Estimation of extended mixed models using latent classes and latent processes: the R package lcmm

The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme), curvilinear and ordinal univariate longitudinal outcomes (lcmm) and curvilinear multivariate outcomes (multlcmm), as well as joint latent class mixed models (Jointlcmm) for a (Gaussian or curvilinear) longitudinal outcome and a time-to-event that can be possibly left-truncated right-censored and defined in a competing setting. Maximum likelihood esimators are obtained using a modified Marquardt algorithm with strict convergence criteria based on the parameters and likelihood stability, and on the negativity of the second derivatives. The package also provides various post-fit functions including goodness-of-fit analyses, classification, plots, predicted trajectories, individual dynamic prediction of the event and predictive accuracy assessment. This paper constitutes a companion paper to the package by introducing each family of models, the estimation technique, some implementation details and giving examples through a dataset on cognitive aging

Choix d'estimateurs base sur le risque de Kullback-Leibler.

Estimators choice is a crucial topic in statistics. The most famous criterion is the Akaike information criterion. It has been constructed as an approximation, up to a constant, of the Kullback-Leibler risk. However, a precise value of the Akaike criterion has no direct interpretation and its variability is often ignored. We propose several approaches to estimate Kullback-Leibler risks. The criteria defined can be used in a parametric, non-parametric or semi-parametric context. An extension of these criteria for incomplete data is presented. The issue of the choice of estimators in the presence of incomplete data is described. Several applications in the survival framework is described: smooth estimators choice for the hazard function, estimators choice from proportional hazard model and stratified model, and estimators choice for markov model and non markov model. Finally, several criteria are defined for selecting estimators based on different observations

A semiparametric approach for a multivariate sample selection model

International audienceMost of the common estimation methods for sample selection models rely heavily on parametric and normality assumptions. We consider in this paper a multivariate semiparametric sample selection model and develop a geometric approach to the estimation of the slope vectors in the outcome equation and in the selection equation. Contrary to most existing methods, we deal symmetrically with both slope vectors. Moreover, the estimation method is link-free and distributionfree. It works in two main steps: a multivariate sliced inverse regression step, and a canonical analysis step. We establish pn-consistency and asymptotic normality of the estimates. We describe how to estimate the observation and selection link functions. The theory is illustrated with a simulation study

Penalized Partial Least Square applied to structured data

Nowadays, data analysis applied to high dimension has arisen. The edification of high-dimensional data can be achieved by the gathering of different independent data. However, each independent set can introduce its own bias. We can cope with this bias introducing the observation set structure into our model. The goal of this article is to build theoretical background for the dimension reduction method sparse Partial Least Square (sPLS) in the context of data presenting such an observation set structure. The innovation consists in building different sPLS models and linking them through a common-Lasso penalization. This theory could be applied to any field, where observation present this kind of structure and, therefore, improve the sPLS in domains, where it is competitive. Furthermore, it can be extended to the particular case, where variables can be gathered in given a priori groups, where sPLS is defined as a sparse group Partial Least Square

Understanding convergence concepts: A visual-minded and graphical simulation-based approach

This paper describes the difficult concepts of convergence in probability, almost sure convergence, convergence in law and in r-th mean using a visual-minded and a graphical simulation-based approach. For this purpose, each probability of events is approximated by a frequency. An R package is available on CRAN which reproduces all the experiments done in this paper

Mesures in-situ d'impacts de vagues sur une digue composite In-situ measurements of wave impacts on a composite breakwater

International audienc

Age-related changes in murine myometrial transcript profile are mediated by exposure to the female sex hormones.

In humans, the risk of operative first delivery increases linearly with maternal age. We previously hypothesized that prolonged, cyclical, prepregnancy exposure to estrogen and progesterone contributes to uterine aging. Here, we test this hypothesis. Myometrium was obtained from four groups of virgin mice: (i) 10- to 12-week- and 28- to 30-week-old mice; (ii) 10- to 12-week- and 38- to 40-week-old mice; (iii) 38-week-old mice that had an ovariectomy or sham operation early in life; (iv) 38-week-old mice that had been treated with progesterone or vehicle containing implants from 8 to 36 weeks. Transcript profiling was carried out using Affymetrix Gene ST 1.1 arrays, and data were normalized. We identified 60 differentially regulated transcripts associated with advancing age (group 1). We validated these changes in group 2 (P for overlap = 5.8 × 10(-46) ). Early ovariectomy prevented the age-related changes in myometrial transcript profile. Similarly, progesterone-mediated long-term ovarian suppression prevented the age-related changes in myometrial transcript profile. Interferon regulatory factor 7 (Irf7) mRNA was regulated by age and hormonal exposure, and was identified as a predicted regulator of the other differentially expressed transcripts by both promoter sequence and canonical pathway activation analysis (P = 8.47 × 10(-5) and P < 10(-10) , respectively). Immunohistochemistry demonstrated IRF7 in both mouse and human myometrium. We conclude the following: (i) Myometrial aging in mice is associated with reproducible changes in transcript profile; (ii) these changes can be prevented by interventions which inhibit cyclical changes in the female sex hormones; and (iii) IRF7 may be an important regulator of myometrial function and aging.This work was supported by the NIHR Cambridge Comprehensive Biomedical Research Centre, Addenbrooke's Charitable Trust and the Evelyn Trust.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1111/acel.1240

A universal approximate cross-validation criterion and its asymptotic distribution

A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and they are assessed through another function (the assessment function). The estimating and assessment functions generally estimate risks. A classical case is that both functions estimate an information risk (specifically cross entropy); in that case Akaike information criterion (AIC) is relevant. In more general cases, the assessment risk can be estimated by leave-one-out crossvalidation. Since leave-one-out crossvalidation is computationally very demanding, an approximation formula can be very useful. A universal approximate crossvalidation criterion (UACV) for the leave-one-out crossvalidation is given. This criterion can be adapted to different types of estimators, including penalized likelihood and maximum a posteriori estimators, and of assessment risk functions, including information risk functions and continuous rank probability score (CRPS). This formula reduces to Takeuchi information criterion (TIC) when cross entropy is the risk for both estimation and assessment. The asymptotic distribution of UACV and of a difference of UACV is given. UACV can be used for comparing estimators of the distributions of ordered categorical data derived from threshold models and models based on continuous approximations. A simulation study and an analysis of real psychometric data are presented.Comment: 23 pages, 2 figure