A Multidimensional Unfolding Latent Trait Model for Binary Data

We introduce a multidimensional latent trait model for binary data with non-monotone item response functions. We assume that the conditional probability of endorsing an item is a normal probability density function, and that the latent traits are normally distributed. The model yields closed form expressions for the moments of the multivariate Bernoulli (MVB) distribution. As a result, cell probabilities can be computed also in closed form, regardless of the dimensionality of the latent traits. The model is an ideal point model in the sense that a respondent - precisely at the ideal point (the mode of the item response function) - endorses the item with probability one.