Discrete Choice Models with Changing Availability

Abstract

In the analyses of previous chapters, resource availability has been modelled as constant over the study period and in most cases with equal availability for individual animals. Often this is reasonable, but in some cases availability changes either with time or individual animals. In that case one approach for data analysis that can sometimes be used is based on discrete choice models, which are also sometimes called polytomous regression models. This approach is covered in the present chapter, with examples based on ice selection by polar bears and estimation of ocean habitat by seabirds. Discrete choice models assume resources are selected in a series of choices, and that a unique set of resource units is available at each choice. The unique set of choices is called the choice set. For example, a choice set might be defined as a number of alternative locations within a small geographic area, of which one is chosen for use by an animal. Then as the animal moves, the choice set changes. Or, an animal might be presented with food items A, B, and C, at one point in time, but the choice might be from food items A, B, and D, at another point in time. With a discrete choice model for resource selection, the ith choice is described by (i) the choice set of resource units (habitat or food) that are available to be chosen; and (ii) values for variables that characterize all resource units in the choice set (e.g., vegetation type, elevation, etc.). There is extensive literature on discrete choice models in situations where humans make the choice (Manski, 1981; McCracken et al., 1998). In fact, there are several alternative models that have been proposed, including the nested logit, multinomial probit, and generalized extreme-value. However, only the most popular model will be considered here, which is variously called polytomous regression, nominal regression and the multinomial logit model. Here the assumption that will be made is that: 150 At the ith choice there are alternative resource units available to an animal, each of which is described by the p variables such that the values of these variables for the jth unit are and that the probability of the jth unit being selected for during the ith choice is proportional to an exponential function of a linear combination of the X variables. 8.1 The Theory of Discrete Choice Models