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Regression analysis for interval-valued symbolic data versus noisy variables and outliers

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Pełka M., Dudek A.
Econometrics. Ekonometria. Advances in Applied Data Analytics
|
2016
|
issue 2 (52)
35-42
EN
Regression analysis is perhaps the best known and most widely used method used for the analysis of dependence; that is, for examining the relationship between a set of independent variables (X’s) and a single dependent variable (Y). In general regression, the model is a linear combination of independent variables that corresponds as closely as possible to the dependent variable [Lattin, Carroll, Green 2003, p. 38]. The aim of the article is to present two suitable adaptations for a regression analysis of symbolic interval-valued data (centre method and centre and range method) and to compare their usefulness when dealing with noisy variables and/or outliers. The empirical part of the paper presents the results of simulation studies based on artificial and real data, without noisy variables and/or outliers and with noisy variable and outliers. The results are compared according to the values of two coefficients of determination 2 RL and 2 . RU The results show that usually the centre and range method obtains better results even when the data set contains noisy variables and outliers, but in some cases the centre method obtains better results than the centre and range method.
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Effectiveness of Symbolic Classification Trees Vs. Noisy Variables

100%
Dudek A., Pełka M., Chair of Econometrics and Informatics U. o. E.
Acta Universitatis Lodziensis. Folia Oeconomica
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2009
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vol. 228
PL
W rzeczywistych problemach badawczych często oprócz zmiennych istotnych mamy do czynienia ze zmiennymi zakłócającymi (nieistotnymi). Nie zawsze można dokonać wyboru zmiennych istotnych, np. za pomocą metody HINoV, lub zmodyfikowanej metody HINoV. W artykule porównano efektywność wykrywania znanej struktury klas za pomocą drzew klasyfikacyjnych dla obiektów symbolicznych oraz jądrowej analizy dyskryminacyjnej obiektów symbolicznych w sytuacji, gdy mamy do czynienia ze zmiennymi zakłócającymi. Badanie efektywności przeprowadzono na symulowanych danych symbolicznych w różnych modelach. Każdy z modeli zawierał znaną liczbę klas. Dodatkowo do każdego modelu dodano różną liczbę zmiennych zakłócających.
EN
In real research problems we usually deal with relevant variables and irrelevant (noisy) variables. Relevant variables sometimes can not be identified, by for example HINoV method or modified HINoV method. This paper compares effectiveness detection o f known class structure with application o f symbolic decision trees and symbolic kernel discriminant analysis in situation where we deal with noisy variables. This research was conducted on artificial symbolic data from a variety o f models. The models contained known structure o f clusters. In addition, the models contained different number o f noisy variables added to obscure the underlying structure.
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