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importance

Compute Importance Values of Variable

Description

This function calculates the relative importance of variables (w+) based on the sum of Akaike weights (model probabilities) of the models that include the variable. Note that this measure of evidence is only appropriate when the variable appears in the same number of models as those that do not include the variable.

Usage

importance(cand.set, parm, modnames = NULL, second.ord = TRUE,
           nobs = NULL, ...)

## S3 method for class 'AICaov.lm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICbetareg'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICsclm.clm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICclm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICclmm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICclogit.coxph'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICcoxme'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICcoxph'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICglm.lm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, ...)

## S3 method for class 'AICglmerMod'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AIClmerModLmerTest'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICglmmTMB'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, ...)

## S3 method for class 'AICgls'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AIClm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AIClme'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AIClmekin'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICmaxlikeFit.list'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, ...)

## S3 method for class 'AICmer'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICmultinom.nnet'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, ...)

## S3 method for class 'AICnegbin.glm.lm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICnlmerMod'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICpolr'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICrlm.lm'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICsurvreg'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, ...)

## S3 method for class 'AICunmarkedFitColExt'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccu'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccuFP'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccuRN'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitPCount'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitPCO'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitDS'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitGDS'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitMPois'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitGMM'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitGPC'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccuMulti'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccuMS'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL,
       ...)

## S3 method for class 'AICunmarkedFitOccuTTD'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL,
       ...)

## S3 method for class 'AICunmarkedFitMMO'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL,
       ...)

## S3 method for class 'AICunmarkedFitDSO'
importance(cand.set, parm, modnames = NULL,
           second.ord = TRUE, nobs = NULL, c.hat = 1, parm.type = NULL,
       ...)

## S3 method for class 'AICvglm'
importance(cand.set, parm, modnames = NULL, 
           second.ord = TRUE, nobs = NULL, c.hat = 1, ...)

## S3 method for class 'AICzeroinfl'
importance(cand.set, parm, modnames = NULL, 
           second.ord = TRUE, nobs = NULL, ...)

Arguments

cand.set

a list storing each of the models in the candidate model set.

parm

the parameter of interest for which a measure of relative importance is required.

modnames

a character vector of model names to facilitate the identification of each model in the model selection table. If NULL, the function uses the names in the cand.set list of candidate models. If no names appear in the list, generic names (e.g., Mod1, Mod2) are supplied in the table in the same order as in the list of candidate models.

second.ord

logical. If TRUE, the function returns the second-order Akaike information criterion (i.e., AICc).

nobs

this argument allows to specify a numeric value other than total sample size to compute the AICc (i.e., nobs defaults to total number of observations). 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.

c.hat

value of overdispersion parameter (i.e., variance inflation factor) such as that obtained from c_hat. Note that values of c.hat different from 1 are only appropriate for binomial GLM's with trials > 1 (i.e., success/trial or cbind(success, failure) syntax), with Poisson GLM's, single-season occupancy models (MacKenzie et al. 2002), dynamic occupancy models (MacKenzie et al. 2003), or N-mixture models (Royle 2004, Dail and Madsen 2011). If c.hat > 1, importance will return the quasi-likelihood analogue of the information criteria requested and multiply the variance-covariance matrix of the estimates by this value (i.e., SE's are multiplied by sqrt(c.hat)). This option is not supported for generalized linear mixed models of the mer or merMod classes.

parm.type

this argument specifies the parameter type on which the variable of interest will be extracted and is only relevant for models of unmarkedFit classes. The character strings supported vary with the type of model fitted. For unmarkedFitOccu and unmarkedFitOccuMulti objects, either psi or detect can be supplied to indicate whether the parameter is on occupancy or detectability, respectively. For unmarkedFitColExt objects, possible values are psi, gamma, epsilon, and detect, for parameters on occupancy in the inital year, colonization, extinction, and detectability, respectively. For unmarkedFitOccuTTD objects, possible values are psi, gamma, epsilon, and detect, for parameters on occupancy in the inital year, colonization, extinction, and time-to-dection (lambda rate parameter), respectively. For unmarkedFitOccuFP objects, one can specify psi, detect, falsepos, and certain, for occupancy, detectability, probability of assigning false-positives, and probability detections are certain, respectively. For unmarkedFitOccuMS objects, possible values are psi, phi, or detect, denoting occupancy, transition, and detection probabilities, respectively. For unmarkedFitOccuRN objects, either lambda or detect can be entered for abundance and detectability parameters, respectively. For unmarkedFitPCount and unmarkedFitMPois objects, lambda or detect denote parameters on abundance and detectability, respectively. For unmarkedFitPCO, unmarkedFitMMO, and unmarkedFitDSO objects, one can enter lambda, gamma, omega, iota, or detect, to specify parameters on abundance, recruitment, apparent survival, immigration, and detectability, respectively. For unmarkedFitDS objects, lambda and detect are supported. For unmarkedFitGDS, lambda, phi, and detect denote abundance, availability, and detection probability, respectively. For unmarkedFitGMM and unmarkedFitGPC objects, lambda, phi, and detect denote abundance, availability, and detectability, respectively.

...

additional arguments passed to the function.

Value

importance returns an object of class importance consisting of the following components:

parm

the parameter for which an importance value is required.
w.plus

the sum of Akaike weights for the models that include the parameter of interest.
w.minus

the sum of Akaike weights for the models that exclude the parameter of interest.

Author(s)

Marc J. Mazerolle

References

Burnham, K. P., and Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.

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.

Royle, J. A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60, 108–115.

See Also

Examples

##example on Orthodont data set in nlme
## Not run: 
require(nlme)

##set up candidate model list
Cand.models <- list( )
Cand.models[[1]] <- lme(distance ~ age, data = Orthodont, method = "ML")
##random is ~ age | Subject
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 = "")

importance(cand.set = Cand.models, parm = "age", modnames = Modnames,
           second.ord = TRUE, nobs = NULL)
##round to 4 digits after decimal point
print(importance(cand.set = Cand.models, parm = "age", modnames = Modnames,
                 second.ord = TRUE, nobs = NULL), digits = 4)
detach(package:nlme)

## End(Not run)


##single-season occupancy model example modified from ?occu
## Not run: 
require(unmarked)
##single season
data(frogs)
pferUMF <- unmarkedFrameOccu(pfer.bin)
## add some fake covariates for illustration
siteCovs(pferUMF) <- data.frame(sitevar1 = rnorm(numSites(pferUMF)),
                                sitevar2 = rnorm(numSites(pferUMF))) 
     
## observation covariates are in site-major, observation-minor order
obsCovs(pferUMF) <- data.frame(obsvar1 = rnorm(numSites(pferUMF) *
                                 obsNum(pferUMF))) 

##set up candidate model set
fm1 <- occu(~ obsvar1 ~ sitevar1, pferUMF)
fm2 <- occu(~ 1 ~ sitevar1, pferUMF)
fm3 <- occu(~ obsvar1 ~ sitevar2, pferUMF)
fm4 <- occu(~ 1 ~ sitevar2, pferUMF)
Cand.mods <- list(fm1, fm2, fm3, fm4)
Modnames <- c("fm1", "fm2", "fm3", "fm4")

##compute importance value for 'sitevar1' on occupancy
importance(cand.set = Cand.mods, modnames = Modnames, parm = "sitevar1",
           parm.type = "psi")
##compute importance value for 'obsvar1' on detectability
importance(cand.set = Cand.mods, modnames = Modnames, parm = "obsvar1",
           parm.type = "detect")


##example with multispecies occupancy modify from ?occuMulti
##Simulate 3 species data
N <- 80
nspecies <- 3
J <- 4
     
occ_covs <- as.data.frame(matrix(rnorm(N * 10),ncol=10))
names(occ_covs) <- paste('par',1:10,sep='')

det_covs <- list()
for (i in 1:nspecies){
    det_covs[[i]] <- matrix(rnorm(N*J),nrow=N)
}
names(det_covs) <- paste('par',1:nspecies,sep='')

##True vals
beta <- c(0.5,0.2,0.4,0.5,-0.1,-0.3,0.2,0.1,-1,0.1)
f1 <- beta[1] + beta[2]*occ_covs$par1
f2 <- beta[3] + beta[4]*occ_covs$par2
f3 <- beta[5] + beta[6]*occ_covs$par3
f4 <- beta[7]
f5 <- beta[8]
f6 <- beta[9]
f7 <- beta[10]
f <- cbind(f1,f2,f3,f4,f5,f6,f7)
z <- expand.grid(rep(list(1:0),nspecies))[,nspecies:1]
colnames(z) <- paste('sp',1:nspecies,sep='')
dm <- model.matrix(as.formula(paste0("~.^",nspecies,"-1")),z)

psi <- exp(f 
psi <- psi/rowSums(psi)

##True state
ztruth <- matrix(NA,nrow=N,ncol=nspecies)
for (i in 1:N){
    ztruth[i,] <- as.matrix(z[sample(8,1,prob=psi[i,]),])
}
     
p_true <- c(0.6,0.7,0.5)

## fake y data
y <- list()
     
for (i in 1:nspecies){
    y[[i]] <- matrix(NA,N,J)
    for (j in 1:N){
        for (k in 1:J){
            y[[i]][j,k] <- rbinom(1,1,ztruth[j,i]*p_true[i])
        }
    }
}
names(y) <- c('coyote','tiger','bear')
     
##Create the unmarked data object
data <- unmarkedFrameOccuMulti(y=y,siteCovs=occ_covs,obsCovs=det_covs)

## Formulas for state and detection processes
## Length should match number/order of columns in fDesign
occFormulas <- c('~par1 + par2','~par2','~par3','~1','~1','~1','~1')
occFormulas2 <- c('~par1 + par3','~par1 + par2','~par1 + par2 + par3',
                  "~ 1", "~1", "~ 1", "~1")

##Length should match number/order of species in data@ylist
detFormulas <- c('~1','~1','~1')
     
fit <- occuMulti(detFormulas,occFormulas,data)
fit2 <- occuMulti(detFormulas,occFormulas2,data)

##importance
importance(cand.set = list(fit, fit2), parm = "[coyote] par2",
           parm.type = "psi")


detach(package:unmarked)

## End(Not run)
AICcmodavg

Model Selection and Multimodel Inference Based on (Q)AIC(c)

v2.3-1
GPL (>= 2)
Authors
Marc J. Mazerolle <marc.mazerolle@sbf.ulaval.ca>
Initial release
2020-08-21

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