surveillance (version 1.5-4)

hhh4_formula: Specify Formulae in a Random Effects HHH Model

Description

The special functions fe and ri are used to specify (unit-specific) effects of covariates and a random intercept term, respectively, in formulae used in the function hhh4.

Usage

fe(x, which = NULL, initial = NULL)
  ri(type = c("iid","car")[1], corr = c("none", "all")[1],
     initial.var = NULL, initial.re = NULL)

Arguments

x

an expression like sin(2*pi*t/52) involving the time variable t , or just 1 for an intercept.

which

vector of logicals indicating which unit should get an unit-specific parameter. If NULL, the effect of the covariate is assumbed to be the same for all units.

initial

initial values (on internal scale!) for the fixed effects used for optimization. Not really used ATM.

type

random intercepts either follow an IID or a CAR model

corr

logical switch indicating whether random effects in different components (such as ar and end) should be correlated or not.

initial.var

initial values (on internal scale!) for the variance components used for optimization. Not really used ATM.

initial.re

initial values (on internal scale!) for the random effects used for optimization. Not really used ATM.

encoding

latin1

See Also

addSeason2formula, usage of formulae in the vignette and in examples of hhh4.

Examples

# some calls of the fitting function 'hhh4': 
# see vignette("hhh4") for further details

## Ex: univariate time series of meningococcal infections in Germany
# Negative binomial model with
# endemic component: Intercept + S = 1 sine/cosine pair
# autoregressive component: Intercept

f.S1 <- addSeason2formula(f = ~ 1, S = 1, period = 52)
hhh4(meningo, control = list(ar = list(f = ~ 1),
                             end = list(f = f.S1), 
                             family = "NegBin1")) 


## Ex: disease-specific intercept in influenza/meningococcal time series
# Negative binomial model with
# autoregressive component: disease-specific intercepts
# neighbour-driven component: only intercept for flu -> men
# endemic component: S=3 and S=1 sine/cosine pairs for flu and men, respectively

f.end <- addSeason2formula(f = ~ -1 + fe(1, which = c(TRUE, TRUE)), 
                           S = c(3, 1),   
                           period = 52)
m <- list(ar = list(f = ~ -1 + fe(1, which = c(TRUE, TRUE))), 
          ne = list(f = ~ -1 + fe(1, which = c(FALSE, TRUE))), 
          end = list(f = f.end),
          family = "NegBinM"
          )
hhh4(fluMen, control = m)


## Ex: (correlated) random intercepts for influenza in Southern Germany
# Negative binomial model with
# autoregressive component: Intercept
# neighbour-driven component: random intercepts
# endemic component: random intercepts + trend + S = 3 sine/cosine pairs

f.end <- addSeason2formula(f = ~ -1 + ri(type = "iid", corr="all") +
                                 I((t-208)/100), S = 3, period = 52)

model.B2 <- list(ar = list(f = ~ 1),
                 ne = list(f = ~ -1 + ri(type = "iid", corr="all"), 
                           weights = wji),
                 end = list(f = f.end, offset = population(flu)),
                 family = "NegBin1")
hhh4(flu, model.B2)


## Ex: measles in Germany
# Poisson model with
# autoregressive component: Intercept + vaccination coverage info
# endemic component: Intercept + S = 1 sine/cosine pair

f.end <- addSeason2formula(f = ~ 1, S = 1, period = 26)
model.A0 <- list(ar = list(f = ~ 1 + logVac0),
                 end = list(f = f.end, offset = population(measles2w)),
                 data = list(t = epoch(measles2w), logVac0 = log(vac0)))
hhh4(measles2w, model.A0)