A non linear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm

Baey, Charlotte; Trevezas, Samis; Cournède, Paul-Henry

doi:10.1080/03610926.2014.930909

Cited by 9 publications

(8 citation statements)

References 45 publications

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“…Such models are often descriptive ones, involving mechanistic parameters. Therefore, considering these parameters as random effects is relevant in order to understand how they vary within a given population [Baey et al, 2016] and statistical tools to identify fixed from random effects are necessary. Therefore, adapted tools to compute precisely the proposed test statistics in nonlinear mixed effects models have to be developed.…”

Section: Discussionmentioning

confidence: 99%

Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

Baey

Cournède

Kuhn

2019

Computational Statistics & Data Analysis

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Mixed effects models are widely used to describe heterogeneity in a population. A crucial issue when adjusting such a model to data consists in identifying fixed and random effects. From a statistical point of view, it remains to test the nullity of the variances of a given subset of random effects. Some authors have proposed to use the likelihood ratio test and have established its asymptotic distribution in some particular cases. Nevertheless, to the best of our knowledge, no general variance components testing procedure has been fully investigated yet. In this paper, we study the likelihood ratio test properties to test that the variances of a general subset of the random effects are equal to zero in both linear and nonlinear mixed effects model, extending the existing results. We prove that the asymptotic distribution of the test is a chi-bar-square distribution, that is to say a mixture of chi-square distributions, and we identify the corresponding weights. We highlight in particular that the limiting distribution depends on the presence of correlations between the random effects but not on the linear or nonlinear structure of the mixed effects model. We illustrate the finite sample size properties of the test procedure through simulation studies and apply the test procedure to two real datasets of dental growth and of coucal growth.

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Section: Discussionmentioning

confidence: 99%

Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

Baey

Cournède

Kuhn

2019

Computational Statistics & Data Analysis

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“…Finally, the real objective is to derive a full population model for Acacia erioloba based on an individual FSPM in order to account for the inter-individual variability. Likewise, and as introduced by [5], both organogenesis and functional parameters should be modelled as mixed effects. The main difficulty will rely on the joint estimation of organogenesis and functioning, especially in the case of interaction between both.…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…Heterogeneity was studied in a sugar beet population in [4] for the organogenesis and in [5] for a full FSPM model. The approach is based on the identification of non-linear mixed effect models with the Stochastic Approximation Expectation Maximization (SAEM) algorithm as proposed by [6].…”

Section: Introductionmentioning

confidence: 99%

Modeling the inter-individual variability of single-stemmed plant development

Noce

Letort

Hansart

et al. 2016

2016 IEEE International Conference on Functional-Structural Plant Growth Modeling, Simulation, Visualization and Applications (

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Modeling the development of single-stemmed plants is classically done by expressing the number of phytomers in the main axis as a function of the thermal time. In many cases, a strong inter-individual variability is encountered, that cannot be straightforwardly associated to any environmental or microenvironmental factors. We propose a methodological framework to describe the heterogeneity of individual responses in a population by hierarchical or mixed-effect models : some regression parameters are random variables identically distributed in the population. The method is illustrated using experimental data collected on young Acacia erioloba plants, grown in CEREEP greenhouse, for which two piecewise-linear models of organogenesis are identified using Expectation-Maximization (EM) algorithm and compared according to their adequacy to the data. The Estep and the M-step of the algorithm are analytic as long as the dependence is linear with respect to the individual parameters, i.e. the latent variables of the mixed-effect model. In the general case, the posterior distribution of the individual parameters cannot be analytically determined. Monte-Carlo Markov Chains are generated with Metropolis-Hasting during the E-step to estimate the distribution. Alternatively, a Laplace approximation of the posterior distribution appeared to be quite relevant in our case. Such framework will be adapted to the identification of a complete FSPM of Acacia growth combining organogenesis and functioning.

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“…A variant of that algorithm is the Stochastic Approximation of the EM (SAEM) in Delyon et al (1999) leveraging the power of Robbins-Monro update (Robbins and Monro, 1951) to ensure pointwise convergence of the vector of estimated parameters using a decreasing stepsize rather than increasing the number of MC samples. The MCEM and the SAEM have been successfully applied in mixed effects models (McCulloch, 1997;Hughes, 1999;Baey et al, 2016) or to do inference for joint modeling of time-to-event data coming from clinical trials in Chakraborty and Das (2010), unsupervised clustering in Ng and McLachlan (2003), variational inference of graphical models in Blei et al (2017) among other applications. An incremental variant of the SAEM was proposed in Kuhn et al (2020) but its analysis is limited to asymptotic consideration.…”

Section: Prior Workmentioning

confidence: 99%

A Class of Two-Timescale Stochastic EM Algorithms for Nonconvex Latent Variable Models

Karimi¹,

Li²

2022

Preprint

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The 1 Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced by Neal and Hinton (1998), using incremental updates to scale to large datasets, and by Wei and Tanner (1990);Delyon et al. (1999), using Monte Carlo (MC) approximations to bypass the intractable conditional expectation of the latent data for most nonconvex models. In this paper, we propose a general class of methods called Two-Timescale EM Methods based on a two-stage approach of stochastic updates to tackle an essential nonconvex optimization task for latent variable models. We motivate the choice of a double dynamic by invoking the variance reduction virtue of each stage of the method on both sources of noise: the index sampling for the incremental update and the MC approximation. We establish finite-time and global convergence bounds for nonconvex objective functions. Numerical applications on various models such as deformable template for image analysis or nonlinear models for pharmacokinetics are also presented to illustrate our findings.

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A non linear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm

Cited by 9 publications

References 45 publications

Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

Modeling the inter-individual variability of single-stemmed plant development

A Class of Two-Timescale Stochastic EM Algorithms for Nonconvex Latent Variable Models

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