Luigi D’Ambra

Non-symmetric correspondence analysis and biplot representation: Comparing differences in market share distribution

In this paper Non-Symmetric Correspondence Analysis (NSCA, Lauro and D’Ambra, 1984; D’Ambra and Lauro, 1989, 1992) is proposed as a useful technique for evaluating contingency table with a dependence structure, in particular within the context of comparing market share differences. Technical aspects of the method are discussed with a view towards application, giving special attention to the biplot representation ofNSCA as compared to the symmetric graphical display. Two examples dealing with canned food and the car market, respectively, are used to illustrate the usefulness of the technique and its kind of representation.

Estimating the Relative Efficiency of Secondary Schools by Stochastic Frontier Analysis

Abstract This study has the aim of evaluating the efficiency of schools of secondary education. We used the first data (pilot survey) gathered from an official survey, in progress, performed by the school management of the Campania Region. The survey covers attributes regarding the environment, territorial context and economic resources. We adopted the Stochastic Frontier Analysis to estimate the efficiency and a Tobit regression model in order to discuss which factors might affect the efficiency.

Joint Non-symmetrical Correspondence Analysis with Ordered Categories

In this paper we study the dependence relationship among a response and two or more predictor variables in a flattened contingency table. Considering ordinal categorical variables, the main aim is to preserve the ordinal compliance of categories by using a monotone function and optimal scaling for the first axis and Partial Least Squares for the remaining ones.

Generalized Constrained Principal Component Analysis

This paper deals with a non-symmetrical analysis of two multiple data sets in order to study the structure of dependence among sets of variables which play different role in the analysis. This approach represents a generalization of the Constrained Principal Component Analysis (CPCA) (D’Ambra and Lauro, 1982).

Decomposition of cumulative chi-squared statistics, with some new tools for their interpretation

It is well known that the Pearson statistic

Design, Implementation and Validation of a Questionnaire for University Teaching Evaluation

\chi ^{2}

Multivariate co-inertia analysis for qualitative data by partial least squares

χ2 can perform poorly in studying the association between ordinal categorical variables. Taguchi’s and Hirotsu’s statistics have been introduced in the literature as simple alternatives to Pearson’s chi-squared test for contingency tables with ordered categorical variables. The aim of this paper is to shed new light on these statistics, stressing their interpretations and characteristics, providing in this way new and different interpretations of these statistics. Moreover, a theoretical scheme is developed showing the links between the different proposals and classes of cumulative chi-squared statistical tests, starting from a unifying index of heterogeneity, unalikeability and variability measures. Users of statistics may find it attractive to understand well the different proposals. Some decompositions of both statistics are also highlighted. This paper presents a case study of optimizing the polysilicon deposition process in a very large-scale integrated circuit, to identify the optimal combination of factor levels. It is obtained by means of the information coming from a correspondence analysis based on Taguchi’s statistic and regression models for binary dependent variables. A new optimal combination of factor levels is obtained, different from many others proposed in the literature for this data.

Fuzzy Correlation and Fuzzy Non-linear Regression Analysis

ABSTRACT 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.