A Non-Gaussian Spatial Generalized Linear Latent Variable Model
نویسندگان
چکیده
We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents.
منابع مشابه
Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation
Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...
متن کاملA comparison of algorithms for maximum likelihood estimation of Spatial GLM models
In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two n...
متن کاملUsing multivariate generalized linear latent variable models to measure the difference in event count for stranded marine animals
BACKGROUND AND OBJECTIVES: The classification of marine animals as protected species makes data and information on them to be very important. Therefore, this led to the need to retrieve and understand the data on the event counts for stranded marine animals based on location emergence, number of individuals, behavior, and threats to their presence. Whales are g...
متن کاملApproximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider app...
متن کاملApproximate Bayesian inference in spatial GLMM with skew normal latent variables
Spatial generalized linear mixed models are common in applied statistics. Most users are satisfied using a Gaussian distribution for the spatial latent variables in this model, but it is unclear whether the Gaussian assumption holds. Wrong Gaussian assumptions cause bias in parameter estimates and affect the accuracy of spatial predictions. Thus, there is a need for more flexible priors for the...
متن کامل