Sergio Camiz

Joint Correspondence Analysis Versus Multiple Correspondence Analysis: A Solution to an Undetected Problem

The problem of the proper dimension of the solution of a Multiple Correspondence Analysis (MCA) is discussed, based on both the re-evaluation of the explained inertia sensu Benzecri (Les Cahiers de l’Analyse des Donnees 4:377–379, 1979) and Greenacre (Multiple correspondence analysis and related methods, Chapman and Hall (Kluwer), Dordrecht, 2006) and a test proposed by Ben Ammou and Saporta (Revue de Statistique Appliquee 46:21–35, 1998). This leads to the consideration of a better reconstruction of the off-diagonal sub-tables of the Burt’s table crossing the nominal characters taken into account. Thus, Greenacre (Biometrika 75:457–467, 1988) Joint Correspondence Analysis (JCA) is introduced, the results obtained on an application are shown, and the quality of reconstruction of both MCA and JCA solutions are compared to that of a series of Simple Correspondence Analyses run on the whole set of two-way tables. It results that JCA’s reduced-dimensional reconstruction is much better than the MCA’s one, that reveals highly biased and non-monotone, but also than the MCA’s re-evaluation, as suggested by Greenacre (Multiple correspondence analysis and related methods, Chapman and Hall (Kluwer), Dordrecht, 2006).

Quantitative Study of Images in Archaeology: II. Symbolic Coding

For the analysis of a corpus of Mesopotamian seals, aiming at studying them on the image structure point of view, the problem of a suitable coding is discussed. For the analysis of the image syntactical composition a special coding was developed, based on hierarchical sequences of symbols, whose differences are measured through a particular Levenshtein distance. The results of principal coordinates analysis on these distances are discussed.

Quantitative Study of Images in Archaeology: I. Textual Coding

For the analysis of a corpus of Mesopotamian seals, aiming at studying them on the image structure point of view, the problem of a suitable coding is discussed. For the analysis of the image composition a textual coding was developed. In this way, both the iconographical elements and attitudes and the subpattern composing the image, can be treated, through textual exploratory techniques. The results of a textual correspondence analysis are discussed.

Recent Experimentation on Euclidean Approximations of Biased Euclidean Distances

Given a set of 16 points on a grid, a set of randomly biased distances matrices is built and ten methods for their Euclidean approximantion are compared to identify which minimize the stress. The Principal Coordinates Analysis of Torgerson’s (1958) matrix of biased distances, limited to positive eigenvalues proved to be more effective than methods based on monotonous transformations’ aiming at getting the corresponding Torgerson’s (1958) matrix positive semidefinite prior to PCoA. Its behaviour resulted close to Kruskal Non-Metric Multidimensional Scaling and Bennani Dosse (1998) Optimal Scaling, with the advantage of the identification a posteriori of the suitable dimension.

Comparison of Euclidean Approximations of non-Euclidean Distances

The different techniques used for Euclidean approximation of distances are discussed. In the special case of points in a Euclidean space, whose distances are biased due to measure errors, accepting negative eigenvalues may help in the interpretation of results that are less biased than those obtained through an additive constant solution. Numerical examples are given.

Interpretation of a Cross-Classification: a New Method and an Application

For the interpretation of a two-way contingency table cross-classification, based on two hierarchies, new indexes are developed, able at evaluating relative contribution of either hierarchy nodes to the other’s nodes or partitions. Indexes are based on groups’ inertia projection onto the orthogonal basis, associated to the explanatory hierarchy, in a vector space with χ2 metrics. An application based on Lombardy municipalities 1991 Census data is given.

ALTERNATIVE METHODS TO MULTIPLE CORRESPONDENCE ANALYSIS IN RECONSTRUCTING THE RELEVANT INFORMATION IN A BURT'S TABLE

In this work, the reconstruction of the Burts table, Greenacre (1988)s Joint Correspondence Analysis (JCA), and Gower & Hand (1996)s Extended Matching Coefficient (EMC) are compared to Multiple Correspondence Analysis (MCA) in order to check the quality of the methods. In particular, for the whole table, the ability is considered separately the diagonal, and the off-diagonal tables, that is the ability to describe either each characters distribution or the interaction between pairs of characters, or both. The theoretical aspects are discussed first, and finally the results obtained in an application are shown and discussed.

Using exploratory analyses to select judges and create the components of a naming test to study aphasia

Aphasia is called the loss of some abilities related to language production and/or comprehension. In the framework of aphasia studies, the ability of the patient to recognize and correctly verbalize a set of images is verified through suitable tests. Since the images are supposed to be easily and unequivocally recognized and named by every person, tailoring images taken from the Snodgrass and Vanderwarts (1980) original test to the Brazilian reality is necessary. We faced the following two issues: the selection of images that are easily recognizable, and the estimate of an index measuring the primitivity of the corresponding word, that is how early in life a person heard the word. To this aim, two surveys have been carried out, where the images were proposed to non-aphasic judges. We report in this paper the results of the exploratory multidimensional analyses carried out to select both images and judges and to define the primitivity index.

A New Method for Cross-Classification Analysis of Contingency Data Tables

For the interpretation of a two-way contingency table cross-classification, based on two hierarchies, new indexes are developed that are able to evaluate the relative contribution of nodes of either hierarchy to the nodes of the other hierarchy or partitions. Indexes are based on the group’s inertia projection onto the orthogonal basis associated with the explanatory hierarchy, in a vector space with χ2 metrics. An application based on the study of family supplies in Eastern Lombardia is given.