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

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

Generalized log odds ratio analysis for the association in two-way contingency table.

The odds ratio is a measure of association used both for the analysis of a contingency table and an contingency table, where I and J are bigger than 2. Nevertheless, the total number of odds ratios to check grows with I and J and several methods have been developed to summarize them. In the present paper we present a general framework for the analysis of the complete set of log odds ratio. Particularly we propose and connect two different methodologies performed on two different data sets. Moreover starting from these methodologies, we focus our attention on the factorial representation of the log odds ratios

The Rasch Model for Evaluating Italian Student Performance

In 1997 the Organisation for Economic Co-operation and Development (OECD) launched the OECD Programme for International Student Assessment (PISA) for collecting information about 15-year-old students in participating countries. Our study analyse the PISA 2006 cognitive test for evaluating the Italian student performance in mathematics, reading and science comparing the results of different local governments. For this purpose the most proper statistic methodology is Item Response Theory - IRT that collects several models, the simplest is Rasch Model – MR (1960). As the items used in the analysis are both dichotomous that polytomous, we apply Partial Credit Model (PCM)

CATANOVA for two-way cross classified categorical data

In this article we develop an extension of categorical analysis of variance for one response and two factors, based on a partitioning of a measure of predictability for three-way contingency tables, known as Gray and Williams’s index. At the first instance moment the decomposition of this multiple measure of association in partial association measures is shown. Finally, for ordinal-scale variables, we propose an extension of this decomposition using a particular set of orthogonal polynomials

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

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