In applied statistics, a frequent problem that the researchers have to solve is the reduction of the statistical variables. The classical statistics faces the reduction of variables by the principal components analysis (PCA), a well known multivariate procedure that carry out transformation of the original variables in some new variables that have to be linear combination of the original ones, have to possess the maximum variance and have to be uncorrelated among them (Härdle and Simar, 2004). The reduction of variables problem has been faced also by Statistical Implicative Analysis (SIA). SIA is based on the cohesion concepts (Gras 2000) and two kinds of variables are identified as “intrinsic” (principal) and “extrinsic” (additional). Thanks to the contribution that each variable furnishes to the class constitution, the implicative power can be evaluated. The concept of distance between two variables or between a variable Ai with all other variables Aj in a class (Counturier et al, 2004) individualizes the leader of a variables class. Blanchard et al. (2002) propose an implicative statistical criterion, based on inertia index in order to reduce the number of variables. The purpose of the present paper is to expose the main methodological issues of SIA for the reduction of variables, to compare this approach to PCA and to apply them on the same data related to matriculation propensity in a sample of students attending the last year of high school in Messina. This application of SIA and PCA for variables reduction on social data shows the concordance between the results obtained by the two different approaches; therefore their combined use may be useful to have a better guarantee of results.

### Statistical Implicative Analysis and Principal Components method: a comparison between two approaches for the analysis of social data

#### Abstract

In applied statistics, a frequent problem that the researchers have to solve is the reduction of the statistical variables. The classical statistics faces the reduction of variables by the principal components analysis (PCA), a well known multivariate procedure that carry out transformation of the original variables in some new variables that have to be linear combination of the original ones, have to possess the maximum variance and have to be uncorrelated among them (Härdle and Simar, 2004). The reduction of variables problem has been faced also by Statistical Implicative Analysis (SIA). SIA is based on the cohesion concepts (Gras 2000) and two kinds of variables are identified as “intrinsic” (principal) and “extrinsic” (additional). Thanks to the contribution that each variable furnishes to the class constitution, the implicative power can be evaluated. The concept of distance between two variables or between a variable Ai with all other variables Aj in a class (Counturier et al, 2004) individualizes the leader of a variables class. Blanchard et al. (2002) propose an implicative statistical criterion, based on inertia index in order to reduce the number of variables. The purpose of the present paper is to expose the main methodological issues of SIA for the reduction of variables, to compare this approach to PCA and to apply them on the same data related to matriculation propensity in a sample of students attending the last year of high school in Messina. This application of SIA and PCA for variables reduction on social data shows the concordance between the results obtained by the two different approaches; therefore their combined use may be useful to have a better guarantee of results.
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2010
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/1901703`
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