varTestnlme: An R Package for Variance Components Testing in Linear and Nonlinear Mixed-Effects Models

The issue of variance components testing arises naturally when building mixed-effects models, to decide which effects should be modeled as fixed or random or to build parsimonious models. While tests for fixed effects are available in R for models fitted with lme4, tools are missing when it comes to random effects. The varTestnlme package for R aims at filling this gap. It allows to test whether a subset of the variances and covariances corresponding to a subset of the random effects, are equal to zero using asymptotic property of the likelihood ratio test statistic. It also offers the possibility to test simultaneously for fixed effects and variance components. It can be used for linear, generalized linear or nonlinear mixed-effects models fitted via lme4, nlme or saemix. Numerical methods used to implement the test procedure are detailed and examples based on different real datasets using different mixed models are provided. Theoretical properties of the used likelihood ratio test are recalled

Using a hierarchical segmented model to assess the dynamics of leaf appearance in plant populations.

International audienceModeling inter-individual variability in plant populations is a key issue to enhance the predictive capacity of plant growth models at field level. In sugar beet, this variability is well illustrated by the phyllochron (thermal time elapsing between two successive leaf appearances): even if the mean phyllochron remains stable within a given variety, there is a high heterogeneity between individuals. When considering the dynamics of leaf appearance as a function of thermal time in sugar beet, two linear phases can be observed, leading to the definition of a hierarchical segmented model with four random parameters varying from one individual to another: thermal time of initiation, first phyllochron, rupture thermal time and second phyllochron. The SAEM-MCMC algorithm is used to estimate the model parameters.L'amélioration des capacités prédictives des modèles de croissance de plantes passe par la modélisation de la variabilité inter-individus au sein de la population de plantes. Dans le cas de la betterave à sucre, cette variabilité se retrouve dans le phyllochrone (temps thermique nécessaire à l'élaboration d'une feuille): si le phyllochrone moyen reste stable pour une variété donnée, de fortes variations existent d'une plante à l'autre. Deux phases linéaires peuvent être observées dans la dynamique d'apparition des feuilles en fonction du temps thermique, nous amenant à considérer un modèle hiérarchique segmenté à quatre paramètres aléatoires: le temps thermique d'initiation, le premier phyllochrone, le temps thermique de rupture, et le second phyllochrone. Les paramètres du modèle ont été estimés à l'aide de l'algorithme SAEM-MCMC

A nonlinear mixed effects model to explain inter-individual variability in plant populations

15th Applied Stochastic Models and Data Analysis Conference (Accepted)International audienceIt is common knowledge that the genetic variability of plants, even of the same variety, can be very important and, if we add locally varying climatic effects, the development of two neighboring similar plants could be highly different. This is one of the reasons why population-based methods for modeling plant growth are of great interest. A highly promising individual-based plant growth model is the GreenLab model which was recently shown to have a good predictive capacity among competing models. In this study, we extend the GreenLab formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce into the GreenLab model appropriate random effects. Under some assumptions, the resulting model can be cast into the framework of nonlinear mixed effects models. A stochastic variant of an EM-type algorithm (Expectation-Maximization) is generally needed to perform MLE for this type of incomplete data models and the interest is focused on the design of an efficient algorithm. In this direction, we propose a suitable Monte-Carlo EM (MCEM) algorithm for our model, where at each EM-iteration, MCMC is used to draw from the hidden states given the observed data. Data consist in organ mass measurements and are treated sequentially as first proposed in Trevezas and Cournède (2013). The performance of the algorithm is illustrated on simulated data from the sugar beet plant. Some possible extensions and improvements are also discussed

Efficient preconditioned stochastic gradient descent for estimation in latent variable models

Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this paper, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm. Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variables models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed effects model and in a stochastic block model

Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model

International audienceModelling the interindividual variability in plant populations is a key issue to enhance the predictive capacity of plant growth models at the field scale. In the case of sugar beet, this variability is well illustrated by rate of leaf appearance, or by its inverse the phyllochron. Indeed, if the mean phyllochron remains stable among seasons, there is a strong variability between individuals, which is not taken into account when using models based only on mean population values. In this paper, we proposed a nonlinear mixed model to assess the variability of the dynamics of leaf appearance in sugar beet crops. As two linear phases can be observed in the development of new leaves, we used a piecewise-linear mixed model. Four parameters were considered: thermal time of initiation, rate of leaf appearance in the first phase, rupture thermal time, and difference in leaf appearance rates between the two phases. The mean population values as well as the interindividual variabilities (IIV) of the parameters were estimated by the model for a standard population of sugar beet, and we showed that the IIV of the four parameters were significant. Also, the rupture thermal time was found to be non significantly correlated to the other three parameters. We compared our piecewise-linear formulation with other formulations such as sigmoïd or Gompertz models, but they provided higher AIC and BIC. A method to assess the effects of environmental factors on model parameters was also studied and applied to the comparison of three levels of Nitrogen (control, standard and high dose). Taking into account the IIV, our model showed that plants receiving Nitrogen tended to have a later time of initiation, a higher rate of leaf appearance, and an earlier rupture time, but these differences were not dose-dependent (no differences between standard and high dose of Nitrogen). No differences were found on the leaf appearance rate of the second phase between the three treatments

Development and Evaluation of Plant Growth Models: Methodology and Implementation in the PYGMALION platform

International audienceMathematical models of plant growth are generally characterized by a large number of interacting processes, a large number of model parameters and costly experimental data acquisition. Such complexities make model parameterization a difficult process. Moreover, there is a large variety of models that coexist in the literature with generally an absence of benchmarking between the different approaches and insufficient model evaluation. In this context, this paper aims at enhancing good modelling practices in the plant growth modeling community and at increasing model design efficiency. It gives an overview of the different steps in modelling and specify them in the case of plant growth models specifically regarding their above mentioned characteristics. Different methods allowing to perform these steps are implemented in a dedicated platform PYGMALION (Plant Growth Model Analysis, Identification and Optimization). Some of these methods are original. The C++ platform proposes a framework in which stochastic or deterministic discrete dynamic models can be implemented, and several efficient methods for sensitivity analysis, uncertainty analysis, parameter estimation, model selection or data assimilation can be used for model design, evaluation or application. Finally, a new model, the LNAS model for sugar beet growth, is presented and serves to illustrate how the different methods in PYGMALION can be used for its parameterization, its evaluation and its application to yield prediction. The model is evaluated from real data and is shown to have interesting predictive capacities when coupled with data assimilation techniques

Evaluation of the Predictive Capacity of Five Plant Growth Models for Sugar Beet

International audienceA lot of plant growth models coexist, with different modelling approaches and levels of complexity. In the case of sugar beet, many of them are used as predictive tools, even when they were not originally designed for this purpose. We propose the evaluation and comparison of five plant growth models that rely on the same energetic production of biomass, but with different levels of description (per plant or per square meter) and different biomass repartition (empirical or via allocation): Greenlab, LNAS, CERES, PILOTE and STICS. The models were calibrated on a first set of data, and their predictive capacities were compared on an independent data set from the same variety and similar environmental conditions, using the root mean squared error of prediction (RMSEP) and modelling efficiency (EF) for the total dry matter production and the dry matter of root. All the models tended to overestimate both the total dry matter and the dry matter of root. Greenlab gave the best predictions for the root biomass, and CERES the best total biomass predictions. The overestimation was partly explained by a hail episode that caused a lot of damages to the leaves in the validation year. The five models also provided similar yield prediction errors