Comparison of prediction methods in multiple linear regression
1995
Fonton, H.N.
Poor predictive quality of the regression equations led us to examine the least squares principles which characterizes the used techniques. After scanning the literature on alternatives to least squares methods, thirteen variables selection methods and six methods of coefficient estimation were examined, thus providing 78 models of regression. These methods were chosen with regard to their specificity to reduce the mean square error of coefficient estimation or the selection bias. Simulation of linear models has been used to cover a wide range of data structures. 54 data structures were studied, 18 of them being characterized by a number of independent variables (k) superior to that of observations (n). Furthermore, three sets of real data are analysed for illustration purposes. The models are compared on the basis of the predictive quality, the accuracy of coefficient estimation as well as the adjustement quality. The results show the good performance of the biased estimators to approach the "true" model and reveal the unmeasured optimism of the least square method. The improvements of the predictive quality and the accuracy of the coefficient estimation of the alternative methods in comparison with least square are respectively of order of 3 per cent to 19 per cent and of 5 per cent to 60 per cent. The best models are the combinations of LAWLESS and WANG method with its derived selection method for k inferior to n and with stepwise for k superior to n. Despite the improvements attaining 15 per cent with regard to the reference model, these models bring an additional variability when k/n is too high. Consequently, practical recommendations are given.
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