used. For dichotomous traits it is common to use binomial distribution with logit link function, which is also known as logistic regression. However, due to the central limit theorem, many distributions converge to the normal distribution, which is widely used in traditional multiple regression models. Thus, the purpose of this study was to compare the use of normal and binomial distributions in fitting a GLM for presence of ectoparasites in Anglo-Nubian goats in function of the dichotomous variables submandibular edema, rough hair coat, mange, caseous lymphadenitis, sex, farm and physiological status. Information of 962 female adult goats was used. Intensive farming system was predominant, in which animals received supplemented feed (voluminous and concentrate), with free access to mineralization and water. Sex, farm and physiological status were considered as systemic effects. Submandibular edema, rough hair coat, caseous lymphadenitis, ectoparasites and mange were firstly analyzed assuming normal distribution, and later binomial distribution was also tested. The generalized linear model methodology was used assuming that all traits were dichotomous. A logistic regression and a GLM were fitted with link function. The selection of the best model was carried out by means of the measure of fitting quality of models (AIC e BIC) and by residual analysis. AIC of normal and binomial GLM were -176.46 and 244.35, respectively. BIC were -68.77 and 347.36 for the traditional model and for the logistic, respectively. In both scenarios the normal model was the best, and the residual analysis showed to be more promising. The residuals of the normal model showed better QQ-plot graphics and an expected value in order 10^-16, which was lower than that of binomial model (10^-2). These results indicate a preference of the normal model when compared to the binomial, despite it does not represent an intuitive choose. It is noteworthy that the results showed in the present study are promising, however, a more powerful analysis should be performed in each scenario, aiming to avoid taking wrong decisions.