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.
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.
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.
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.