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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

`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.

- 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.

Marc J. Mazerolle

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.

`AICc`

, `aictab`

, `c_hat`

,
`confset`

, `evidence`

, `modavg`

,
`modavgShrink`

, `modavgPred`