AIC.secr  R Documentation 
Terse report on the fit of one or more spatially explicit capture–recapture models. Models with smaller values of AIC (Akaike's Information Criterion) are preferred. Extraction ([) and logLik methods are included.
## S3 method for class 'secr'
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"), chat = NULL)
## S3 method for class 'secrlist'
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"), chat = NULL)
## S3 method for class 'secr'
logLik(object, ...)
secrlist(...)
## S3 method for class 'secrlist'
x[i]
object 

... 
other 
sort 
logical for whether rows should be sorted by ascending AICc 
k 
numeric, penalty per parameter to be used; always k = 2 in this method 
dmax 
numeric, maximum AIC difference for inclusion in confidence set 
criterion 
character, criterion to use for model comparison and weights 
chat 
numeric optional variance inflation factor for quasiAIC 
x 
secrlist 
i 
indices 
Models to be compared must have been fitted to the same data and use the
same likelihood method (full vs conditional). From version 4.1 a warning is
issued if AICcompatible
reveals a problem.
AIC is given by
\mbox{AIC} = 2\log(L(\hat{\theta})) + 2K
where K
is the number of "beta" parameters estimated.
AIC with small sample adjustment is given by
\mbox{AIC}_c = 2\log(L(\hat{\theta})) + 2K +
\frac{2K(K+1)}{nK1}.
The sample size n
is the number of individuals observed at least once (i.e. the
number of rows in capthist
).
Model weights are calculated as
w_i = \frac{\exp(\Delta_i / 2),}{
\sum{\exp(\Delta_i / 2)}}
where \Delta
refers to differences in AIC or AICc depending on the
argument ‘criterion’. AICc is widely used, but AIC may be better (Fletcher 2018, p. 60).
Models for which delta > dmax
are given a weight of zero and are
excluded from the summation. Model weights may be used to form
modelaveraged estimates of real or beta parameters with
modelAverage
(see also Buckland et al. 1997, Burnham and
Anderson 2002).
The argument k
is included for consistency with the generic method AIC
.
secrlist
forms a list of fitted models (an object of class
‘secrlist’) from the fitted models in .... Arguments may include
secrlists. If secr components are named the model names will be retained
(see Examples).
If chat (\hat c
) is provided then quasiAIC values are computed (secr >= 4.6.0):
\mbox{QAIC} = 2\log(L(\hat{\theta}))/ \hat c + 2K.
A data frame with one row per model. By default, rows are sorted by ascending 'criterion' (default AICc).
model 
character string describing the fitted model 
detectfn 
shape of detection function fitted (halfnormal vs hazardrate) 
npar 
number of parameters estimated 
logLik 
maximized log likelihood 
AIC 
Akaike's Information Criterion 
AICc 
AIC with smallsample adjustment of Hurvich & Tsai (1989) 
And depending on criterion
:
dAICc 
difference between AICc of this model and the one with smallest AICc 
AICcwt 
AICc model weight 
or
dAIC 
difference between AIC of this model and the one with smallest AIC 
AICwt 
AIC model weight 
logLik.secr
returns an object of class ‘logLik’ that has
attribute df
(degrees of freedom = number of estimated
parameters).
If the variance inflation factor 'chat' is provided then outputs AIC, AICc etc. are replaced by the corresponding quasiAIC values labelled QAIC, QAICc etc.
It is not be meaningful to compare models by AIC if they relate to
different data (see AICcompatible
).
Specifically:
an ‘secrlist’ generated and saved to file by mask.check
may be supplied as the object argument of AIC.secrlist
, but the
results are not informative
models fitted by the conditional likelihood (CL = TRUE
) and
full likelihood (CL = FALSE
) methods cannot be compared
hybrid mixture models (using hcov argument of secr.fit) should not be compared with other models
grouped models (using groups argument of secr.fit) should not be compared with other models
multisession models should not be compared with singlesession models based on the same data.
A likelihoodratio test (LR.test
) is a more direct way to
compare two models.
The issue of goodnessoffit and possible adjustment of AIC for overdispersion has yet to be addressed (cf QAIC in MARK).
From version 2.6.0 the user may select between AIC and AICc for comparing models, whereas previously only AICc was used and AICc weights were reported as ‘AICwt’). There is evidence that AIC may be better for model averaging even when samples are small sizes  Turek and Fletcher (2012).
Buckland S. T., Burnham K. P. and Augustin, N. H. (1997) Model selection: an integral part of inference. Biometrics 53, 603–618.
Burnham, K. P. and Anderson, D. R. (2002) Model Selection and Multimodel Inference: A Practical InformationTheoretic Approach. Second edition. New York: SpringerVerlag.
Fletcher, D. (2019) Model averaging. SpringerBriefs in Statistics. Berlin: SpringerVerlag.
Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples. Biometrika 76, 297–307.
Turek, D. and Fletcher, D. (2012) Modelaveraged Wald confidence intervals. Computational statistics and data analysis 56, 2809–2815.
AICcompatible
,
modelAverage
,
AIC
,
secr.fit
,
print.secr
,
score.test
,
LR.test
,
deviance.secr
## Compare two models fitted previously
## secrdemo.0 is a null model
## secrdemo.b has a learned trap response
AIC(secrdemo.0, secrdemo.b)
## Form secrlist and pass to AIC.secr
temp < secrlist(null = secrdemo.0, learnedresponse = secrdemo.b)
AIC(temp)
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