[Paper Review] Using Multivariate Generalised Linear Mixed Models for Studying Roots Development: An Example Based on Minirhizotron Observations

Jeanett S. Pelck, Rodrigo Labouriau|arXiv (Cornell University)|Nov 1, 2020

Rice Cultivation and Yield Improvement19 references4 citations

TL;DR

This paper proposes a multivariate generalised linear mixed model (GLMM) that jointly models root scatter (presence/absence in minirhizotron windows) and root intensity (number of root crossings per window) using binomial and Poisson mixed models, respectively. It reveals a positive association between scatter and intensity at each time point and identifies a first-order Markovian temporal dependence pattern, indicating no long-term causal effects on root development—insights unattainable with univariate models.

ABSTRACT

The characterisation of the spatial and temporal distribution of the root system in a cultivated field depends on the soil volume occupied by the root systems (the scatter), and the local intensity of the root colonisation in the field (the intensity). We introduce a multivariate generalised linear mixed model for simultaneously describing the scatter and the intensity using data obtained with minirhizotrons (i.e., tubes with observation windows, which are inserted in the soil, enabling to observe the roots directly). The models presented allow studying intricate spatial and temporal dependence patterns using a graphical model to represent the dependence structure of latent random components. The scatter is described by a binomial mixed model (presence of roots in observation windows). The number of roots crossing the reference lines in the observational windows of the minirhizotron is used to estimate the intensity through a specially defined Poisson mixed model. We explore the fact that it is possible to construct multivariate extensions of generalised linear mixed models that allow to simultaneously represent patterns of dependency of the scatter and the intensity along with time and space. We present an example where the intensity and scatter are simultaneously determined at three different time points. A positive association between the intensity and scatter at each time point was found, suggesting that the plants are not compensating a reduced occupation of the soil by increasing the number of roots per volume of soil. Using the general properties of graphical models, we identify a first-order Markovian dependence pattern between successively observed scatters and intensities. This lack of memory indicates that no long-lasting temporal causal effects are affecting the roots' development. The two dependence patterns described above cannot be detected with univariate models.

Motivation & Objective

• To develop a statistical model that simultaneously captures spatial and temporal patterns in root system development using minirhizotron data.
• To address the challenge of modeling two distinct root characteristics—scatter (binomial) and intensity (Poisson)—within a single coherent statistical framework.
• To identify complex dependence structures across time and space using graphical models applied to latent random components in multivariate GLMMs.
• To detect temporal causal effects or memory patterns in root development that are invisible to univariate analyses.
• To provide a methodological advance for integrating heterogeneous response types (binary and count) in ecological and agricultural modeling.

Proposed method

• Uses a binomial mixed model to represent root scatter, defined as presence or absence of roots in minirhizotron observation windows.
• Employs a specially designed Poisson mixed model to estimate root intensity based on the number of root crossings over reference lines in each window.
• Applies a multivariate GLMM framework to jointly model scatter and intensity across multiple time points and spatial locations.
• Utilises graphical models to represent the dependence structure of latent random effects, enabling inference on conditional independence.
• Employs covariance selection via BIC minimisation to estimate the graphical structure of random effects, identifying conditional independence relationships.
• Uses stochastic geometric arguments to link root crossing counts to estimates of root length, enabling intensity estimation.

Experimental results

Research questions

• RQ1 Is there a significant association between root scatter and root intensity at different time points in the field?
• RQ2 What is the temporal dependence pattern governing root scatter and intensity over successive observation periods?
• RQ3 Can a single multivariate model effectively capture the joint dynamics of two fundamentally different response types—binary presence/absence and count-based intensity?
• RQ4 Are there long-term causal effects in root development, as indicated by memory in the dependence structure?
• RQ5 Can graphical models be effectively applied to multivariate GLMMs with non-identical response distributions (binomial and Poisson)?

Key findings

• A positive association was found between root scatter and intensity at each of the three observed time points, indicating no compensatory root growth in less colonised areas.
• The magnitude of the association between scatter and intensity decreased at the final observation time, suggesting a dynamic shift in root system development.
• A first-order Markovian dependence pattern was identified between successively observed scatters and intensities, implying no long-lasting temporal causal effects.
• Conditional independence analysis revealed that all information from early time points about later responses is fully captured by the intermediate random effects, confirming the Markov property.
• The multivariate GLMM with graphical model integration successfully captured complex spatial-temporal dependencies that univariate models could not detect.
• The methodological framework enables the use of non-CG graphical models for mixed-type responses (binomial and Poisson), overcoming limitations of standard conditional Gaussian models.