algo.hhh.grid: Function to try multiple starting values
In jimhester/surveillance: Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

Description Usage Arguments Value Author(s) References See Also Examples

Tries multiple starting values in algo.hhh. Starting values are provided in a matrix with gridSize rows, the grid search is conducted until either all starting values are used or a time limit maxTime is exceeded. The result with the highest likelihood is returned.

algo.hhh.grid(disProgObj, control=list(lambda=TRUE, neighbours=FALSE, 
   linear=FALSE, nseason=0,
   negbin=c("none", "single", "multiple"), 
   proportion=c("none", "single", "multiple"),lag.range=NULL), 
   thetastartMatrix, maxTime=1800, verbose=FALSE)

`disProgObj`	object of class `disProg`
`control`	control object: `lambda` If `TRUE` an autoregressive parameter λ is included, if `lambda` is a vector of logicals, unit-specific parameters λ_i are included. By default, observations y_t-lag at the previous time points, i.e. lag=1, are used for the autoregression. Other lags can be used by specifying `lambda` as a vector of integers, see Examples and `algo.hhh` for details. `neighbours` If `TRUE` an autoregressive parameter for adjacent units φ is included, if `neighbours` is a vector of logicals, unit-specific parameters φ_i are included. By default, observations y_t-lag at the previous time points, i.e. lag=1, are used for the autoregression. Other lags can be used by specifying `neighbours` as a vector of integers. `linear` a `logical` (or a vector of logicals) indicating wether a linear trend β (or a linear trend β_i for each unit) is included `nseason` integer number of Fourier frequencies; if `nseason` is a vector of integers, each unit i gets its own seasonal parameters `negbin` if `"single"` negative binomial rather than poisson is used, if `"multiple"` unit-specific overdispersion parameters are used. `proportion` see details in `algo.hhh` `lag.range` determines which observations are used to fit the model
`thetastartMatrix`	matrix with initial values for all parameters specified in the control object as rows.
`verbose`	if `true` progress information is printed
`maxTime`	maximum of time (in seconds) to elapse until algorithm stopps.

Returns an object of class ahg with elements

`best`	result of a call to `algo.hhh` with highest likelihood
`allLoglik`	values of loglikelihood for all starting values used
`gridSize`	number of different starting values in thetastartMatrix
`gridUsed`	number of used starting values
`time`	elapsed time
`convergence`	if `false` `algo.hhh` did not converge for all (used) starting values

M. Paul, L. Held

Held, L., HÃ¶hle, M., Hofmann, M. (2005) A statistical framework for the analysis of multivariate infectious disease surveillance counts, Statistical Modelling, 5, 187–199.

Paul, M., Held, L. and Toschke, A. M. (2008) Multivariate modelling of infectious disease surveillance data, Statistics in Medicine, 27, 6250–6267.

algo.hhh, create.grid

## Not run: 
## monthly counts of menigococcal infections in France
data(meningo.age)
            
# specify model for algo.hhh.grid
model1 <- list(lambda=TRUE)

# create grid of inital values
grid1 <- create.grid(meningo.age, model1, 
                     params = list(epidemic=c(0.1,0.9,5)))
                     
# try multiple starting values, print progress information
algo.hhh.grid(meningo.age, control=model1, thetastartMatrix=grid1,
               verbose=TRUE)

# specify model
model2 <- list(lambda=TRUE, neighbours=TRUE, negbin="single",
               nseason=1)
grid2 <- create.grid(meningo.age, model2, 
                     params = list(epidemic=c(0.1,0.9,3), 
                                   endemic=c(-0.5,0.5,3), 
                                   negbin = c(0.3, 12, 10)))
                                 
# run algo.hhh.grid, search time is limited to 30 sec
algo.hhh.grid(meningo.age, control=model2, thetastartMatrix=grid2,
              maxTime=30)
              
## weekly counts of influenza and meningococcal infections in Germany, 2001-2006
data(influMen)

# specify model with two autoregressive parameters lambda_i, overdispersion
# parameters psi_i, an autoregressive parameter phi for meningococcal infections
# (i.e. nu_flu,t = lambda_flu * y_flu,t-1  
#  and  nu_men,t = lambda_men * y_men,t-1 + phi_men*y_flu,t-1 )
# and S=(3,1) Fourier frequencies
model <- list(lambda=c(TRUE,TRUE), neighbours=c(FALSE,TRUE),
              linear=FALSE, nseason=c(3,1),negbin="multiple")
              
# create grid of initial values
grid <- create.grid(influMen,model, list(epidemic=c(.1,.9,3),
              endemic=c(-.5,.5,3), negbin=c(.3,15,10)))
# run algo.hhh.grid, search time is limited to 30 sec
algo.hhh.grid(influMen, control=model, thetastartMatrix=grid, maxTime=30)

# now meningococcal infections in the same week should enter as covariates
# (i.e. nu_flu,t = lambda_flu * y_flu,t-1  
#  and  nu_men,t = lambda_men * y_men,t-1 + phi_men*y_flu,t )
model2 <- list(lambda=c(1,1), neighbours=c(NA,0),
              linear=FALSE,nseason=c(3,1),negbin="multiple")
              
algo.hhh.grid(influMen, control=model2, thetastartMatrix=grid, maxTime=30)

## End(Not run)