SpatioTemporal (version 1.1.2)

est.mesa.model: Examples of estimateSTmodel Structure

Description

Example of a model structure holding parameter estimates for the model in mesa.model using estimate.STmodel. Estimation results are also provided for models including spatio-temporal covariates.

format

A list with elements, see the return description in estimate.STmodel.

source

Contains parametere estimates for the Spatio-Temporal model applied to monitoring data from the MESA Air project, see Cohen et.al. (2009) and mesa.data.raw for details.

References

M. A. Cohen, S. D. Adar, R. W. Allen, E. Avol, C. L. Curl, T. Gould, D. Hardie, A. Ho, P. Kinney, T. V. Larson, P. D. Sampson, L. Sheppard, K. D. Stukovsky, S. S. Swan, L. S. Liu, J. D. Kaufman. (2009) Approach to Estimating Participant Pollutant Exposures in the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air). Environmental Science & Technology: 43(13), 4687-4693.

See Also

estimate.STmodel for parameter estimation. createSTmodel for creation of the originating STmodel object.

Other example data: est.cv.mesa, MCMC.mesa.model, mesa.data, mesa.data.raw, mesa.model, pred.mesa.model

Examples

##load data
data(mesa.data)
data(mesa.model)

##create vector of initial values
dim <- loglikeSTdim(mesa.model)
x.init <- cbind(rep(2,dim$nparam.cov),c(rep(c(1,-3),dim$m+1),-3))
##estimate parameters
  est.mesa.model <- estimate(mesa.model, x.init, type="p", hessian.all=TRUE)

##create model structure with ST-covariates
mesa.model.ST <- createSTmodel(mesa.data, LUR=mesa.model$LUR.list,
                               ST="lax.conc.1500")
mesa.data.0 <- removeSTcovarMean(mesa.data)
##add intercept to the mean model
LUR.ST0 <- c( list( c(all.vars(mesa.model$LUR.list[[1]]),
                      "mean.lax.conc.1500")), mesa.model$LUR.list[-1] )
mesa.model.ST.0 <- createSTmodel(mesa.data.0, LUR=LUR.ST0,
                                 ST="mean.0.lax.conc.1500")

##estimate parameters
  est.mesa.model.ST <- estimate(mesa.model.ST, x.init, hessian.all=TRUE)
  est.mesa.model.ST.0 <- estimate(mesa.model.ST.0, x.init, hessian.all=TRUE)

##time consuming estimation, load pre-computed results instead
data(est.mesa.model)

#estimation results
print(est.mesa.model)

##extract the estimated parameters and approximate uncertainties
x <- coef(est.mesa.model)

##compare estimated parameters
##plot the estimated parameters with uncertainties
par(mfrow=c(1,1),mar=c(13.5,2.5,.5,.5))
plot(x$par, ylim=range(c( x$par-1.96*x$sd, x$par+1.96*x$sd )),
     xlab="", xaxt="n")
points(x$par - 1.96*x$sd, pch=3)
points(x$par + 1.96*x$sd, pch=3)
##add axis labels
axis(1, 1:length(x$par), rownames(x), las=2)

##estimation results for the Spatio-temporal covariates
print(est.mesa.model.ST)
print(est.mesa.model.ST.0)

##extract the estimated parameters and approximate uncertainties
x.ST <- coef(est.mesa.model.ST)
x.ST0 <- coef(est.mesa.model.ST.0)

##plot the estimated parameters
par(mfrow=c(1,1),mar=c(13.5,2.5,.5,.5))
plot(c(1:5,7:19), x.ST$par, ylab="", xlab="", xaxt="n")
points(1:19, x.ST0$par, pch=3, col=2)
points(c(2:5,7:19), x$par, pch=4, col=3)
abline(h=0, col="grey")
axis(1, 1:length(x.ST0$par), rownames(x.ST0), las=2)
legend("bottomleft", col = c(3,2,1), pch = c(4,3,1), 
       legend=c("mesa.model", "mesa.model.ST.mean0", "mesa.model.ST"))