A new specification of generalized linear models for categorical data

Regression models for categorical data are specified in heterogeneous ways. We propose to unify the specification of such models. This allows us to define the family of reference models for nominal data. We introduce the notion of reversible models for ordinal data that distinguishes adjacent and cumulative models from sequential ones. The combination of the proposed specification with the definition of reference and reversible models and various invariance properties leads to a new view of regression models for categorical data.Comment: 31 pages, 13 figure

Partitioned conditional generalized linear models for categorical data

In categorical data analysis, several regression models have been proposed for hierarchically-structured response variables, e.g. the nested logit model. But they have been formally defined for only two or three levels in the hierarchy. Here, we introduce the class of partitioned conditional generalized linear models (PCGLMs) defined for any numbers of levels. The hierarchical structure of these models is fully specified by a partition tree of categories. Using the genericity of the (r,F,Z) specification, the PCGLM can handle nominal, ordinal but also partially-ordered response variables.Comment: 25 pages, 13 figure

A statistical model for analyzing jointly growth phases, the influence of environmental factors and inter-individual heterogeneity : Applications to forest trees

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Regularising Generalised Linear Mixed Models with an autoregressive random effect

International audienceWe address regularised versions of the Expectation-Maximisation (EM) algorithm for Generalised Linear Mixed Models (GLMM) in the context of panel data (measured on several individuals at different time-points). A random response y is modelled by a GLMM, using a set X of explanatory variables and two random effects. The first one introduces the dependence within individuals on which data is repeatedly collected while the second one embodies the serially correlated time-specific effect shared by all the individuals. Variables in X are assumed many and redundant, so that regression demands regularisation. In this context, we first propose a L2-penalised EM algorithm, and then a supervised component-based regularised EM algorithm as an alternative

A Bayesian Regularization Procedure for a Better Extremal Fit

In Structural Reliability, special attention is devoted to model distribution tails. This is important when one wants to estimate the occurrence probability of rare events as critical failures, extreme charges, resistance measures, frequency of stressing events, etc. People try to find distribution models having a good overall fit to the data. Particularly, the distributions are strongly required to fit the upper observations and provide a good picture of the tail above the maximal observation. Specific goodness-of-fit tests such as the ET test can be constructed to check this tail fit. Then what can we do with distributions having a good central fit and a bad extremal fit ? We propose a regularization procedure, that is to say a procedure which preserves the general form of the initial distribution and allows a better fit in the distribution tail. It is based on Bayesian tools and takes the opinion of experts into account. Predictive distributions are proposed as model distributions. They are obtained as a mixture of the model family density functions according to the posterior distribution. Therefore, they are rather smooth and can easily be simulated. We numerically investigate this method on normal, lognormal, exponential, gamma and Weibull distributions. Our method is illustrated on both simulated and real data sets

Supervised-Component versus PLS regression. The case of GLMMs with autoregressive random effect

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Component-based regularisation of multivariate generalised linear mixed models

International audienceWe address the component-based regularisation of a multivariate Generalised Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory variables, a set A of additional explanatory variables, and random effects to introduce the within-group dependence of observations. Variables in X are assumed many and redundant so that regression demands regularisation. This is not the case for A, which contains few and selected variables. Regularisation is performed building an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X. To estimate the model, we propose to maximise a criterion specific to the Supervised Component-based Generalised Linear Regression (SCGLR) within an adaptation of Schall's algorithm. This extension of SCGLR is tested on both simulated and real grouped data, and compared to ridge and LASSO regularisations. Supplementary material for this article is available online

Les GL2M : extension de la méthode GAR

Nous nous intéressons ici à l'estimation de paramètres dans des modèles linéaires généra­lisés mixtes (GL2M). Gilmour, Anderson et Rae en 1985 ont proposé une méthode d'estimation dans un modèle avec lien probit pour des données binomiales. En 1993, Foulley et Im ont adapté la méthode GAR au cas de données poissoniennes. Pour ces deux modélisations, nous proposons une nouvelle lecture de la méthode en levant l'hypothèse d'homogé­néi­té des variances des variables sous-jacentes. Ensuite, nous présentons une adaptation à des données exponentielles et donnons, pour finir, une formalisation qui permet d'envisager le cas de données binomiales dans un modèle avec lien logit