Comparison of the performance of multi-layer perceptron and linear regression for epidemiological data

Neural networks are used increasingly as statistical models. The performance of multilayer perceptron (MLP) and that of linear regression (LR) were compared, with regard to the quality of prediction and estimation and the robustness to deviations from underlying assumptions of normality, homoscedasticity and independence of errors. Taking into account those deviations, five designs were constructed, and, for each of them, 3000 data were simulated. The comparison between connectionist and linear models was achieved by graphic means including prediction intervals, as well as by classical criteria including goodness-of-fit and relative errors. The empirical distribution of estimations and the stability of MLP and LR were studied by re-sampling methods. MLP and linear regression had comparable performance and robustness. Despite the flexibility of connectionist models, their predictions were stable. The empirical variances of weight estimations result from the distributed representation of the information among the processing elements. This emphasizes the major role of variances of weight estimations in the interpretation of neural networks. This needs, however, to be confirmed by further studies. Therefore MLP could be useful statistical models, as long as convergence conditions are respected. (C) 2002 Elsevier B.V. All rights reserved.