simHHH {surveillance}R Documentation

Simulates data based on the model proposed by Held et. al (2005)

Description

Simulates a multivariate time series of counts based on the Poisson/Negative Binomial model as described in Held et al. (2005).

Usage

## Default S3 method:
simHHH(model=NULL, control = list(coefs = list(alpha=1, gamma = 0, delta = 0,
       lambda = 0, phi = NULL, psi = NULL, period = 52),
       neighbourhood = NULL, population = NULL, start = NULL),
       length)

## S3 method for class 'ah':
simHHH(model, control = model$control, length)

Arguments

control list with
coefs
list with the following parameters of the model - if not specified, those parameters are omitted
alpha
vector of length m with intercepts for m units or geographic areas respectively
gamma
vector with parameters for the "sine" part of nu_{i,t}
delta
vector with parameters for the "cosine" part of nu_{i,t}
lambda
autoregressive parameter
phi
autoregressive parameter for adjacent units
psi
overdispersion parameter of the negative binomial model; NULL corresponds to a Poisson model
period
period of the seasonal component, defaults to 52 for weekly data
neighbourhood
neighbourhood matrix of size m times m with element 1 if two units are adjacent; the default NULL assumes that there are no neighbours
population
matrix with population proportions; the default NULL sets n_{i,t}=1
start
if NULL, the means of the endemic part in the m units is used as initial values y_{i,0}
model Result of a model fit with algo.hhh, the estimated parameters are used to simulate data
length number of time points to simulate

Details

Simulates data from a Poisson or a Negative Binomial model with mean

μ_{it} = λ y_{i,t-1} + phi sum_{j sim i} y_{j,t-1} + n_{it} nu_{it}

where

log nu_{it} = α_i + sum_{s=1}^{S}(gamma_s sin(omega_s t) + delta_s cos(omega_s t))

omega_s = 2sπ/period are Fourier frequencies and n_{it} are possibly standardized population sizes.

Value

Returns a list with elements

data disProgObj of simulated data
mean matrix with mean μ_{i,t} that was used to simulate the data
endemic matrix with only the endemic part nu_{i,t}
coefs list with parameters of the model

Note

The model does not contain a linear trend.

Source

Held, L., Höhle, M., Hofmann, M. (2005). A statistical framework for the analysis of multivariate infectious disease surveillance counts. Statistical Modelling, 5, p. 187-199.


[Package surveillance version 1.0-3 Index]