Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Les proches dans le Code civil

Le législateur du Code civil a introduit le terme « proche » dans de nombreuses dispositions, mais n'en propose aucune définition, ce qui laisse une grande marge de manoeuvre pour son interprétation et son application. La signification et la portée du terme ne seront ainsi pas les mêmes selon le domaine juridique et la situation de fait analysés. Face à cette grande diversité d'usage du terme, l'auteure de la contribution propose de l'appréhender selon les domaines et les buts dans lesquels il est utilisé par le législateur afin de réussir à tracer les contours des différents cercles de proches envisageables.

Rapport sur le projet d'un code pénal, fait à l'assemblée générale de l'État de la Louisiane , par M. Édouard Livingston, suivi des Observations sur les conditions nécessaires à la perfection d'un code pénal, par M. Mill, avec une introduction et des notes, par M. A.-H. Taillandier,...

Comprend : Observations sur les conditions nécessaires à la perfection d'un code pénal...

Allelic proportions of 16 STR loci-including the new European Standard Set (ESS) loci-in a Swiss population sample.

Allele frequencies and forensically relevant population statistics of 16 STR loci, including the new European Standard Set (ESS) loci, were estimated from 668 unrelated individuals of Caucasian appearance living in different parts of Switzerland. The samples were amplified with a combination of the following three kits: AmpFlSTR® NGM SElect?, PowerPlex® ESI17 and PowerPlex® ESX 17. All loci were highly polymorphic and no significant departure from Hardy-Weinberg equilibrium and linkage equilibrium was detected after correction for sampling.

Quelques conséquences de l'application du nouveau code pénal suisse sur la psychiatrie légale [Some consequences of the application of the new Swiss penal code on legal psychiatry]

The new text of the Swiss penal code, which entered into effect at the beginning of 2007, has many incidences on the practice of the psychiatrists realizing expertises in the penal field or engaged in the application of legal measures imposing a treatment. The most notable consequences of this text are, on the one hand, a new definition of the concept of penal irresponsibility which is not necessarily any more related to a psychiatric diagnosis and, on the other hand, a new definition of legal constraints that justice can take to prevent new punishable acts and which appreciably modifies the place of the psychiatrists in the questions binding psychiatric care and social control.

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

Report on applying agreed-upon procedures to the City of Protivin’s certification of compliance with Chapter 388.10 of the Code of Iowa

Report on applying agreed-upon procedures to the City of Protivin’s certification of compliance with Chapter 388.10 of the Code of Iowa