Generalized linear models with random effects for the description of data with excess zeros

Abstract. In this paper count data with excess zeros and repeated observations per subject are evaluated. If the number of values observed for the zero event in the trial substantially exceeds the expected number (derived from the Poisson or from the negative binomial distribution), then there is an excess of zeros. Hurdle and zero-inflated models with random effects are available in order to evaluate this type of data. In this paper both model approaches are presented and are used for the evaluation of the number of visits to the feeder per cow per hour. Finally, for the analysis of the target trait a hurdle model with random effects based on a negative binomial distribution was used. This analysis was derived from a detailed comparison of models and was needed because of a simpler computer implementation. For improved interpretation of the results, the levels of the explanatory factors (for example, the classes of lactation) were not averaged in the link scale, but rather in the response scale. The deciding explanatory variables for the pattern of visiting activities in the 24-hour cycle are the milking and cleaning times at hours 4, 7, 12 and 20. The highly significant differences in the visiting frequencies of cows of the first lactation and those of higher lactations were explained by competition for access to the feeder and thus to the feed.