Spatially varying dynamic coefficient models

Paez, Marina Silva; Friel, Nial; Landim, Flávia; Salazar, Esther

doi:10.1016/j.jspi.2007.03.060

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…The results presented by equations (13), (14) and (15) remain valid except that all variances should be multiplied by σ 2 . The predictive distribution (one-step ahead) in this case (after integrating σ 2 out) is obtained by replacing the Normal distributions by a Student T distributions with n t degrees of freedom and substituting σ 2 by its estimate d t /n t .…”

Section: Updating and Forecasting: Unknown Variances Casementioning

confidence: 76%

“…Preliminary analysis showed strong correlation between the transformed response variables log(SO 2 ) and log(N O 3 ). Paez et al (2008) worked with observations of 22 monitoring stations and left the other 2 to validate the models (stations LRL and SPD, which can be seen in Figure 2).…”

Section: General Model Frameworkmentioning

confidence: 99%

“…The motivation for this extension is that, sometimes, it is not possible to work under the hypothesis of normality of the observations that otherwise could be modeled through the Hierarchical Dynamic Models with structure in space proposed by Paez et al (2008).…”

Section: Dynamic Hierarchical Models: Exponential Family Observationsmentioning

confidence: 99%

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Hierarchical Dynamic Models

Paez

2013

The SAGE Handbook of Multilevel Modeling

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Suppose now that the scores are obtained yearly for a certain period of time. It is reasonable to expect that the conditions of each school could be changing through time. Therefore, a modification can be made in the model described above to allow the regression intercept to vary between schools and also through time. In a more general framework, all the regression coefficients can be allowed to vary within these dimensions. Hierarchical models that consider a time variation for the parameters through dynamic linear models (Harrison and Stevens, 1979), are denominated Dynamic Hierarchical Models. These models are well documented in Gamerman and Migon (1993). Dynamic Hierarchical Models can be applied to data in many fields of interest. Specifically, many applications are made to environmental data due to the usual need of modeling their variation in time, and many times in space as well. Some motivating examples and applications to real data-sets are presented throughout this chapter. The remainder of the chapter is organized as follows: in Section 2, the Dynamic Hierarchical Models are presented, and inference for these models is presented in Section 3. Section 4 presents extensions of these models for observations in time and space. Finally Section 5 presents some concluding remarks.

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Section: Updating and Forecasting: Unknown Variances Casementioning

confidence: 76%

Section: General Model Frameworkmentioning

confidence: 99%

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Hierarchical Dynamic Models

Paez

2013

The SAGE Handbook of Multilevel Modeling

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“…Gelfand et al proposed a spatial process modeling for univariate and multivariate dynamic spatial data. Paez et al developed spatially varying dynamic coefficient models.…”

Section: Introductionmentioning

confidence: 99%

Bayesian semiparametric model with spatially–temporally varying coefficients selection

Cai

Lawson

Hossain

et al. 2013

Statistics in Medicine

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In spatio-temporal analysis, the effect of a covariate on the outcome usually varies across areas and time. The spatial configuration of the areas may potentially depend on not only the structured random intercept but also spatially varying coefficients of covariates. In addition, the normality assumption of the distribution of spatially varying coefficients could lead to potential biases of estimations. In this article, we propose a Bayesian semiparametric space-time model where the spatially-temporally varying coefficient is decomposed as fixed, spatially varying and temporally varying coefficients. The spatially varying coefficients of space-time covariates are modeled nonparametrically by using the area-specific Dirichlet process prior with weights transformed via a generalized transformation. Temporally varying coefficients of covariates are modeled through the dynamic model. Uncertainty of inclusion of the spatially-temporally varying coefficients is also taken into account by variable selection procedure through determining the probabilities of different effects for each covariate. The proposed semiparametric approach shows the improvement compared to the Bayesian spatial-temporal models with normality assumption on spatial random effects and the Bayesian model with the Dirichlet process prior on the random intercept. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. An application to low birth weight data in South Carolina is used for an illustration.

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“…In practice, the space-time-dependent effect of a specific space-time covariate on responses is also of substantial interest (e.g., effects of poverty rates on low birth weight may vary across different regions and time points). Although some work has been done (Gelfand et al , 2005; Paez et al , 2008), there is still lack of development for such models. Typically, one may consider a space-time model based on linear combinations of covariates such as

η_{i t} = x_{i t}^{'} β_{i t} + u_{i} + ν_{i} + δ_{t}

.…”

Section: Introductionmentioning

confidence: 99%

Bayesian latent structure models with space-time dependent covariates

Cai

Lawson²,

Hossain³

et al. 2012

Statistical Modelling

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Spatial-temporal data requires flexible regression models which can model the dependence of responses on space- and time-dependent covariates. In this paper, we describe a semiparametric space-time model from a Bayesian perspective. Nonlinear time dependence of covariates and the interactions among the covariates are constructed by local linear and piecewise linear models, allowing for more flexible orientation and position of the covariate plane by using time-varying basis functions. Space-varying covariate linkage coefficients are also incorporated to allow for the variation of space structures across the geographical location. The formulation accommodates uncertainty in the number and locations of the piecewise basis functions to characterize the global effects, spatially structured and unstructured random effects in relation to covariates. The proposed approach relies on variable selection-type mixture priors for uncertainty in the number and locations of basis functions and in the space-varying linkage coefficients. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. A real data example is used for illustration.

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Spatially varying dynamic coefficient models

Cited by 8 publications

References 16 publications

Hierarchical Dynamic Models

Hierarchical Dynamic Models

Bayesian semiparametric model with spatially–temporally varying coefficients selection

Bayesian latent structure models with space-time dependent covariates

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