BAMP includes a data example.
data(apc)
plot(cases[,1],type="l",ylim=range(cases), ylab="cases", xlab="year", main="cases per age group")
for (i in 2:8)lines(cases[,i], col=i)
bamp() automatically performs a check for MCMC convergence using Gelman and Rubin’s convergence diagnostic. We can manually check the convergence again:
## [1] TRUE
Now we have a look at the model results. This includes estimates of smoothing parameters and deviance and DIC:
##
## Model:
## age (rw1) - period (rw1) - cohort (rw1) model
## Deviance: 231.46
## pD: 36.99
## DIC: 268.45
##
##
## Hyper parameters: 5% 50% 95%
## age 0.360 0.901 1.997
## period 66.801 200.355 630.834
## cohort 33.961 59.218 97.429
##
##
## Markov Chains convergence checked succesfully using Gelman's R (potential scale reduction factor).
We can plot the main APC effects using point-wise quantiles:
More quantiles are possible:
model2 <- bamp(cases, population, age="rw2", period="rw2", cohort="rw2",
periods_per_agegroup = 5,
mcmc.options=list("number_of_iterations"=200000, "burn_in"=100000, "step"=50, "tuning"=500),
hyperpar=list("age"=c(1,.5), "period"=c(1,0.05), "cohort"=c(1,0.05)))
## [1] TRUE
##
## Model:
## age (rw2) - period (rw2) - cohort (rw2) model
## Deviance: 234.38
## pD: 37.07
## DIC: 271.44
##
##
## Hyper parameters: 5% 50% 95%
## age 1.041 2.942 6.574
## period 16.373 41.251 90.391
## cohort 23.480 44.714 80.963
##
##
## Markov Chains convergence checked succesfully using Gelman's R (potential scale reduction factor).
## [1] TRUE
##
## Model:
## age (rw1) cohort (rw2) model
## Deviance: 276.77
## pD: 30.38
## DIC: 307.15
##
##
## Hyper parameters: 5% 50% 95%
## age 0.291 0.714 1.500
## cohort 37.705 74.057 138.728
##
##
## Markov Chains convergence checked succesfully using Gelman's R (potential scale reduction factor).
(model4<-bamp(cases, population, age="rw1", period="rw1", cohort="rw1",
cohort_covariate = cov_c, periods_per_agegroup = 5))
##
## Model:
## age (rw1) - period (rw1) - cohort (rw1) model
## Deviance: 231.24
## pD: 36.87
## DIC: 268.11
##
##
## Hyper parameters: 5% 50% 95%
## age 0.344 0.922 1.899
## period 69.196 203.391 636.627
## cohort 34.668 58.941 98.535
##
##
## Markov Chains convergence checked succesfully using Gelman's R (potential scale reduction factor).
(model5<-bamp(cases, population, age="rw1", period="rw1", cohort="rw1",
period_covariate = cov_p, periods_per_agegroup = 5))
##
## Model:
## age (rw1) - period (rw1) - cohort (rw1) model
## Deviance: 231.32
## pD: 36.83
## DIC: 268.15
##
##
## Hyper parameters: 5% 50% 95%
## age 0.342 0.905 1.922
## period 69.944 203.613 639.038
## cohort 34.877 59.449 97.862
##
##
## Markov Chains convergence checked succesfully using Gelman's R (potential scale reduction factor).