Abstract

GUERRERO, Sara C.  and  MELO, Oscar O.. A methodology for treating multicolinearity via multidimensional scaling. Ciencia en Desarrollo [online]. 2017, vol.8, n.2, pp.9-24. ISSN 0121-7488.

We present the multidimensional scaling analysis as an alternative strategy to treat the multicollinearity problem in the multiple regression analysis, when the regressor variables are qualitative, quantitative or mixed (quantitative and qualitative) and the response variable is continuous. Our purpose is to obtain the matrix of the principal coordinates, using as a metric the Gower distanc when the predictives variables are mixed, or otherwise, the researcher must select an appropriate Euclidean distance and with this matrix to estimate the regression model. To observe the kindness of the proposed method, two cases of simulation are realized: the first one without presence of multicolinearity and the second one with presence of multi-colinearity. Two application cases are illustrated, which were analyzed by [46] using multiple regressions. In both cases simulated and in the applications, the R package was used. The results of the simulations and applications are compared with the classical multiple regression and regression based on principal component. The analysis strategy proposal is an alternative modeling that corrects collinearity, and allows work with predicted variables without loss of information, Additionally, this technique when transforming the original variables into coordinates, in its modeling hides the effect of the observed variables, so that the results are not manipulated.

Keywords : Collinearity; Principal coordinates; Gower Distance; Multiple Regression; Principal Components.

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