Olfactometer experiments are used to study the responses of arthropods to potential attractants, for purposes such as understanding natural defenses of plants against their herbivores. Such experiments typically lead to multivariate data consisting of small correlated counts, which are overdispersed relative to standard models. In this paper models that account for the overdispersion under different hypotheses on insect behaviour are described and illustrated with an example, and a graphical approach to discriminating among them is briefly discussed.