Commenced in January 2007
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Edition: International
Paper Count: 4

Search results for: Linear mixed model

4 An Estimation of Variance Components in Linear Mixed Model

Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Keywords: Linear mixed model, Random effects, Parameter estimation, Stein function.

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3 Spatio-Temporal Analysis and Mapping of Malaria in Thailand

Authors: Krisada Lekdee, Sunee Sammatat, Nittaya Boonsit

Abstract:

This paper proposes a GLMM with spatial and temporal effects for malaria data in Thailand. A Bayesian method is used for parameter estimation via Gibbs sampling MCMC. A conditional autoregressive (CAR) model is assumed to present the spatial effects. The temporal correlation is presented through the covariance matrix of the random effects. The malaria quarterly data have been extracted from the Bureau of Epidemiology, Ministry of Public Health of Thailand. The factors considered are rainfall and temperature. The result shows that rainfall and temperature are positively related to the malaria morbidity rate. The posterior means of the estimated morbidity rates are used to construct the malaria maps. The top 5 highest morbidity rates (per 100,000 population) are in Trat (Q3, 111.70), Chiang Mai (Q3, 104.70), Narathiwat (Q4, 97.69), Chiang Mai (Q2, 88.51), and Chanthaburi (Q3, 86.82). According to the DIC criterion, the proposed model has a better performance than the GLMM with spatial effects but without temporal terms.

Keywords: Bayesian method, generalized linear mixed model (GLMM), malaria, spatial effects, temporal correlation.

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2 Risk Factors for Defective Autoparts Products Using Bayesian Method in Poisson Generalized Linear Mixed Model

Authors: Pitsanu Tongkhow, Pichet Jiraprasertwong

Abstract:

This research investigates risk factors for defective products in autoparts factories. Under a Bayesian framework, a generalized linear mixed model (GLMM) in which the dependent variable, the number of defective products, has a Poisson distribution is adopted. Its performance is compared with the Poisson GLM under a Bayesian framework. The factors considered are production process, machines, and workers. The products coded RT50 are observed. The study found that the Poisson GLMM is more appropriate than the Poisson GLM. For the production Process factor, the highest risk of producing defective products is Process 1, for the Machine factor, the highest risk is Machine 5, and for the Worker factor, the highest risk is Worker 6.

Keywords: Defective autoparts products, Bayesian framework, Generalized linear mixed model (GLMM), Risk factors.

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1 Spatial Time Series Models for Rice and Cassava Yields Based On Bayesian Linear Mixed Models

Authors: Panudet Saengseedam, Nanthachai Kantanantha

Abstract:

This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, Linear mixed model, Multivariate conditional autoregressive model, Spatial time series.

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