ANalysis Of VAriance (ANOVA) is a method to decompose the total variation of the observations into sum of variations due to different factors and the residual component. When the data are nominal, the usual approach of considering the total variation in response variable as measure of dispersion about the mean is not well defined. Light and Margolin (1971) proposed CATegorical ANalysis Of VAriance (CATANOVA), to analyze the categorical data. Onukogu (1985) extended the CATANOVA method to two-way classified nominal data. The components (sums of squares) are, however, not orthogonal. Singh (1996) developed a CATANOVA procedure that gives orthogonal sums of squares and defined test statistics and their asymptotic null distributions. In order to study which exploratory categories are influential factors for the response variable we propose to apply Non-Symmetrical Correspondence Analysis (D'Ambra and Lauro, 1989) on significant components. Finally, we illustrate the analysis numerically, with a practical example.

Visualization of the Significant Explicative Categories using Catanova Method and Non-Symmetrical Correspondence Analysis for Evaluation of Passenger Satisfaction

D'AMBRA, LUIGI
2010

Abstract

ANalysis Of VAriance (ANOVA) is a method to decompose the total variation of the observations into sum of variations due to different factors and the residual component. When the data are nominal, the usual approach of considering the total variation in response variable as measure of dispersion about the mean is not well defined. Light and Margolin (1971) proposed CATegorical ANalysis Of VAriance (CATANOVA), to analyze the categorical data. Onukogu (1985) extended the CATANOVA method to two-way classified nominal data. The components (sums of squares) are, however, not orthogonal. Singh (1996) developed a CATANOVA procedure that gives orthogonal sums of squares and defined test statistics and their asymptotic null distributions. In order to study which exploratory categories are influential factors for the response variable we propose to apply Non-Symmetrical Correspondence Analysis (D'Ambra and Lauro, 1989) on significant components. Finally, we illustrate the analysis numerically, with a practical example.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/364943
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