simHHH: Simulates data based on the model proposed by Held et. al... In surveillance: Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

Description

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

Usage

 1 2 3 4 5 6 7 8 ## 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 coefslist with the following parameters of the model - if not specified, those parameters are omitted alphavector of length m with intercepts for m units or geographic areas respectively gammavector with parameters for the "sine" part of ν_{i,t} deltavector with parameters for the "cosine" part of ν_{i,t} lambdaautoregressive parameter phiautoregressive parameter for adjacent units psioverdispersion parameter of the negative binomial model; NULL corresponds to a Poisson model periodperiod of the seasonal component, defaults to 52 for weekly data neighbourhoodneighbourhood matrix of size m \times m with element 1 if two units are adjacent; the default NULL assumes that there are no neighbours populationmatrix with population proportions; the default NULL sets n_{i,t}=1 startif 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} + φ ∑_{j \sim i} y_{j,t-1} + n_{it} ν_{it}

where

\log ν_{it} = α_i + ∑_{s=1}^{S}(γ_s sin(ω_s t) + δ_s cos(ω_s t))

ω_s = 2sπ/\code{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 ν_{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.

surveillance documentation built on July 25, 2018, 1:01 a.m.