Multivariate dynamic model for ordinal outcomes

Abstract

Individual or stand-level biomass is not easy to measure. The current methods employed, based on cutting down a representative sample of plantations, make it possible to assess the biomasses for various compartments (bark, dead branches, leaves, . . . ). However, this felling makes individual longitudinal follow-up impossible. In this context, we propose a method to evaluate individual biomasses by compartments when these are ordinals. Biomass is measured visually and observations are therefore not destructive. The technique is based on a probit model redefined in terms of latent variables. A generalization of the univariate case to the multivariate case is then natural and takes into account of dependency between compartment biomasses. These models are then extended to the longitudinal case by developing a Dynamic Multivariate Ordinal Probit Model. The performance of the MCMC algorithm used for the estimation is illustrated by means of simulations built from known biomass models. The quality of the estimates and the impact of certain parameters, are then discussed.

A multivariate statistical model for emotion dynamics.

“…First, when the observations are assumed to be non-Gaussian realizations of an underlying Gaussian process, a link function can be used to transform the latent Gaussian scores into estimated observed non-Gaussian scores. Examples are a probit link for ordinal data (Chaubert, Mortier, & Saint André, 2008), or the log link for count data (assuming a Poisson distribution; Krone, Albers, & Timmerman, 2016a; Terui, Ban, & Maki, 2010). However, this adds more complexity to the model, requiring a larger sample size to estimate the model parameters with reasonable precision.…”

A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields

“…Ordinal variables were addressed using the distribution that follows from the multivariate ordinal probit model. This approach had been widely used as a generalization of Euclidian distance for mixed continuous and discrete data (Bedrick, Lapidus, and Powell, 2000; Mortier et al, 2006; Chaubert et al, 2008). Recently, in a spatial context, Augustin et al (2007) used this model with nonlinear effects of covariates and spatial random effects to predict ordinal variables.…”

“…We generalize Diggle et al's (1998) method to the multivariate case. In particular, our model can take ordinal spatial processes into account through generalization of the multivariate ordinal probit model to the spatial case (Chaubert, Mortier, and Saint‐André, 2008). Our modeling introduces spatial Gaussian latent processes to model spatial dependence.…”

Coupling models in forestry: What are the limitations?

“…Ce modèle étant linéaire, et pour peu que les mêmes variables explicatives ln(D), ln(D) 2 et ln(D) 3 soient systématiquement utilisées pour chacune des composantes de la biomasse, le biais de prédiction lié au couplage additif des tarifs sera nul (en raisonnant sur les données log-transformées). Cependant, même dans ce cas, la variance des prédictions ne sera généralement pas la même selon que l'on ajuste les tarifs séparément pour chacune des composantes, ou globalement pour l'ensemble des composantes, car les différentes composantes de la biomasse d'un arbre ont généralement des erreurs résiduelles corrélés entre elles (Chaubert et al, 2008).…”