Exploratory analysis of three-way data by simultaneous latent budget model (Q2711721)

The latent budget model can be fruitfully used to analyse tables with constant row sum data. Such a row vector is called observed budget and can include compositional data, time-budgets, mobility tables, budgets of preferences, or, in general, contingency tables with data collected under the product-multinomial sampling scheme with fixed row margins. The model approximates the observed budgets by a mixture of latent compositions called ``latent budgets''.NEWLINENEWLINENEWLINETwo estimation procedures are available. The first uses a maximum likelihood procedure EM-algorithm starting from probabilistic assumptions on the data. The second one is a constrained least-squares procedure for the estimation of the latent budget model when the probabilistic assumptions are violated. It is shown how the constrained least-squares procedure can be applied to the estimation of the unconstrained simultaneous latent budget model and to the model with across-group homogeneity constraints. An exploratory approach to the simultaneous model is thus proposed. The results are illustrated with some examples.