Neural Networks for Latent Budget Analysis of Compositional Data

Abstract

Compositional data are non-negative data collected in a rectangular matrix with a constant row sum. Due to the non-negativity the focus is on conditional proportions that add up to 1 for each row. A row of conditional proportions is called an observed budget. Latent budget analysis (LBA) assumes a mixture of latent budgets that explains the observed budgets. LBA is usually fitted to a contingency table, where the rows are levels of one or more explanatory variables and the columns the levels of a response variable. In prospective studies, there is only knowledge about the explanatory variables of individuals and interest goes out to predicting the response variable. Thus, a form of LBA is needed that has the functionality of prediction. Previous studies proposed a constrained neural network (NN) extension of LBA that was hampered by an unsatisfying prediction ability. Here we propose LBA-NN, a feed forward NN model that yields a similar interpretation to LBA but equips LBA with a better ability of prediction. A stable and plausible interpretation of LBA-NN is obtained through the use of importance plots and table, that show the relative importance of all explanatory variables on the response variable. An LBA-NN-K- means approach that applies K-means clustering on the importance table is used to produce K clusters that are comparable to K latent budgets in LBA. Here we provide different experiments where LBA-NN is implemented and compared with LBA. In our analysis, LBA-NN outperforms LBA in prediction in terms of accuracy, specificity, recall and mean square error. We provide open-source software at GitHub.