Compare SECR Models
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"))
## S3 method for class 'secrlist'
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"))
## 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 |
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 with small sample adjustment is given by
AICc = -2log(L(theta-hat)) + 2K + 2K(K+1)/(n-K-1)
where K is the number of "beta" parameters estimated. 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 = exp(-delta_i / 2) / sum{ exp(-delta_i / 2) }
, where delta refers to differences in AIC or AICc depending on the argument ‘criterion’.
Models for which delta > dmax are given a weight of zero and are
excluded from the summation. Model weights may be used to form
model-averaged estimates of real or beta parameters with
model.average (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).
A data frame with one row per model. By default, rows are sorted by ascending AICc.
model |
character string describing the fitted model |
detectfn |
shape of detection function fitted (halfnormal vs hazard-rate) |
npar |
number of parameters estimated |
logLik |
maximized log likelihood |
AIC |
Akaike's Information Criterion |
AICc |
AIC with small-sample 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).
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
multi-session models should not be compared with single-session models based on the same data.
A likelihood-ratio test (LR.test) is a more direct way to
compare two models.
The issue of goodness-of-fit 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 Information-Theoretic Approach. Second edition. New York: Springer-Verlag.
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) Model-averaged Wald confidence intervals. Computational statistics and data analysis 56, 2809–2815.
## 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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