modavgShrink {AICcmodavg} | R Documentation |
Compute Model-averaged Parameter Estimate with Shrinkage (Multimodel Inference)
Description
This function computes an alternative version of model-averaging
parameter estimates that consists in shrinking estimates toward 0 to
reduce model selection bias as in Burnham and Anderson (2002, p. 152),
Anderson (2008, pp. 130-132) and Lukacs et al. (2010). Specifically,
models without the parameter of interest have an estimate and variance
of 0. modavgShrink
also returns unconditional standard errors
and unconditional confidence intervals as described in Buckland et
al. (1997) and Burnham and Anderson (2002).
Usage
modavgShrink(cand.set, parm, modnames = NULL, second.ord = TRUE,
nobs = NULL, uncond.se = "revised", conf.level = 0.95,
...)
## S3 method for class 'AICaov.lm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICbetareg'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICsclm.clm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICclm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICclmm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICcoxme'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICcoxph'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICglm.lm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, gamdisp = NULL, ...)
## S3 method for class 'AICgls'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICglmmTMB'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, ...)
## S3 method for class 'AIChurdle'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AIClm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AIClme'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AIClmekin'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICmer'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICglmerMod'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AIClmerMod'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AIClmerModLmerTest'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICmaxlikeFit.list'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, ...)
## S3 method for class 'AICmultinom.nnet'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, ...)
## S3 method for class 'AICnegbin.glm.lm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICpolr'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICrlm.lm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICsurvreg'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICvglm'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, ...)
## S3 method for class 'AICzeroinfl'
modavgShrink(cand.set, parm, modnames = NULL,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
## S3 method for class 'AICunmarkedFitOccu'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitColExt'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, c.hat = 1, parm.type = NULL,
...)
## S3 method for class 'AICunmarkedFitOccuRN'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitPCount'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitPCO'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitDS'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitGDS'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitOccuFP'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitMPois'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitGMM'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitGPC'
modavgShrink(cand.set, parm, modnames
= NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitOccuMulti'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitOccuMS'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitOccuTTD'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitMMO'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
## S3 method for class 'AICunmarkedFitDSO'
modavgShrink(cand.set, parm, modnames =
NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, c.hat = 1, parm.type = NULL, ...)
Arguments
cand.set |
a list storing each of the models in the candidate model set. |
parm |
the parameter of interest, enclosed between quotes, for which a model-averaged estimate is required. For a categorical variable, the label of the estimate must be included as it appears in the output (see 'Details' below). |
modnames |
a character vector of model names to facilitate the identification of
each model in the model selection table. If |
second.ord |
logical. If |
nobs |
this argument allows to specify a numeric value other than total
sample size to compute the AICc (i.e., |
uncond.se |
either, |
conf.level |
the confidence level ( |
c.hat |
value of overdispersion parameter (i.e., variance inflation factor) such
as that obtained from |
gamdisp |
if gamma GLM is used, the dispersion parameter should be specified here to apply the same value to each model. |
parm.type |
this argument specifies the parameter type on which the
model-averaged estimate of a predictor will be computed and is only
relevant for models of |
... |
additional arguments passed to the function. |
Details
The parameter for which a model-averaged estimate is requested must be
specified with the parm
argument and must be identical to its
label in the model output (e.g., from summary
). For factors, one
must specify the name of the variable and the level of interest. The
shrinkage version of model averaging is only appropriate for cases where
each parameter is given an equal weighting in the model (i.e., each
parameter must appear the same number of times in the models) and has
the same interpretation across all models. As a result, models with
interaction terms or polynomial terms are not supported by
modavgShrink
.
modavgShrink
is implemented for a list containing objects of
aov
, betareg
, clm
, clmm
, clogit
,
coxme
, coxph
, glm
, glmmTMB
, gls
,
hurdle
, lm
, lme
, lmekin
, maxlikeFit
,
mer
, glmerMod
, lmerMod
, lmerModLmerTest
,
multinom
, polr
, rlm
, survreg
, vglm
,
zeroinfl
classes as well as various models of unmarkedFit
classes.
Value
modavgShrink
creates an object of class modavgShrink
with the following components:
Parameter |
the parameter for which a model-averaged estimate with shrinkage was obtained. |
Mod.avg.table |
the model selection table based on models including the parameter of interest. |
Mod.avg.beta |
the model-averaged estimate based on all models. |
Uncond.SE |
the unconditional standard error for the model-averaged estimate (as opposed to the conditional SE based on a single model). |
Conf.level |
the confidence level used to compute the confidence interval. |
Lower.CL |
the lower confidence limit. |
Upper.CL |
the upper confidence limit. |
Author(s)
Marc J. Mazerolle
References
Anderson, D. R. (2008) Model-based Inference in the Life Sciences: a primer on evidence. Springer: New York.
Buckland, S. T., Burnham, K. P., Augustin, N. H. (1997) Model selection: an integral part of inference. Biometrics 53, 603–618.
Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.
Burnham, K. P., Anderson, D. R. (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods and Research 33, 261–304.
Dail, D., Madsen, L. (2011) Models for estimating abundance from repeated counts of an open population. Biometrics 67, 577–587.
Lukacs, P. M., Burnham, K. P., Anderson, D. R. (2010) Model selection bias and Freedman's paradox. Annals of the Institute of Statistical Mathematics 62, 117–125.
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.
Royle, J. A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60, 108–115.
See Also
AICc
, aictab
, c_hat
,
importance
, confset
, evidence
,
modavg
, modavgCustom
,
modavgPred
Examples
##cement example in Burnham and Anderson 2002
data(cement)
##setup same model set as in Table 3.2, p. 102
Cand.models <- list( )
Cand.models[[1]] <- lm(y ~ x1 + x2, data = cement)
Cand.models[[2]] <- lm(y ~ x1 + x2 + x4, data = cement)
Cand.models[[3]] <- lm(y ~ x1 + x2 + x3, data = cement)
Cand.models[[4]] <- lm(y ~ x1 + x4, data = cement)
Cand.models[[5]] <- lm(y ~ x1 + x3 + x4, data = cement)
Cand.models[[6]] <- lm(y ~ x2 + x3 + x4, data = cement)
Cand.models[[7]] <- lm(y ~ x1 + x2 + x3 + x4, data = cement)
Cand.models[[8]] <- lm(y ~ x3 + x4, data = cement)
Cand.models[[9]] <- lm(y ~ x2 + x3, data = cement)
Cand.models[[10]] <- lm(y ~ x4, data = cement)
Cand.models[[11]] <- lm(y ~ x2, data = cement)
Cand.models[[12]] <- lm(y ~ x2 + x4, data = cement)
Cand.models[[13]] <- lm(y ~ x1, data = cement)
Cand.models[[14]] <- lm(y ~ x1 + x3, data = cement)
Cand.models[[15]] <- lm(y ~ x3, data = cement)
##vector of model names
Modnames <- paste("mod", 1:15, sep="")
##AICc
aictab(cand.set = Cand.models, modnames = Modnames)
##compute model-averaged estimate with shrinkage - each parameter
##appears 8 times in the models
modavgShrink(cand.set = Cand.models, modnames = Modnames, parm = "x1")
##compare against classic model-averaging
modavg(cand.set = Cand.models, modnames = Modnames, parm = "x1")
##note that model-averaged estimate with shrinkage is closer to 0 than
##with the classic version
##remove a few models from the set and run again
Cand.unbalanced <- Cand.models[-c(3, 14, 15)]
##set up model names
Modnames <- paste("mod", 1:length(Cand.unbalanced), sep="")
##issues an error because some parameters appear more often than others
## Not run: modavgShrink(cand.set = Cand.unbalanced,
modnames = Modnames, parm = "x1")
## End(Not run)
##example on Orthodont data set in nlme
## Not run:
require(nlme)
##set up candidate model list
##age and sex parameters appear in the same number of models
##same number of models with and without these parameters
Cand.models <- list( )
Cand.models[[1]] <- lme(distance ~ age, data = Orthodont, method = "ML")
##random is ~ age | Subject as it is a grouped data frame
Cand.models[[2]] <- lme(distance ~ age + Sex, data = Orthodont,
random = ~ 1, method = "ML")
Cand.models[[3]] <- lme(distance ~ 1, data = Orthodont, random = ~ 1,
method = "ML")
Cand.models[[4]] <- lme(distance ~ Sex, data = Orthodont, random = ~ 1,
method = "ML")
##create a vector of model names
Modnames <- paste("mod", 1:length(Cand.models), sep = "")
##compute importance values for age
imp.age <- importance(cand.set = Cand.models, parm = "age",
modnames = Modnames, second.ord = TRUE,
nobs = NULL)
##compute shrinkage version of model averaging on age
mod.avg.age.shrink <- modavgShrink(cand.set = Cand.models,
parm = "age", modnames = Modnames,
second.ord = TRUE, nobs = NULL)
##compute classic version of model averaging on age
mod.avg.age.classic <- modavg(cand.set = Cand.models, parm = "age",
modnames = Modnames, second.ord = TRUE,
nobs = NULL)
##correspondence between shrinkage version and classic version of
##model averaging
mod.avg.age.shrink$Mod.avg.beta/imp.age$w.plus
mod.avg.age.classic$Mod.avg.beta
detach(package:nlme)
## End(Not run)
##example of N-mixture model modified from ?pcount
## Not run:
require(unmarked)
data(mallard)
mallardUMF <- unmarkedFramePCount(mallard.y, siteCovs = mallard.site,
obsCovs = mallard.obs)
##set up models so that each variable on abundance appears twice
fm.mall.one <- pcount(~ ivel + date ~ length + forest, mallardUMF,
K = 30)
fm.mall.two <- pcount(~ ivel + date ~ elev + forest, mallardUMF,
K = 30)
fm.mall.three <- pcount(~ ivel + date ~ length + elev, mallardUMF,
K = 30)
##model list and names
Cands <- list(fm.mall.one, fm.mall.two, fm.mall.three)
Modnames <- c("length + forest", "elev + forest", "length + elev")
##compute model-averaged estimate with shrinkage for elev on abundance
modavgShrink(cand.set = Cands, modnames = Modnames, parm = "elev",
parm.type = "lambda")
detach(package:unmarked)
## End(Not run)