Investigating habitat selection of animals aims at the detection of preferred and avoided habitat types as well as at the identification of covariates influencing the choice of certain habitat types. The final goal of such analyses is an improvement of the conservation of animals. Usually, habitat selection by larger animals is assessed by radio-tracking or visual observation studies, where the chosen habitat is determined for a number of animals at a set of time points. Hence the resulting data often have the following structure: A categorical variable indicating the habitat type selected by an animal at a specific time point is repeatedly observed and shall be explained by covariates. These may either describe properties of the habitat types currently available and / or properties of the animal. In this paper, we present a general approach for the analysis of such data in a categorical regression setup. The proposed model generalises and improves upon several of the approaches previously discussed in the literature and in particular allows to account for changing habitat availability due to the movement of animals within the observation area. It incorporates both habitat- and animal-specific covariates, and includes individual-specific random effects in order to account for correlations introduced by the repeated measurements on single animals. The methodology is implemented in a freely available software package. We demonstrate the general applicability and the capabilities of the proposed approach in two case studies: The analysis of a songbird in South-America and a study on brown bears in Central Europe.