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5. A FURTHER MODIFICATION OF GUTTMANN’S RULE IN DETERMINING THE NUMBER OF COMPONENTS IN PRINCIPAL COMPONENT ANALYSIS by Mohammed A., Zakari Y. and Muhammad I. Volume 52 (July & Sept., 2019 Issue)
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A FURTHER MODIFICATION OF GUTTMANN’S RULE IN DETERMINING THE NUMBER OF COMPONENTS IN PRINCIPAL COMPONENT ANALYSIS

Mohammed A., Zakari Y. and Muhammad I.

Division of Academic Planning, Federal Polytechnic, Bida, Nigeria.

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.

Department of Statistics, Binyaminu Usman Polytechnic, Hadejia, Nigeria.

Abstract

Principal components analysis is a widely used multivariate technique where by researchers attempt to reduce the dimension of a large number of interrelated variables into few non related variables and retaining as much as possible the variation present in the data set. To decide how many components to be retained in principal components analysis remained a very challenging task to researchers. A decision which if made wrongly has drastic effect. Several methods were introduced or modified in many studies. In this study, two new modifications were introduced. The first method looked at confidence intervals around each eigenvalue and components are retained, if the square root of the entire eigenvalue is greater than one (1.0). Method of Monte Carlo was used to simulate multivariate normal data for the analysis. Three different levels of sample size, components loading strengths and numbers of components were used to perform principal components analysis based on correlation matrix.  Results from this first method (HGR1) shows that the method is better than the traditional Guttmann rule (GR) and has the same bias as MGR. The second method (HGR2) uses the square root of eigenvalues, and then confidence intervals are constructed around these eigenvalues. Components are therefore selected if the entire confidence interval is greater than one (1.0). HGR2 was the best overall method in all conditions.

Keywords: Gutmann’s rule, principal component, eigenvalue, confidence interval

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