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Antimicrobial resistance in livestock is a matter of general concern. To develop hygiene measures and methods for resistance prevention and control, epidemiological studies on a population level are needed to detect factors associated with antimicrobial resistance in livestock holdings. In general, regression models are used to describe these relationships between environmental factors and resistance outcome. Besides the study design, the correlation structures of the different outcomes of antibiotic resistance and structural zero measurements on the resistance outcome as well as on the exposure side are challenges for the epidemiological model building process. The use of appropriate regression models that acknowledge these complexities is essential to assure valid epidemiological interpretations. The aims of this paper are (i) to explain the model building process comparing several competing models for count data (negative binomial model, quasi-Poisson model, zero-inflated model, and hurdle model) and (ii) to compare these models using data from a cross-sectional study on antibiotic resistance in animal husbandry. These goals are essential to evaluate which model is most suitable to identify potential prevention measures. The dataset used as an example in our analyses was generated initially to study the prevalence and associated factors for the appearance of cefotaxime-resistant Escherichia coli in 48 German fattening pig farms. For each farm, the outcome was the count of samples with resistant bacteria. There was almost no overdispersion and only moderate evidence of excess zeros in the data. Our analyses show that it is essential to evaluate regression models in studies analyzing the relationship between environmental factors and antibiotic resistances in livestock. After model comparison based on evaluation of model predictions, Akaike information criterion, and Pearson residuals, here the hurdle model was judged to be the most appropriate model.