checkResidualProcess function

Check the residual process of a fitted twinSIR or twinstim

Transform the residual process (cf. the residuals methods for classes "twinSIR" and "twinstim") such that the transformed residuals should be uniformly distributed if the fitted model well describes the true conditional intensity function. Graphically check this using ks.plot.unif. The transformation for the residuals tau is 1 - exp(-diff(c(0,tau))) (cf. Ogata, 1988). Another plot inspects the serial correlation between the transformed residuals (scatterplot between $u_i$ and $u_{i+1}$).

checkResidualProcess(object, plot = 1:2, mfrow = c(1,length(plot)), ...)

Arguments

• object: an object of class "twinSIR" or "twinstim".
• plot: logical (or integer index) vector indicating if (which) plots of the transformed residuals should be produced. The plot index 1 corresponds to a ks.plot.unif to check for deviations of the transformed residuals from the uniform distribution. The plot index 2 corresponds to a scatterplot of $u_i$ vs. $u_{i+1}$. By default (plot = 1:2), both plots are produced.
• mfrow: see par.
• ...: further arguments passed to ks.plot.unif.

Returns

A list (returned invisibly, if plot = TRUE) with the following components:

• tau: the residual process obtained by residuals(object).
• U: the transformed residuals which should be distributed as U(0,1).
• ks: the result of the ks.test for the uniform distribution of U.

References

Ogata, Y. (1988) Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83, 9-27

Author(s)

Sebastian Meyer

See Also

ks.plot.unif and the residuals-method for classes "twinSIR" and "twinstim".

Examples

data("hagelloch")
fit <- twinSIR(~ household, data = hagelloch)  # a simplistic model
## extract the "residual process", i.e., the fitted cumulative intensities
residuals(fit)
## assess goodness of fit based on these residuals
checkResidualProcess(fit)  # could be better