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Results n° 1 to 8 of 167 matches
| Title |
When the utility, the annoyance or the comfort are recorded with ordered categories, the interaction in the multivariate context |
| Author |
MAURIN Michel |
| Keywords |
Category scales, Conjoint measurement, Interaction, Measurement theory, Successive intervals, Utility |
| Topics |
Contingency table, Data Analysis, Measure - Measurement, Orders and preorders, Scale, Utility |
| Abstract |
This note is related to ordered categorical responses coming from experimental subjects as we generally do with the «utility» in econometry, annoyance in environmental surveys, or discomfort in ergonomy. Here we are working in the measurement theory framework. The appropriate measurement method is to use the successive intervals of Adams and Messick, which are well suited for univariate conditions when responses are given in relation to one descriptive variable; here we examine the multivariate extension, the first formal properties and the possibility to explicit the interaction between variables. |
| Number |
188, Winter 2009 |
| Language |
 French | Read the article
| Title |
Tree representations of qualitative proximities |
| Author |
BURIGANA Luigi |
| Keywords |
Betweenness, Proximity, Representation, Tree |
| Topics |
Distances, Graphs, Orders and preorders, Trees |
| Abstract |
On a family of sets, a ternary relation may be defined by stating that, for U, V, W members of the family, V is «between» U and W if and only if V includes the intersection of U and W . The relation is called «intersection-betweenness» and may be understood as the description of proximities between objects associated with sets in the family. The problem of using a tree graph for representing such a relation is discussed. Characterisations are proven both for full tree representation (there is a
tree-betweenness identical to the given intersection-betweenness: Section 2) and for partial tree representation (there is a tree-betweenness
included in the given intersection-betweenness: Section 3). Procedures for actually finding solutions to full and partial tree representation problems are illustrated in Section 4. In Section 5 some related paradigms of modern psychometrics are mentioned, to highlight the peculiar aspects of the proposed approach. |
| Number |
185, Spring 2009 |
| Language |
 English | Read the article
| Title |
From a Guttman ordinal scale to a Rasch ratio scale |
| Author |
BERTRAND Daisy, EL AHMADI Abdessadek, HEUCHENNE Christian |
| Keywords |
Biorder, Guttman, measurement, Rasch, Ratio scale |
| Topics |
Measure - Measurement, Orders and preorders, Psychology |
| Abstract |
In this paper, increasingly restrictive measurement models are presented (Guttman scale, stochastic Guttman order, ratio scale and Rasch model) with, in parallel, their increasingly restrictive necessary and sufficient conditions (Ferrers relation, stochastic version of Ferrers, ...). |
| Number |
184, Winter 2008 |
| Language |
French | Read the article
| Title |
Foundations, construction and significant nodes of an implicative binary hierarchy |
| Author |
LERMAN Israël-César |
| Keywords |
"Significant" levels, "significant" nodes, Implicative analysis, Implicative tree, Oriented ascendant hierarchical classification |
| Topics |
Classification - Clustering - Partitioning, Combinatorics, Data Analysis, Orders and preorders |
| Abstract |
Implicative data analysis is a specific method of data analysis, employing asymmetrical similarities and based on a construction of an ascendant binary hierarchical classification. This method has been introduced and developed by R. Gras and collaborators. Statistical descriptive attributes (generally, boolean attributes) are organized as a binary implicative tree. In this article we reconsider in a new and systematic manner this approach. The analysis of its foundations leads us to a new axiomatic and to new constructive and combinatorial properties. We provide and motivate a new interpretation of the results obtained by this type of data analysis method.The mathematical properties of the statistical construction of the binary implicative tree are studied. Finally, we analyze in a precise and complete manner our criteria for identifying the most "significant" levels and the most "significant" nodes of the implicative binary tree. |
| Number |
184, Winter 2008 |
| Language |
French | Read the article
| Title |
A Gutman effect in PCA |
| Author |
FLAMENT Claude, MILLAND Laurent |
| Keywords |
Guttman effect, Principal composant analysis, Social representation |
| Topics |
Data Analysis, Orders and preorders, Social Psychology |
| Abstract |
The recourse to multidimensional methods in the data treatment allows for extracting structures of unidimensional data, when they exist, and one speaks then about Guttman effect. If the disclosure of such an effect is well-known in Correspondences Analysis, it can be also carried out in Principal Component Analysis, as presented here, while studying special properties of this effect (component of size, diagonal component, etc). The study of such a structure offers a very particular intelligibility to the results of research undertaken in the field of the social sciences, as connection with the social representation of homosexuality on the one hand and intelligence in its relationship with gender on the other hand. |
| Number |
171, Fall 2005 |
| Language |
French | Read the article
| Title |
Study of the french tennis classification system: modelisation and statistical analysis with the Monte-Carlo method |
| Author |
PARIS Nicolas, GERVILLE-REACHE Léo |
| Keywords |
Classement, Mixed strategy, Modelling, Monte-Carlo, Tennis, Training |
| Topics |
Game Theory, Modelling, Orders and preorders, Sports, Statistics |
| Abstract |
The procedure of the French tennis classification system is hard to grasp for players and trainers. Via statistical analyses and numerical simulations, we identify and measure properties of the current method of classification. We show that the ranking increases as a function of the number of matches played during the year. |
| Number |
170, Spring 2005, special issue: Mathematics, sport games, sociology |
| Language |
French | Read the article
| Title |
Invariant relations in a finite domain |
| Author |
BURIGANA Luigi |
| Keywords |
Boolean operation, Galois connection, Invariance, Lattice, Relation, Semigroup |
| Topics |
Algebra, Discrete Mathematics, Orders and preorders |
| Abstract |
Some results of an abstract inquiry into the concept of invariance are presented. The objects to be judged in their possible invariance are relations of arbitrary degrees in one single domain, when they are represented as sets of strings of elements in that domain. The domain itself is presumed to be a finite size, and the transformations with respect to which invariance is judged are injective functions between parts of it. The study focuses on correspondences between algebraic structures of possible relations and algebraic structures of possible transformations, as they are dually interrelated through the invariance condition. |
| Number |
169, Spring 2005 |
| Language |
English | Read the article
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