In many situations the available amount of data is huge and can be intractable. When the data set is single valued, latent structure models are recognized techniques, which provide a useful compression of the information. This is done by considering a regression model between observed and unobserved (latent) fuzzy variables. In this paper, an extension of latent structure analysis to deal with fuzzy data is proposed. Our extension follows the possibilistic approach, widely used both in the cluster and regression frameworks. In this case, the possibilistic approach involves the formulation of a latent structure analysis for fuzzy data by optimization. Specifically, a non-linear programming problem in which the fuzziness of the model is minimized is introduced. In order to show how our model works, the results of two applications are given.