This function takes in a ‘carbayes’ model object and computes the posterior distribution and posterior quantiles of a linear combination of the covariates from the linear predictor. For example, if a quadratic effect of a covariate on the response was specified, then this function allows you to compute the posterior distribution of the quadratic relationship.
Fit a spatial generalised linear mixed model to areal unit data, where the response variable can be binomial, Gaussian or Poisson. The linear predictor is modelled by known covariates and a vector of random effects. The latter are modelled by the conditional autoregressive prior proposed by Leroux et al. (1999), and further details are given in the vignette accompanying this package. Independent random effects can be obtained by setting (fix.rho=TRUE, rho=0) similar to the old function S.independent(), in which case the neighbourhood matrix W is not part of the model. In this case enter a fake W matrix that is a K by K matrix of zeros, where K is the number of data points. Similarly, the intrinsic CAR model can be obtained by setting (fix.rho=TRUE, rho=1) similar to the old function S.CARiar(). Inference is conducted in a Bayesian setting using Markov chain Monte Carlo (McMC) simulation. Missing (NA) values are allowed in the response, and posterior predictive distributions are created for the missing values for predictive purposes. These are saved in the‘samples’ argument in the output of the function and are denoted by ‘Y’.
This function takes in a matrix of Markov chain Monte Carlo (McMC) samples from a ‘carbayes’ model object, such as a set of parameters or fitted values, and calculates posterior quantiles and exceeedence probabilities. The latter are probabilities of the form P(quantity > c|data), where c is a threshold chosen by the user.
This function combines a data frame with a shapefile to create a SpatialPolygonsDataFrame object from the ‘sp’ package. The creation of this object allows the variables in the data frame to be mapped using the ‘spplot()’ function, and the neighbourhood matrix W to be created using the ‘poly2nb’ and ‘nb2mat’ functions. An example is given in the vignette accompanying this package. The mapping of the data to the shapefile is done by matching the rownames of the data frame to the first column in the dbf file.
Fit a spatial generalised linear mixed model to areal unit data, where the response variable can be binomial, or Poisson. Note, a Gaussian likelihood is not allowed because of a lack of identifiability among the parameters. The linear predictor is modelled by known covariates and a vector of random effects. The latter are modelled by the BYM conditional autoregressive prior proposed by Besag et al. (1991), and further details are given in the vignette accompanying this package. Inference is conducted in a Bayesian setting using Markov chain Monte Carlo (McMC) simulation. Missing (NA) values are allowed in the response, and posterior predictive distributions are created for the missing values for predictive purposes. These are saved in the ‘samples’ argument in the output of the function and are denoted by ‘Y’.
Implements a class of univariate and multivariate spatial generalised linear mixed models for areal unit data, with inference in a Bayesian setting using Markov chain Monte Carlo (McMC) simulation. The response variable can be binomial, Gaussian or Poisson. Spatial autocorrelation is modelled by a set of random effects, which are assigned a conditional autoregressive (CAR) prior distribution. A number of different CAR priors are available for the random effects, including a multivariate CAR (MCAR) model for multivariate spatial data. Full details are given in the vignette accompanying this package. The initial creation of this package was supported by the Economic and Social Research Council (ESRC) grant RES-000-22-4256, and on-going development was supported by the Engineering and Physical Science Research Council (EPSRC) grant EP/J017442/1. Version 4.6 has one minor change from version 4.5, namely the removal of errors in the R code in the vignette.
Creates a SpatialPoints object identifying a subset of borders between neighbouring areas, which allows them to be overlayed on a map. An example is given in the vignette accompanying this package.
Fit a spatial generalised linear mixed model to areal unit data, where the response variable can be binomial or Poisson. Note, a Gaussian likelihood is not allowed because of a lack of identifiability among the parameters. The linear predictor is modelled by known covariates, a vector of random effects and a piecewise constant intercept process. The random effects are modelled by an intrinsic CAR prior, while the piecewise constant intercept process was proposed by Lee and Sarran (2015), and allow neighbouring areas to have very different values. Further details are given in the vignette accompanying this package. Inference is conducted in a Bayesian setting using Markov chain Monte Carlo (McMC) simulation. Missing (NA) values are not allowed in this model.
Fit a multivariate spatial generalised linear mixed model to areal unit data, where the response variable can be binomial or Poisson. The linear predictor is modelled by known covariates and a vector of random effects. The latter account for both spatial and between variable correlation, via a Kronecker product formulation. Spatial correlation is captured by the conditional autoregressive (CAR) prior proposed by Leroux et al. (1999), and between variable correlation is captured by a between variable covariance matrix with no fixed structure. This is a type of multivariate conditional autoregressive (MCAR).Further details are given in the vignette accompanying this package. Independent (over space) random effects can be obtained by setting (fix.rho=TRUE, rho=0), in which case the neighbourhood matrix W is not part of the model. In this case enter a fake W matrix that is a K by K matrix of zeros, where K is the number of spatial units. Similarly, the intrinsic MCAR model can be obtained by setting (fix.rho=TRUE, rho=1). Inference is conducted in a Bayesian setting using Markov chain Monte Carlo (McMC) simulation. Missing (NA) values are allowed in the response, and posterior predictive distributions are created for the missing values for predictive purposes. These are saved in the‘samples’ argument in the output of the function and are denoted by ‘Y’.
Fit a spatial generalised linear mixed model to areal unit data, where the response variable can be binomial, Gaussian or Poisson. The linear predictor is modelled by known covariates and a vector of random effects. The latter are modelled by the localised conditional autoregressive prior proposed by Lee and Mitchell (2012), and further details are given in the vignette accompanying this package. Inference is conducted in a Bayesian setting using Markov chain Monte Carlo (McMC) simulation. Missing (NA) values are allowed in the response, and posterior predictive distributions are created for the missing values for predictive purposes. These are saved in the ‘samples’ argument in the output of the function and are denoted by ‘Y’.
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