Goodness of fit testing for detection function models. For continuous
distances Kolmogorov-Smirnov and Cramer-von Mises tests can be used, when
binned or continuous distances are used a
\chi^2 test can be used.
plot = TRUE,
chisq = FALSE,
nboot = 100,
ks = FALSE,
nc = NULL,
breaks = NULL,
a fitted detection function.
number of replicates to use to calculate p-values for the Kolmogorov-Smirnov goodness of fit test statistics
perform the Kolmogorov-Smirnov test (this involves many bootstraps so can take a while)
number of evenly-spaced distance classes for chi-squared test, if
vector of cutpoints to use for binning, if
other arguments to be passed to
Kolmogorov-Smirnov and Cramer-von Mises tests are based on looking at the
quantile-quantile plot produced by
deviations from the line
The Kolmogorov-Smirnov test asks the question "what's the largest vertical
distance between a point and the
y=x line?" It uses this distance as a
statistic to test the null hypothesis that the samples (EDF and CDF in our
case) are from the same distribution (and hence our model fits well). If the
deviation between the
y=x line and the points is too large we reject
the null hypothesis and say the model doesn't have a good fit.
Rather than looking at the single biggest difference between the y=x line and the points in the Q-Q plot, we might prefer to think about all the differences between line and points, since there may be many smaller differences that we want to take into account rather than looking for one large deviation. Its null hypothesis is the same, but the statistic it uses is the sum of the deviations from each of the point to the line.
A chi-squared test is also run if
chisq=TRUE. In this case binning of
distances is required if distance data are continuous. This can be specified
as a number of equally-spaced bins (using the argument
nc=) or the
cutpoints of bins (using
breaks=). The test compares the number of
observations in a given bin to the number predicted under the fitted
Note that a bootstrap procedure is required for the Kolmogorov-Smirnov test
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. The
nboot parameter controls the number of bootstraps
to use. Set to
0 to avoid computing bootstraps (much faster but with no
Kolmogorov-Smirnov results, of course).
## Not run:
# fit and test a simple model for the golf tee data
tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1)
ds.model <- ds(tee.data,4)
# don't make plot
## End(Not run)
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