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Showing 2 results for Spatial Generalized Linear Mixed Model

Mohsen Mohammadzadeh Darrodi, ,
Volume 12, Issue 1 (11-2012)
Abstract

Spatial generalized linear mixed models are usually used for modeling non-Gaussian and discrete spatial responses. In these models, spatial correlation of the data can be considered via latent variables. Estimation of the latent variables at the sampled locations, the model parameters and the prediction of the latent variables at un-sampled locations are of the most important interest in SGLMM. Often the normal assumption for latent variables is considered just for convenient in practice. Although this assumption simplifies the calculations, in practice, it is not necessarily true or possible to be tested. In this paper, a closed skew normal distribution is proposed for the spatial latent variables. This distribution includes the normal distribution and also remains closed under linear conditioning and marginalization. In these models, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, for maximum likelihood estimation of the model parameters and predictions of latent variables, an approximate algorithm is introduced that is faster than the former method. The performance of the proposed model and algorithm are illustrated through a simulation study.
Fatemeh Hosseini, Omid Karimi, Mohsen Mohammadzadeh,
Volume 13, Issue 3 (11-2013)
Abstract

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models, such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models, since there are the latent variables and non-Gaussian spatial response variables, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions, that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method, the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally, the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.

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