La représentation d'une matrice par biplot

in Notes de Statistique et d'Informatique (2012), (2), 1-22

Matrix factorization by means of singular value decomposition is examined and used to produce a graphical representation of a data matrix called biplot. The link between this biplot and the plots of the ... [more ▼]

Matrix factorization by means of singular value decomposition is examined and used to produce a graphical representation of a data matrix called biplot. The link between this biplot and the plots of the variables and of the individuals usually given in principal component analysis is discussed and applied to an example. [less ▲]

Evolution des dépenses alimentaires en produits d'origine animale des ménages wallons

Poster (2012, March 07)

Programme de Gestion Durable de l'Azote en agriculture. Considérations pratiques et conceptuelles sur la méthodologie du contrôle public du reliquat d'azote nitrique dans le sol des exploitations agricoles wallonnes

in Biotechnologie, Agronomie, Société et Environnement = Biotechnology, Agronomy, Society and Environment [=BASE] (2012), 16(1), 25-32

Within the Walloon Action Programme, transposition of the Nitrates Directive, the Administration organizes each year a control of the soil nitrate nitrogen residues in about 900 parcels located in ... [more ▼]

Within the Walloon Action Programme, transposition of the Nitrates Directive, the Administration organizes each year a control of the soil nitrate nitrogen residues in about 900 parcels located in vulnerable zone in order to verify if the practices of nitrogen spreading by the farmers are in accordance with the Walloon Action Programme. The current method is to yearly spot “suspects” by a control in three parcels in about 300 farms and to follow “suspects” by an observation programme wich leads after maximum six years to a penalty or to the end of this programme. The present statistical study means to assess the public control’s methodology: what is the probability to penalize a “good” farmer, to forget a “bad” farmer? This study is based on real data and on a theoretical approach. Both conclusions indicate that the official methodology is sufficiently appropriate. [less ▲]

Inférence statistique et critères de qualité de l'ajustement en régression logistique binaire

in Notes de Statistique et d'Informatique (2011), (5), 32

The principles of statistical inference based on the maximum likelihood function are described and applied to binary logistic regression. Several goodness of fit statistics are also given. These topics ... [more ▼]

The principles of statistical inference based on the maximum likelihood function are described and applied to binary logistic regression. Several goodness of fit statistics are also given. These topics are illustrated by an example processed by Minitab and SAS softwares. [less ▲]

Simuler pour comprendre : un didacticiel pour l'apprentissage de notions de base en statistique inférentielle

in Statistique et Enseignement (2011), 2(1), 77-84

Macro Minitab pour la régression logistique ordinale basée sur les catégories adjacentes supérieures cumulées

Software (2011)

Principaux modèles utilisés en régression logistique

in Biotechnologie, Agronomie, Société et Environnement = Biotechnology, Agronomy, Society and Environment [=BASE] (2011), 15(3), 425-433

Regression is a commonly used technique for describing the relationship between a response variable and one or more explanatory variables. When the response variable is a categorical variable, usual ... [more ▼]

Regression is a commonly used technique for describing the relationship between a response variable and one or more explanatory variables. When the response variable is a categorical variable, usual regression based on ordinary least squares should be replaced by logistic regression. Binary logistic regression should be used to perform a regression on a dichotomous response. Nominal polytomous logistic regression applies to a categorical response variable that has more than two levels with a natural ordering. And ordinal polytomous logistic regression is used when the response is a categorical variable that has more than two levels with a natural ordering. This note gives an overview of these logistic regression methods and describes three models commonly used when performing ordinal logistic regression. These models are illustrated by an example related to oak decline in the Walloon Region (Belgium). [less ▲]

Plant species extinction debt in a temperate biodiversity hotspot: community, species and functional traits approaches

in Biological Conservation (2011), 144

Destruction and fragmentation of (semi-) natural habitats are considered the main causes of biodiversity loss worldwide. Plant species may exhibit a slow response to fragmentation, resulting in the ... [more ▼]

Destruction and fragmentation of (semi-) natural habitats are considered the main causes of biodiversity loss worldwide. Plant species may exhibit a slow response to fragmentation, resulting in the development of an extinction debt in fragmented plant communities. The detection of extinction debt is of primary importance in habitat conservation strategies. We applied two different approaches proposed in the literature to identify extinction debt in Southeast Belgium calcareous grasslands. The first method compared species richness between stable and fragmented habitat patches. The second explored correlations between current species richness and current and past landscape configurations using multiple regression analyses. We subsequently examined results generated by both methods. In addition, we proposed techniques to identify species that are more likely to support extinction debt and associated functional traits. We estimated a respective extinction debt of approximately 28% and 35% of the total and specialist species richness. Similar results were obtained from both methods. We identified 15 threatened specialist species under the current landscape configuration. It is likely the landscape configuration no longer supports the species habitat requirements. We demonstrated that non-clonal species are most threatened, as well as taxa that cannot persist in degraded habitats and form only sparsely distributed populations. We discussed our results in light of other studies in similar habitats, and the overall implications for habitat conservation. [less ▲]

Validity Limit of the Linear Regression Models for the Prediction

in International Journal of Applied Mathematics & Statistics (2010), 16(M10), 38-48

Monte Carlo simulation methods was used to study the effects of the data structure on the quality of the predictions in linear multiple regression. Five hundred forty (540) data files were generated of ... [more ▼]

Monte Carlo simulation methods was used to study the effects of the data structure on the quality of the predictions in linear multiple regression. Five hundred forty (540) data files were generated of which the number of variables, R-square, the collinearity between the explanatory variables and the index of coefficient, that measures the importance of the explanatory variables in the model, were controlled. Predictions were influenced by the theoretical value of R-square, the method used to establish the model and, to a lesser extent, the collinearity between the explanatory variables. The determination of the minimal sample size which leads to predicted values better than those obtained by the mean of the dependant variable indicated that this size depends on the number of the explanatory variables, the theretical value of the R-square and the method used to establish the model. The minimal sample size increases with the models without variables selection and gradually decreases with the intensity of the selection. [less ▲]

Extinction debt and colonization credit: When both phenomena are integrated

Conference (2010)

Calcareous grasslands are among the most species-rich ecosystems in temperate countries. These ecosystems suffered a high fragmentation process during the last century. Fragmentation can lead to the ... [more ▼]

Calcareous grasslands are among the most species-rich ecosystems in temperate countries. These ecosystems suffered a high fragmentation process during the last century. Fragmentation can lead to the creation of an extinction debt in remaining habitat patches. In our study site, it was shown in a previous study that Fragmented habitat patches (area loss since 1965 >80%) exhibited an extinction debt in comparison to Stable habitat patches (area loss since 1965 <80%). However, human activities also created new habitat patches in the landscape and provided therefore opportunities for calcareous grassland plant species to colonize new sites. They also provide opportunities for studying species colonization abilities in the context of habitat restoration. We analyzed species richness in these new patches in comparison to old patches in order to detect colonization credit. When taking as reference Fragmented patches (that exhibit an extinction debt) or all old patches (Fragmented and Stable), we concluded to the occurrence of a colonization credit in New patches. However, when the reference is Stable patches (the less likely to exhibit an extinction debt) alone, no colonization credit could be detected. Moreover, correspondence analysis revealed that New patches were similar to old patches in term of species composition. These results are encouraging for restoration programs. They also showed that the presence of an extinction debt in reference habitats can lead to mistaken conclusion in restoration monitoring. Extinction debt occurrence should be taken into account in the choice of reference habitats for evaluation of restoration success. [less ▲]