Serial nonparticipation in nonmarket valuation using choice data is a pattern of behavior in which an individual always appears to choose the status quo or ‘no program’ alternative. From a choice modelling perspective serial nonparticipation may be viewed as belonging to a class of ‘discontinuous preferences,’ which also includes other behavioral patterns, such as serial participation (never choosing the status quo), as well as lexicographic preferences (e.g. always choosing the alternative with the greatest health benefit). Discontinuous preferences are likely to be especially relevant in the context of environmental goods, due to the lack of familiarity that individuals have with valuing these goods in markets. In the case of discrete choice data, logit-based choice models are ill-equipped for identifying such preferences, because conditional logit choice probabilities cannot take a value of zero or one for any finite parameter estimates. Here we extend latent class choice models to account for discontinuous preferences. Our methodological innovation is to specify for each latent class a subset of alternatives that are avoided with certainty. This results in class membership being partially observable, since we then know with certainty that an individual does not belong to a class if she selects any alternatives avoided by that class. We apply our model to data from a discrete choice experiment on mosquito control programs to reduce West Nile virus risk and nuisance disamenities in Madison, Wisconsin. We find that our ‘generalized latent class model’ (GLCM) outperforms standard latent class models in terms of information criteria metrics, and provides significantly different estimates for willingness-to-pay. We also argue that GLCMs are useful for identifying some alternatives for which valuation estimates may not be identified in a given dataset, thus reducing the risk of invalid inference from discrete choice data.