Geoscience Reference
In-Depth Information
Anderson et al. (1994) showed that use of
ˆ
seems to work well, with a good
balance between over- and underfitting of models when these are selected
on the basis of the quasi-AIC (QAIC)
QAIC = −2 log
e
(
L
max
)/
ˆ
+ 2
K
.
(8.27)
Apart from its use with model selection, the VIF can also be used to adjust
the variances of parameter estimates. This can be done by multiplying the
variances that are obtained from the usual model-fitting process by
ˆ
.
If an adjustment using a VIF is used on a routine basis, then it should be
realized that the correct value will generally be one or more. Consequently,
if Equation (8.26) gives
ˆ
< 1, then this should be changed to
ˆ = 1; that is, it
should be assumed that there is no overdispersion.
8.7 Tests of Goodness of Fit
Burnham et al
.
(1987) discussed three tests for the goodness of fit of models
for mark-recapture data. TEST 1 is applicable when there are two or more
groups of animals receiving different treatments. This is not considered fur-
ther here because the test cannot be applied with most sets of data. TEST 2
tests the null hypothesis that survival and capture probabilities are the same
for all animals for a particular sample or period between samples, that is,
that the JS model is correct. TEST 3 also tests whether the assumptions of the
JS model are correct, but against the alternative hypothesis that survival and
capture probabilities vary with the time of release. See the work of Burnham
et al. (1987) for more information about these tests.
8.8 An Example of Mark-Recapture Modeling
Examples of the use of the methods that have been described are now con-
sidered. The calculations needed for these examples were carried out using
three computer programs, MRA-LGE, MRA36, and the mra package for R
(see the Supplementary Material for this chapter), although other programs
such as MARK or routines in the RMark packages for R could have been
used instead. Basically, MRA-LGE fits any mark-recapture model to data
where the probabilities of survival and capture can be expressed through
logistic functions of the form of Equations (8.20) and (8.21), and MRA36 fits
the 36 models described in Section 8.6 to data with two groups of animals,
such as males and females, or fits the relevant subset of nine models if there
