Compute BMA of fitted.values from a list of INLA objects

Description

This functions performs a weighted average of the component fitted.values from a list of INLA objects.

Usage

BMArho(models, rho, logrhoprior = rep(1, length(rho)))

Arguments

Details

The different fitted.values are weighted using the values of the marginal likelihood of the fitted models and the prior of parameter rho. rho is a parameter that is fixed when computing models and that have a log-prior density defined in pogrhoprior.

Value

Vector of averaged fitted values.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2014). Approximate Bayesian inference for spatial econometrics models. Spatial Statistics, Volume 9, 146-165.

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2015). Spatial Data Analysis with R-INLA with Some Extensions. Journal of Statistical Software, 63(20), 1-31. URL http://www.jstatsoft.org/v63/i20/.

See Also

INLABMA

Perform complete Bayesian Model Averaging on some Spatial Econometrics models

Description

This function performs Bayesian Model Averaging on a list of different Spatial Econometrics models. These models have been computed under different values of the spatial autocorrelation parameter rho.

Usage

INLABMA(models, rho, logrhoprior = rep(1, length(rho)), impacts = FALSE, 
 usenormal = FALSE)

Arguments

Details

This functions perfomrs BMA on most of the compponents of an INLA model using the marginal likelihoods of the models and the provided log-prior density of rho.

Value

A list with the averaged components. Another component called rho is added, with its posterior marginal and some other summary information.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2014). Approximate Bayesian inference for spatial econometrics models. Spatial Statistics, Volume 9, 146-165.

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2015). Spatial Data Analysis with R-INLA with Some Extensions. Journal of Statistical Software, 63(20), 1-31. URL http://www.jstatsoft.org/v63/i20/.

See Also

sem.inla, slm.inla, sdm.inla

Perform INLA with MCMC.

Description

This function implements the Metropolis-Hastings algorithm using repeated calls to R-INLA to fint conditional model on the current state of the MCMC simulations.

Usage

INLAMH(d, fit.inla, b.init, rq, dq, prior, n.sim = 200, n.burnin = 100,
  n.thin = 1, n.errors = 20, verbose = FALSE)

Arguments

Details

This function implements the Metropolis-Hastings algorithm using INLA (i.e., INLA within MCMC) at every step. In practice, only a few of the model parameters are sampled in the MCMC steps and the posterior marginal of the remainder of parameters is obtained by Bayesian model averaging of the conditional marginals returned by R-INLA at each step of the Metropolis-Hastings algorithm.

Value

A list with three components:

Author(s)

Virgilio Gómez-Rubio.

References

Virgilio Gómez-Rubio and Haavard Rue (2017). Markov Chain Monte Carlo with the Integrated Nested Laplace Approximation. doi:10.1007/s11222-017-9778-y.

Fit posterior marginal distributions to points

Description

Compute (and re-scale, if necessary) the marginal from a set of points x and values of log-likelihood logy and log-prior density logp.

Usage

fitmarg(x, logy, logp = 0, usenormal = FALSE)

Arguments

Details

Fits a marginal at a set of points x from their log-likelihood and log-prior. The fitted marginal is re-scaled to integrate one if necessary. If usenormal=TRUE then the fitted marginal is supposed to be Normal, which is computed using the posterior mean and standard deviation of x.

Value

A function with the fitted marginal is returned.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

See Also

fitmargBMA, fitmargBMA2,mysplinefun

Compute marginals using Bayesian Model Averaging

Description

fitmargBMA takes a list of marginal distributions and weights (presumably, based on some marginal likelihoods) and computes a final distribution by weighting.

fitmargBMA2 takes a list of INLA models and computes Bayesian Model Averaging on some of their components.

fitmatrixBMA performs averaging on a list of matrices.

fitlistBMA performs averaging of elements in lists.

Usage

fitmargBMA(margs, ws, len = 100)
fitmargBMA2(models, ws, item)
fitmatrixBMA(models, ws, item)
fitlistBMA(models, ws, item)

Arguments

Details

For fitmargBMA, distributions provided are averaging according to the weights provided. A new probability distribution is obtained.

fitmargBMA2 uses a list of INLA models to compute Model Averaging on some of their components (for example, the fitted values).

fitmatrixBMA performs averaging on a list of matrices.

fitlistBMA performs averaging of a list of a list of matrices.

Value

fitmargBMA returns a 2-column matrix with the weighted marginal distribution.

fitmargBMA2 returns a list of weighted components.

fitmatrixBMA returns a matrix.

fitlistBMA returns a list.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

Fit Leroux et al's spatial model.

Description

This function fits the model by Leroux et al. for a given value of the parameter lambda, i.e., the mixture parameter that appears in the variance..

Usage

leroux.inla(formula, d, W, lambda, improve = TRUE, fhyper = NULL, ...)

Arguments

Details

This function fits the model proposed by Leroux et al. (1999) for a given value of parameter lambda. This parameter controls the mixture between a diagonal precission (lambda=1) and an intrinsic CAR precission (lambda=0).

The marginal log-likelihood is corrected to add half the log-determinant of the precission matrix.

Value

An INLA object.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

Leroux B, Lei X, Breslow N (1999). Estimation of Disease Rates in Small Areas: A New Mixed Model for Spatial Dependence. In M Halloran, D Berry (eds.), Statistical Models in Epidemiology, the Environment and Clinical Trials, pp. 135-178. Springer-Verlag, New York.

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2014). Approximate Bayesian inference for spatial econometrics models. Spatial Statistics, Volume 9, 146-165.

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2015). Spatial Data Analysis with R-INLA with Some Extensions. Journal of Statistical Software, 63(20), 1-31. URL http://www.jstatsoft.org/v63/i20/.

See Also

sem.inla,slm.inla,sdm.inla

Log-prior density for the spatial autocorrelation parameter rho

Description

Compute log-prior density for rho

Usage

logprrho(rho)

Arguments

Details

This function computes the log-density of the prior for rho according to logit(rho) ~ N(0, prec=.1). THis is one of the default priors in R-INLA for spatial autocorrelation parameters.

Value

Numerical.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

Examples

rrho<-seq(.01, .99, length.out=100)
plot(rrho, exp(logprrho(rrho)))

Compute spline function

Description

This function is similar to splinefun but it returns 0 outside the range of x.

Usage

mysplinefun(x, y = NULL, method = c("fmm", "periodic", "natural", "monoH.FC")[1],
   ties = mean)

Arguments

Details

This function calls splinefun and returns a function with the fitted spline. The main difference is that this new function returns 0 outside the range of 0.

Value

Returns a function with x and deriv arguments. See splinefun for details.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

See Also

splinefun

Recompute the impact summaries from the marginals

Description

This functions recomputes the impacts summaries using the (approximated) marginals rather than by weighting on the different summaries.

Usage

recompute.impacts(obj, impacts = c("total", "direct", "indirect"))

Arguments

Details

This function uses the impacts marginals to compute some summary statistics. By default, the summary of the impacts is obtained by weighting the different summaries used in Bayesian MOdel Averaging with function INLABMA.

Value

Original object with the updated summary statistics of the impacts.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

Bivand et al. (2013)

See Also

INLABMA

Re-scale marginal distribution to compute the distribution of w*x

Description

This function takes a marginal distribution (represetend by a 2-column matrix) and computes the marginal distribution of w*x.

Usage

rescalemarg(xx, w)

Arguments

Details

This function simply re-scales

Value

A 2-column matrix with the new values of w*x and their associated probability densities. This is also an object of classes inla.marginal.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

INLA

See Also

inla.tmarginal

Examples

if(requireNamespace("INLA", quietly = TRUE)) {
require(INLA)
x<-seq(-3,3, by=.01)
xx<-cbind(x, dnorm(x))

xx2<-rescalemarg(xx, 3)

plot(xx, type="l", xlim=c(-9,9))
lines(xx2, col="red")
}

Fit spatial econometrics models with INLA

Description

These functions fit some spatial econometrics models for a given value of rho (the spatial autocorrelation parameter). sem.inla fits a spatial error model, slm fits a spatial lag model and sdm.inla fits a spatial Durbin model.

Usage

sem.inla(formula, d, W, rho, improve = TRUE, impacts = FALSE, fhyper = NULL, 
   probit = FALSE, ...)
slm.inla(formula, d, W, rho, mmatrix = NULL, improve = TRUE, impacts = FALSE, 
   fhyper = NULL, probit = FALSE, ...)
sdm.inla(formula, d, W, rho, mmatrix = NULL, intercept = TRUE, impacts = FALSE,
   improve = TRUE, fhyper = NULL, probit = FALSE, ...)
sac.inla(formula, d, W.rho, W.lambda, rho, lambda, mmatrix = NULL, 
   improve = TRUE, impacts = FALSE, fhyper = NULL, probit = FALSE, ...)

Arguments

Details

These functions fit a spatial econometrics model with a fixed value of the spatial autocorrelation parameter rho.

In addition, the marginal -log-likelihood is corrected to account for the variance-covariance matrix of the error term or random effects.

Value

An inla object.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2014). Approximate Bayesian inference for spatial econometrics models. Spatial Statistics, Volume 9, 146-165.

Roger S. Bivand, Virgilio Gómez-Rubio, Hĺvard Rue (2015). Spatial Data Analysis with R-INLA with Some Extensions. Journal of Statistical Software, 63(20), 1-31. URL http://www.jstatsoft.org/v63/i20/.

Virgilio Gómez-Rubio and Francisco-Palmí Perales (2016). Spatial Models with the Integrated Nested Laplace Approximation within Markov Chain Monte Carlo. Submitted.

See Also

leroux.inla

Examples

## Not run: 

if(requireNamespace("INLA", quietly = TRUE)) {
require(INLA)
require(spdep)

data(columbus)

lw <- nb2listw(col.gal.nb, style="W")

#Maximum Likelihood (ML) estimation
colsemml <- errorsarlm(CRIME ~ INC + HOVAL, data=columbus, lw, method="eigen", 
	quiet=FALSE)
colslmml <- lagsarlm(CRIME ~ INC + HOVAL, data=columbus, lw, method="eigen", 
	type="lag", quiet=FALSE)
colsdmml <- lagsarlm(CRIME ~ INC + HOVAL, data=columbus, lw, method="eigen", 
	type="mixed", quiet=FALSE)

#Define grid on rho
rrho<-seq(-1, .95, length.out=40)

#Adjacency matrix
W <- as(as_dgRMatrix_listw(nb2listw(col.gal.nb)), "CsparseMatrix")
#Index for spatial random effects
columbus$idx<-1:nrow(columbus)

#Formula
form<- CRIME ~ INC + HOVAL

zero.variance = list(prec=list(initial = 25, fixed=TRUE))



seminla<-mclapply(rrho, function(rho){

                sem.inla(form, d=columbus, W=W, rho=rho,
                        family = "gaussian", impacts=FALSE,
                        control.family = list(hyper = zero.variance),
                        control.predictor=list(compute=TRUE),
                        control.compute=list(dic=TRUE, cpo=TRUE),
                        control.inla=list(print.joint.hyper=TRUE), 
				#tolerance=1e-20, h=1e-6),
			verbose=FALSE
                )

})



slminla<-mclapply(rrho, function(rho){

                slm.inla(form, d=columbus, W=W, rho=rho,
                        family = "gaussian", impacts=FALSE,
                        control.family = list(hyper = zero.variance),
                        control.predictor=list(compute=TRUE),
                        control.compute=list(dic=TRUE, cpo=TRUE),
                        control.inla=list(print.joint.hyper=TRUE), 
				#tolerance=1e-20, h=1e-6),
			verbose=FALSE
                )
})


sdminla<-mclapply(rrho, function(rho){

                sdm.inla(form, d=columbus, W=W, rho=rho,
                        family = "gaussian", impacts=FALSE,
                        control.family = list(hyper = zero.variance),
                        control.predictor=list(compute=TRUE),
                        control.compute=list(dic=TRUE, cpo=TRUE),
                        control.inla=list(print.joint.hyper=TRUE), 
				#tolerance=1e-20, h=1e-6),
			verbose=FALSE
                )
})

#BMA using a uniform prior (in the log-scale) and using a Gaussian 
#approximation to the marginal
sembma<-INLABMA(seminla, rrho, 0, usenormal=TRUE)
slmbma<-INLABMA(slminla, rrho, 0, usenormal=TRUE)
sdmbma<-INLABMA(sdminla, rrho, 0, usenormal=TRUE)

#Display results
plot(sembma$rho$marginal, type="l", ylim=c(0,5))
lines(slmbma$rho$marginal, lty=2)
lines(sdmbma$rho$marginal, lty=3)
#Add ML estimates
abline(v=colsemml$lambda, col="red")
abline(v=colslmml$rho, col="red", lty=2)
abline(v=colsdmml$rho, col="red", lty=3)
#Legend
legend(-1,5, c("SEM", "SLM", "SDM"), lty=1:3)
}


## End(Not run)

Compute trace of (I-rho*W)^{-1} matrix

Description

This function computes (or estimates) the trace of matrix (I-rho*W)^{-1}, which is often needed when computing impacts in some spatial econometrics models.

Usage

trIrhoWinv(W, rho, offset = 0, order = 20, direct = TRUE, Df = Matrix::Diagonal(nrow(W)))

Arguments

Details

This function computes the trace of (I-rho*W)^{-1}, which is later used to computed the impacts. This is an internal function.

Value

Numerica value.

Author(s)

Virgilio Gómez-Rubio <virgilio.gomez@uclm.es>

References

LeSage and Page (2008) Bivand et al. (2013)

See Also

sem.inla, slm.inla, sdm.inla