meanResponse {surveillance}R Documentation

Calculate mean response needed in algo.hhh

Description

Calculates the mean response for the model specified in designRes according to equations (1.2) and (1.1) in Held et al., 2005 for univariate time series and equations (3.3) and (3.2) for multivariate time series. See details.

Usage

  meanResponse(theta, designRes)

Arguments

theta vector of parameters

theta = (λ, phi, β, gamma_1, delta_1, gamma_2, delta_2, ..., psi, α_1, α_2, ...).

If the model specifies less parameters, those components are omitted.

designRes Result of a call to make.design

Details

Calculates the mean response for a Poisson or a Negative Binomial model with mean

μ_t = nu_t + λ y_{t-1}

where

log nu_t = α + β t + sum_{s=1}^{S}(gamma_s sin(omega_s t) + delta_s cos(omega_s t))

and Fourier frequencies omega_s = 2sπ/period for a univariate time series. For multivariate time series the mean structure is

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 + β t + sum_{s=1}^{S}(gamma_s sin(omega_s t) + delta_s cos(omega_s t))

and n_{it} are standardized population counts.

Value

Returns a matrix of dimension n times m with the calculated mean response for each time point and unit, where n is the number of time points and m is the number of units.

Author(s)

M. Paul, L. Held

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.

See Also

Examples






[Package surveillance version 0.9-6 Index]