qqplot.ddf: Quantile-quantile plot and goodness of fit tests for detection functions

Description

Constructs a quantile-quantile (Q-Q) plot for fitted model as a graphical check of goodness of fit. Formal goodness of fit testing for detection function models using Kolmogorov-Smirnov and Cramer-von Mises tests. Both tests are based on looking at the quantile-quantile plot produced by qqplot.ddf and deviations from the line x=y.

Usage

qqplot.ddf(model, plot = TRUE, nboot = 100, ks = FALSE, ...)

Value

A list of goodness of fit related values:

edf: matrix of lower and upper empirical distribution function values
cdf: fitted cumulative distribution function values
ks: list with K-S statistic (Dn) and p-value (p)
CvM: list with CvM statistic (W) and p-value (p)

Arguments

model: fitted distance detection function model object
plot: the Q-Q plot be plotted or just report statistics?
nboot: number of replicates to use to calculate p-values for the goodness of fit test statistics
ks: perform the Kolmogorov-Smirnov test (this involves many bootstraps so can take a while)
...: additional arguments passed to plot

Author

Jeff Laake, David L Miller

Details

Note that a bootstrap procedure is required to ensure that the p-values from the procedure are correct as the we are comparing the cumulative distribution function (CDF) and empirical distribution function (EDF) and we have estimated the parameters of the detection function.

References

Burnham, K.P., S.T. Buckland, J.L. Laake, D.L. Borchers, T.A. Marques, J.R.B. Bishop, and L. Thomas. 2004. Further topics in distance sampling. pp: 385-389. In: Advanced Distance Sampling, eds. S.T. Buckland, D.R.Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, and L. Thomas. Oxford University Press.