Unconditional Latent Budget Analysis: a Neural Network Approach

The latent budget model is a reduced rank model for the analysis of compositional data. The model can be also understood as a supervised neural network model with weights interpreted as conditional probabilities. Main advantage of this approach is that a classification rule for budget data can be defined for new observed cases. In this paper, a constrained (weighted) least-squares algorithm — which is alternative to the one already introduced in literature for standard latent budget model — is proposed for the estimation of the parameters. A distinction is made between conditional latent budget analysis (the standard approach) and unconditional latent budget analysis (the neural network approach).