anovaOD: Likelihood-Ratio Test Corrected for Overdispersion
In AICcmodavg: Model Selection and Multimodel Inference Based on (Q)AIC(c)
anovaOD R Documentation
Likelihood-Ratio Test Corrected for Overdispersion
Description
Compute likelihood-ratio test between a given model and a simpler model.
Usage
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'glm'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccu'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitColExt'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuRN'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitPCount'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitPCO'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitDS'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitGDS'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuFP'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitMPois'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitGMM'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitGPC'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuMS'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuTTD'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitMMO'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitDSO'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'glmerMod'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'maxlikeFit'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'multinom'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'vglm'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
Arguments
mod.simple
an object of class glm, glmmTMB,
maxlikeFit, mer, merMod, multinom,
vglm, and various unmarkedFit classes containing
the output of a model. This model should be a simpler version of
mod.complex resulting from a deletion of certain terms (i.e.,
nested model).
mod.complex
an object of the same class as mod.simple.
c.hat
value of overdispersion parameter (i.e., variance inflation factor)
such as that obtained from c_hat, mb.gof.test, or
Nmix.gof.test. Typically, this value should be computed for
the most complex model and applied to simpler models.
nobs
the number of observations used in the analysis. If nobs =
NULL, the total number of rows are used as the sample size to
compute the residual degrees of freedom as nobs - K, where
K is the number of estimated parameters. This is relevant
only for mixed models or various models of unmarkedFit
classes where sample size is not straightforward. In such cases,
one might use total number of observations or number of independent
clusters (e.g., sites) as the value of nobs.
...
additional arguments passed to the function.
Details
This function applies a correction for overdispersion on the
likelihood-ratio test between a model and its simpler counterpart.
The simpler model must be nested within the more complex model,
typically as the result of deleting terms. You should supply the
c.hat value of the most complex of the two models you are
comparing.
When 1 < c.hat < 4, the likelihood-ratio test is computed
as:
LR = \frac{-2 * (LL.simple - LL.complex)}{(K.complex - K.simple)
* c.hat}
where LL.simple and LL.complex are the log-likelihoods
of the simple and complex models, respectively, and where
K.complex and K.simple are the number of estimated
parameters in each model. The test statistic is approximately
distributed as F_{K.complex - K.simple, n - K.complex}, where
n is the number of observations (i.e., nobs) used in the
analysis (Venables and Ripley 2002).
When nobs = NULL, the number of observations is based on the
number of rows of the data frame used in the analysis. For mixed
models or various models of unmarkedFit, sample size is less
straightforward, and nobs could be based on the total number of
observations or on the number of independent clusters (e.g., sites),
among other choices.
When c.hat = 1, the likelihood-ratio test simplifies to:
LR = -2 * (LL.simple - LL.complex)
where in this case the test statistic is distributed as a
\chi^2_{K.complex - K.simple} (McCullagh and Nelder 1989).
The function supports different model types such as Poisson GLM's and
GLMM's, single-season and dynamic occupancy models (MacKenzie et
al. 2002, 2003), and various N-mixture models (Royle 2004,
Dail and Madsen 2011).
Value
anovaOD returns an object of class anovaOD as a list with
the following components:
form.simple
a character string of the parameters estimated in mod.simple.
form.complex
a character string of the parameters estimated in mod.complex.
c.hat
the c.hat estimate used to adjust the
likelihood-ratio test.
devMat
a matrix storing as columns the number of parameters
estimated (K), the log-likelihood of each model logLik,
the difference in estimated parameters between the two models
(Kdiff), minus twice the difference in log-likelihoods between
the models (-2LL), the test statistic, and the associated
P-value.
Author(s)
Marc J. Mazerolle
References
Dail, D., Madsen, L. (2011) Models for estimating abundance from
repeated counts of an open population. Biometrics 67,
577–587.
MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle,
J. A., Langtimm, C. A. (2002) Estimating site occupancy rates when
detection probabilities are less than one. Ecology 83,
2248–2255.
MacKenzie, D. I., Nichols, J. D., Hines, J. E., Knutson, M. G.,
Franklin, A. B. (2003) Estimating site occupancy, colonization, and
local extinction when a species is detected imperfectly. Ecology
84, 2200–2207.
Mazerolle, M. J. (2006) Improving data analysis in herpetology: using
Akaike's Information Criterion (AIC) to assess the strength of
biological hypotheses. Amphibia-Reptilia 27, 169–180.
McCullagh, P., Nelder, J. A. (1989) Generalized Linear
Models. Second edition. Chapman and Hall: New York.
Royle, J. A. (2004) N-mixture models for estimating population
size from spatially replicated counts. Biometrics 60,
108–115.
Venables, W. N., Ripley, B. D. (2002) Modern Applied Statistics
with S. Second edition. Springer-Verlag: New York.
See Also
c_hat, mb.gof.test,
Nmix.gof.test, summaryOD
Examples
##anuran larvae example from Mazerolle (2006)
data(min.trap)
##assign "UPLAND" as the reference level as in Mazerolle (2006)
min.trap$Type <- relevel(min.trap$Type, ref = "UPLAND")
##run model
m1 <- glm(Num_anura ~ Type + log.Perimeter + Num_ranatra,
family = poisson, offset = log(Effort),
data = min.trap)
##null model
m0 <- glm(Num_anura ~ 1,
family = poisson, offset = log(Effort),
data = min.trap)
##check c-hat for global model
c_hat(m1) #uses Pearson's chi-square/df
##likelihood ratio test corrected for overdispersion
anovaOD(mod.simple = m0, mod.complex = m1, c.hat = c_hat(m1))
##compare without overdispersion correction
anovaOD(mod.simple = m0, mod.complex = m1)
##example with occupancy model
## Not run:
##load unmarked package
if(require(unmarked)){
data(bullfrog)
##detection data
detections <- bullfrog[, 3:9]
##assemble in unmarkedFrameOccu
bfrog <- unmarkedFrameOccu(y = detections)
##run model
fm <- occu(~ 1 ~ Reed.presence, data = bfrog)
##null model
fm0 <- occu(~ 1 ~ 1, data = bfrog)
##check GOF
##GOF <- mb.gof.test(fm, nsim = 1000)
##estimate of c-hat: 1.89
##display results after overdispersion adjustment
anovaOD(fm0, fm, c.hat = 1.89)
detach(package:unmarked)
}
## End(Not run)
AICcmodavg documentation built on Nov. 17, 2023, 1:08 a.m.
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| anovaOD | R Documentation |
Likelihood-Ratio Test Corrected for Overdispersion
Description
Compute likelihood-ratio test between a given model and a simpler model.
Usage
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'glm'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccu'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitColExt'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuRN'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitPCount'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitPCO'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitDS'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitGDS'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuFP'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitMPois'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitGMM'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitGPC'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuMS'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitOccuTTD'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitMMO'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'unmarkedFitDSO'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'glmerMod'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'maxlikeFit'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'multinom'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
## S3 method for class 'vglm'
anovaOD(mod.simple, mod.complex, c.hat = 1,
nobs = NULL, ...)
Arguments
mod.simple |
an object of class |
mod.complex |
an object of the same class as |
c.hat |
value of overdispersion parameter (i.e., variance inflation factor)
such as that obtained from |
nobs |
the number of observations used in the analysis. If |
... |
additional arguments passed to the function. |
Details
This function applies a correction for overdispersion on the
likelihood-ratio test between a model and its simpler counterpart.
The simpler model must be nested within the more complex model,
typically as the result of deleting terms. You should supply the
c.hat value of the most complex of the two models you are
comparing.
When 1 < c.hat < 4, the likelihood-ratio test is computed
as:
LR = \frac{-2 * (LL.simple - LL.complex)}{(K.complex - K.simple)
* c.hat}
where LL.simple and LL.complex are the log-likelihoods
of the simple and complex models, respectively, and where
K.complex and K.simple are the number of estimated
parameters in each model. The test statistic is approximately
distributed as F_{K.complex - K.simple, n - K.complex}, where
n is the number of observations (i.e., nobs) used in the
analysis (Venables and Ripley 2002).
When nobs = NULL, the number of observations is based on the
number of rows of the data frame used in the analysis. For mixed
models or various models of unmarkedFit, sample size is less
straightforward, and nobs could be based on the total number of
observations or on the number of independent clusters (e.g., sites),
among other choices.
When c.hat = 1, the likelihood-ratio test simplifies to:
LR = -2 * (LL.simple - LL.complex)
where in this case the test statistic is distributed as a
\chi^2_{K.complex - K.simple} (McCullagh and Nelder 1989).
The function supports different model types such as Poisson GLM's and GLMM's, single-season and dynamic occupancy models (MacKenzie et al. 2002, 2003), and various N-mixture models (Royle 2004, Dail and Madsen 2011).
Value
anovaOD returns an object of class anovaOD as a list with
the following components:
form.simple |
a character string of the parameters estimated in |
form.complex |
a character string of the parameters estimated in |
c.hat |
the |
devMat |
a matrix storing as columns the number of parameters
estimated ( |
Author(s)
Marc J. Mazerolle
References
Dail, D., Madsen, L. (2011) Models for estimating abundance from repeated counts of an open population. Biometrics 67, 577–587.
MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle, J. A., Langtimm, C. A. (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83, 2248–2255.
MacKenzie, D. I., Nichols, J. D., Hines, J. E., Knutson, M. G., Franklin, A. B. (2003) Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84, 2200–2207.
Mazerolle, M. J. (2006) Improving data analysis in herpetology: using Akaike's Information Criterion (AIC) to assess the strength of biological hypotheses. Amphibia-Reptilia 27, 169–180.
McCullagh, P., Nelder, J. A. (1989) Generalized Linear Models. Second edition. Chapman and Hall: New York.
Royle, J. A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60, 108–115.
Venables, W. N., Ripley, B. D. (2002) Modern Applied Statistics with S. Second edition. Springer-Verlag: New York.
See Also
c_hat, mb.gof.test,
Nmix.gof.test, summaryOD
Examples
##anuran larvae example from Mazerolle (2006)
data(min.trap)
##assign "UPLAND" as the reference level as in Mazerolle (2006)
min.trap$Type <- relevel(min.trap$Type, ref = "UPLAND")
##run model
m1 <- glm(Num_anura ~ Type + log.Perimeter + Num_ranatra,
family = poisson, offset = log(Effort),
data = min.trap)
##null model
m0 <- glm(Num_anura ~ 1,
family = poisson, offset = log(Effort),
data = min.trap)
##check c-hat for global model
c_hat(m1) #uses Pearson's chi-square/df
##likelihood ratio test corrected for overdispersion
anovaOD(mod.simple = m0, mod.complex = m1, c.hat = c_hat(m1))
##compare without overdispersion correction
anovaOD(mod.simple = m0, mod.complex = m1)
##example with occupancy model
## Not run:
##load unmarked package
if(require(unmarked)){
data(bullfrog)
##detection data
detections <- bullfrog[, 3:9]
##assemble in unmarkedFrameOccu
bfrog <- unmarkedFrameOccu(y = detections)
##run model
fm <- occu(~ 1 ~ Reed.presence, data = bfrog)
##null model
fm0 <- occu(~ 1 ~ 1, data = bfrog)
##check GOF
##GOF <- mb.gof.test(fm, nsim = 1000)
##estimate of c-hat: 1.89
##display results after overdispersion adjustment
anovaOD(fm0, fm, c.hat = 1.89)
detach(package:unmarked)
}
## End(Not run)
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