epilike function

Calculates the log likelihood

Calculates the log likelihood for the specified individual level model and data set

epilike (object, tmin = NULL, tmax, sus.par, trans.par = NULL,

         beta = NULL, spark = NULL, Sformula = NULL, Tformula = NULL)

Arguments

• object: An object of class epidata that can be the output of epidata or as.epidata.

• tmin: The first time point at which data is observed, default value is one.

• tmax: The last time point at which data is observed.

• sus.par: Susceptibility parameter(>0).

• trans.par: Transmissibility parameter(>0).

• beta: Spatial parameter(s) (>0) or network parameter (s) (>0) if contact network is used.

• spark: Sparks parameter(>=0), representing infections unexplained by other parts of the model or infections coming in from outside the observed population, default value is zero.

• Sformula: An object of class formula. See formula .

  Individual-level covariate information associated with susceptibility can be passed through this argument. An expression of the form ~ model is interpreted as a specification that the susceptibility function, $\Omega_S(i)$ is modelled by a linear predictor specified symbolically by the model term. Such a model consists of a series of terms separated by + and - operators. If there is no susceptibility covariate information, Sformula is null.

• Tformula: An object of class formula. See formula .

  Individual-level covariate information associated with transmissibility can be passed through this argument. An expression of the form ~ -1+model is interpreted as a specification that the transmissibility function, $\Omega_T(j)$ is modelled by a linear predictor specified symbolically by the model terms without the incorporation of the intercept term. Such a model consists of a series of terms separated by + and - operators. If there is no transmissibility covariate information, Tformula is null.

Returns

Returns the value of the log-likelihood function.

See Also

epimcmc.

Examples

## Example 1:  spatial SI model
# generate 100 individuals

x <- runif(100, 0, 10)

y <- runif(100, 0, 10)

covariate <- runif(100, 0, 2)

out1 <- epidata(type = "SI", n = 100, Sformula = ~covariate, tmax = 15,
              sus.par = c(0.1, 0.3), beta = 5.0, x = x, y = y)

epilike(out1, tmax = 15,
         sus.par = c(0.1, 0.3), beta = 5, Sformula = ~covariate)

## Example 2: spatial SIR model
# generate infectious period (=3) for 100 individuals

lambda <- rep(3, 100)

out2 <- epidata(type = "SIR", n = 100, tmax = 15, sus.par  =0.3, beta = 5.0,
              infperiod = lambda, x = x, y = y)

epilike(out2,
        tmax = 15, sus.par = 0.3, beta = 5.0)

References

Deardon R, Brooks, S. P., Grenfell, B. T., Keeling, M. J., Tildesley, M. J., Savill, N. J., Shaw, D. J., Woolhouse, M. E. (2010). Inference for individual level models of infectious diseases in large populations. Statistica Sinica, 20, 239-261.