Dimensionality reduction methods for contingency tables with ordinal variables

Correspondence analysis is a widely used tool for obtaining a graphical representation of the interdependence between the rows and columns of a contingency table, by using a dimensionality reduction of the spaces. The maximum information regarding the association between the two categorical variables is then visualized allowing to understand its nature. Several extensions of this method take directly into account the possible ordinal structure of the variables by using different dimensionality reduction tools. Aim of this paper is to present an unified theoretical framework of several methods of correspondence analysis with ordinal variables

Cumulative chi-squared statistics for the service quality improvement: new properties and tools for the evaluation

In service quality evaluation, data are often categorical variables with ordered categories and collected in two way contingency table. The Taguchi’s statistic is a measure of the association between these variables as a simple alternative to Pearson’s test. An extension of this statistic for three way contingency tables handled in two way mode is introduced.We highlight its several properties, the approximated distribution, a decomposition according to orthogonal quantities reflecting the main effects and the interaction terms, and an extension of cumulative correspondence analysis based on it

CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods

In the context of categorical data analysis, the CATegorical ANalysis Of Variance (CATANOVA) has been proposed to analyse the scheme variable-factor, both for nominal and ordinal variables. This method is based on the C statistic and allows to test the statistical significance of the tau index using its relationship with the C statistic. Through Emerson orthogonal polynomials (EOP) a useful decomposition of C statistic into bivariate moments (location, dispersion and higher order components) has been developed. In the construction of EOP the categories are replaced by scores, typically natural scores. In the paper, we provide an overview of the main scoring schemes focusing on the advantages and the statistical properties; we pay special attention to the impact of the chosen scores on the C statistic of CATANOVA and the graphical representations of doubly ordered non-symmetrical correspondence analysis. Through a real data example, we show the impact of the scoring schemes and we consider the RV and multidimensional scaling as tools to measure similarity among the results achieved with each method

Weighted log ratio analysis by means of Poisson factor models: a case study to evaluate the quality of the public services offered to the citizens

In this paper we analyse the degree of dissatisfaction expressed by citizens regarding the quality of public services offered by municipalities in an average size city in the south of Italy. A previous study, carried out by multiple correspondence analysis, showed that the degree of dissatisfaction was closely linked to the age and education level of interviewed subjects, and the urban area (neighbourhood) in which they lived. On the basis of this result, we created two contingency tables. The first contingency, N , represents a cross classification of n dissatisfied individuals based upon three variables: Urban area (residential neighbourhood), age, and education. Taking population distribution (based on Age and Education) within each neighbourhood into account, we considered another table, S , which intersects the same variable and represents the target population. We started with a Goodman RC(M) association model, and obtained a weighted log ratio analysis. In particular, we propose a weighted log ratio analysis using Poisson factor models that explicitly considers count nature and automatically incorporates an offset. Moreover, we have compared the results of the log ratio analysis with and without offset by means of the RV coefficient

Correspondence Analysis with Linear Constraints of Ordinal Cross-Classifications

Correspondence analysis, Ordinal correspondence analysis, Linear constraints, External information, Orthogonal polynomials,

A Panel Data Approach to Evaluate the Passenger Satisfaction of a Public Transport Service

AbstractIn the present work we analyze the passenger satisfaction of a public transport service by means of a panel data approach. Improving the quality and efficiency of public transport is important if we are to change the daily transport habits of the public. The congestion in urban areas and its immediate and wider consequences on the climate are pushing central and local governments to instigate sustainable transport policies. These policies require an ever more personalised attention to the desires of the customer, to know and quantify the most influential variables on their decision to travel in public transport. The quality of a public transport system is covered by many factors, such as considerations relative to comfort and safety within the vehicle, the time taken to cover the routes and the convenience and existence of any supporting infrastructure. The techniques that we have used to analyse the panel data are: fixed effects and random effects