This master’s thesis investigates how well a generalized mixed model fits different dominance data sets. The data sets mainly represent disputes between individuals in a closed group, and the model to be used is an adjusted, intransitive extension of the Bradley-Terry model. Two approaches of model fitting are applied; a frequentist and a Bayesian one. The model is fitted to the data sets both with and without random effects (RE) added. The thesis investigates the relationship between the use of random effects and the accuracy, significance and reliability of the regression coefficients and whether or not the random effects affect the statistical significance of a term modelling intransitivity. The results of the analysis in general suggest that models including random effects better explain the data than models without REs. In general, regression coefficients that appear to be significant in the model excluding REs, seem to remain significant when REs are taken into account. However the underlying variance of the regression coefficients have a clear tendency to increase as REs are included, indicating that the estimates obtained may be less reliable than what is obtained otherwise. Further, data sets fitting to transitive models without REs taken into account also, in general, seem to remain transitive when REs are taken into account.