modavg: Compute Model-averaged Parameter Estimate (Multimodel Inference)

Description

This function model-averages the estimate of a parameter of interest among a set of candidate models, computes the unconditional standard error and unconditional confidence intervals as described in Buckland et al. (1997) and Burnham and Anderson (2002). This model-averaged estimate is also referred to as a natural average of the estimate by Burnham and Anderson (2002, p. 152).

Usage

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modavg(cand.set, parm, modnames = NULL, second.ord = TRUE, nobs = NULL, 
       uncond.se = "revised", conf.level = 0.95, exclude = NULL, warn =
       TRUE, ...) 

## S3 method for class 'AICaov.lm'
modavg(cand.set, parm, modnames = NULL, second.ord =
        TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICbetareg'
modavg(cand.set, parm, modnames = NULL, second.ord =
        TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICsclm.clm'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICclm'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICclmm'
modavg(cand.set, parm, modnames = NULL, second.ord 
        = TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICcoxme'
modavg(cand.set, parm, modnames = NULL, second.ord
        = TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICcoxph'
modavg(cand.set, parm, modnames = NULL, second.ord
        = TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICglm.lm'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        gamdisp = NULL, ...)

## S3 method for class 'AICgls'
modavg(cand.set, parm, modnames = NULL, second.ord =
           TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
           exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AIChurdle'
modavg(cand.set, parm, modnames = NULL,
         second.ord = TRUE, nobs = NULL, uncond.se = "revised",
         conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AIClm'
modavg(cand.set, parm, modnames = NULL, second.ord =
        TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AIClme'
modavg(cand.set, parm, modnames = NULL, second.ord =
        TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AIClmekin'
modavg(cand.set, parm, modnames = NULL,
         second.ord = TRUE, nobs = NULL, uncond.se = "revised",
         conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICmaxlikeFit.list'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        ...)

## S3 method for class 'AICmer'
modavg(cand.set, parm, modnames = NULL, second.ord =
        TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AIClmerMod'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICglmerMod'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICmultinom.nnet'
modavg(cand.set, parm, modnames = NULL, 
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        ...)

## S3 method for class 'AICpolr'
modavg(cand.set, parm, modnames = NULL, second.ord
        = TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICrlm.lm'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICsurvreg'
modavg(cand.set, parm, modnames = NULL, second.ord =
        TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
        exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICvglm'
modavg(cand.set, parm, modnames = NULL, second.ord
         = TRUE, nobs = NULL, uncond.se = "revised", conf.level = 0.95,
         exclude = NULL, warn = TRUE, c.hat = 1, ...)

## S3 method for class 'AICzeroinfl'
modavg(cand.set, parm, modnames = NULL,
         second.ord = TRUE, nobs = NULL, uncond.se = "revised",
         conf.level = 0.95, exclude = NULL, warn = TRUE, ...)

## S3 method for class 'AICunmarkedFitOccu'
modavg(cand.set, parm, modnames = NULL, 
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitColExt'
modavg(cand.set, parm, modnames =
        NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccuRN'
modavg(cand.set, parm, modnames =
        NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitPCount'
modavg(cand.set, parm, modnames =
        NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitPCO'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitDS'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitGDS'
modavg(cand.set, parm, modnames = NULL,
        second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitOccuFP'
modavg(cand.set, parm, modnames =
        NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitMPois'
modavg(cand.set, parm, modnames =
        NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
        parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitGMM'
modavg(cand.set, parm, modnames =
       NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
       conf.level = 0.95, exclude = NULL, warn = TRUE, c.hat = 1,
       parm.type = NULL, ...)

## S3 method for class 'AICunmarkedFitGPC'
modavg(cand.set, parm, modnames =
        NULL, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
        conf.level = 0.95, exclude = NULL, warn = TRUE, 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 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.

uncond.se

either, "old", or "revised", specifying the equation used to compute the unconditional standard error of a model-averaged estimate. With uncond.se = "old", computations are based on equation 4.9 of Burnham and Anderson (2002), which was the former way to compute unconditional standard errors. With uncond.se = "revised", equation 6.12 of Burnham and Anderson (2002) is used. Anderson (2008, p. 111) recommends use of the revised version for the computation of unconditional standard errors and it is now the default. Note that versions of package AICcmodavg < 1.04 used the old method to compute unconditional standard errors.

conf.level

the confidence level (1 - α) requested for the computation of unconditional confidence intervals.

exclude

this argument excludes models based on the terms specified for the computation of a model-averaged estimate of parm. The exclude argument is set to NULL by default and does not exclude any models other than those without the parm. When parm is a main effect but is also involved in interactions/polynomial terms in some models, one should specify the interaction/polynomial terms as a list to exclude models with these terms from the computation of model-averaged estimate of the main effect (e.g., exclude = list("sex:mass", "mass2")). See 'Details' and 'Examples' below.

warn

logical. If TRUE, modavg performs a check and isssues a warning when the value in parm occurs more than once in any given model. This is a check for potential interaction/polynomial terms in the model when such terms are constructed with the usual operators (e.g., I( ) for polynomial terms, : for interaction terms).

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, modavg 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.

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 effect size will be computed and is only relevant for models of unmarkedFitOccu, unmarkedFitColExt, unmarkedFitOccuFP, unmarkedFitOccuRN, unmarkedFitMPois, unmarkedFitPCount, unmarkedFitPCO, unmarkedFitDS, unmarkedFitGDS, unmarkedFitGMM, and unmarkedFitGPC classes. The character strings supported vary with the type of model fitted. For unmarkedFitOccu objects, either psi or detect can be supplied to indicate whether the parameter is on occupancy or detectability, respectively. For unmarkedFitColExt, possible values are psi, gamma, epsilon, and detect, for parameters on occupancy in the inital year, colonization, extinction, and detectability, respectively. For unmarkedFitOccuFP objects, one can specify psi, detect, or fp, for occupancy, detectability, and probability of assigning false-positives, 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 objects, one can enter lambda, gamma, omega, or detect, to specify parameters on abundance, recruitment, apparent survival, and detectability, respectively. For unmarkedFitDS objects, only lambda is supported for the moment. For unmarkedFitGDS, lambda and phi denote abundance and availability, respectively. For unmarkedFitGMM and unmarkedFitGPC objects, lambda, phi, and detect denote abundance, availability, and detectability, respectively.

...

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. modavg includes checks to find variations of interaction terms specified in the parm and exclude arguments. However, to avoid problems, one should specify interaction terms consistently for all models: e.g., either a:b or b:a for all models, but not a mixture of both.

You must exercise caution when some models include interaction or polynomial terms, because main effect terms do not have the same interpretation when they also appear in an interaction/polynomial term in the same model. In such cases, one should exclude models containing interaction terms where the main effect is involved with the exclude argument of modavg. Note that modavg checks for potential cases of multiple instances of a variable appearing more than once in a given model (presumably in an interaction) and issues a warning. To correctly compute the model-averaged estimate of a main effect involved in interaction/polynomial terms, specify the interaction terms(s) that should not appear in the same model with the exclude argument. This will effectively exclude models from the computation of the model-averaged estimate.

When warn = TRUE, modavg looks for matches among the labels of the estimates with identical. It then compares the results to partial matches with regexpr, and issues a warning whenever they are different. As a result, modavg may issue a warning when some variables or levels of categorical variables have nested names (e.g., treat, treat10; L, TL). When this warning is only due to the presence of similarly named variables in the models (and NOT due to interaction terms), you can suppress this warning by setting warn = FALSE.

The model-averaging estimator implemented in modavg is known to be biased away from 0 when there is substantial model selection uncertainty (Cade 2015). In such instances, it is recommended to use the model-averaging shrinkage estimator (i.e., modavgShrink) for inference on beta estimates or to focus on model-averaged effect sizes (modavgEffect) and model-averaged predictions (modavgPred).

modavg is implemented for a list containing objects of aov, betareg, clm, clmm, clogit, coxme, coxph, glm, gls, hurdle, lm, lme, lmekin, maxlikeFit, mer, glmerMod, lmerMod, multinom, polr, rlm, survreg, vglm, zeroinfl classes as well as various models of unmarkedFit classes.

Value

modavg creates an object of class modavg with the following components:

Parameter

the parameter for which a model-averaged estimate was obtained.

Mod.avg.table

the reduced model selection table based on models including the parameter of interest.

Mod.avg.beta

the model-averaged estimate based on all models including the parameter of interest (see 'Details' above regarding the exclusion of models where parameter of interest is involved in an interaction).

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.

Cade, B. S. (2015) Model averaging and muddled multimodel inferences. Ecology 96, 2370–2382.

Dail, D., Madsen, L. (2011) Models for estimating abundance from repeated counts of an open population. Biometrics 67, 577–587.

Lebreton, J.-D., Burnham, K. P., Clobert, J., Anderson, D. R. (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case-studies. Ecological Monographs 62, 67–118.

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, confset, evidence, importance, modavgCustom, modavgEffect, modavgShrink, modavgPred

Examples

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##anuran larvae example modified from Mazerolle (2006)
##these are different models than in the paper
data(min.trap)
##assign "UPLAND" as the reference level as in Mazerolle (2006)          
min.trap$Type <- relevel(min.trap$Type, ref = "UPLAND") 

##set up candidate models          
Cand.mod <- list( )
##global model          
Cand.mod[[1]] <- glm(Num_anura ~ Type + log.Perimeter +
                     Type:log.Perimeter + Num_ranatra,
                     family = poisson, offset = log(Effort),
                     data = min.trap)
##interactive model
Cand.mod[[2]] <- glm(Num_anura ~ Type + log.Perimeter +
                     Type:log.Perimeter, family = poisson, 
                     offset = log(Effort), data = min.trap)
##additive model
Cand.mod[[3]] <- glm(Num_anura ~ Type + log.Perimeter, family = poisson,
                     offset = log(Effort), data = min.trap)
##Predator model
Cand.mod[[4]] <- glm(Num_anura ~ Type + Num_ranatra, family = poisson,
                     offset = log(Effort), data = min.trap) 
          
##check c-hat for global model
c_hat(Cand.mod[[1]]) #uses Pearson's chi-square/df
##note the very low overdispersion: in this case, the analysis could be
##conducted without correcting for c-hat as its value is reasonably close
##to 1  

##assign names to each model
Modnames <- c("global model", "interactive model",
              "additive model", "invertpred model") 

##model selection
aictab(Cand.mod, Modnames)

##compute model-averaged estimates for parameters appearing in top
##models
modavg(parm = "Num_ranatra", cand.set = Cand.mod, modnames = Modnames)
##round to 4 digits after decimal point
print(modavg(parm = "Num_ranatra", cand.set = Cand.mod,
             modnames = Modnames), digits = 4)

##model-averaging a variable involved in an interaction
##the following produces an error - because the variable is involved
##in an interaction in some candidate models
## Not run: modavg(parm = "TypeBOG", cand.set = Cand.mod,
         modnames = Modnames)
## End(Not run)


##exclude models where the variable is involved in an interaction
##to get model-averaged estimate of main effect
modavg(parm = "TypeBOG", cand.set = Cand.mod, modnames = Modnames,
       exclude = list("Type:log.Perimeter"))

##to get model-averaged estimate of interaction
modavg(parm = "TypeBOG:log.Perimeter", cand.set = Cand.mod,
       modnames = Modnames)



##beware of variables that have similar names
set.seed(seed = 4)
resp <- rnorm(n = 40, mean = 3, sd = 1)
size <- rep(c("small", "medsmall", "high", "medhigh"), times = 10)
set.seed(seed = 4)
mass <- rnorm(n = 40, mean = 2, sd = 0.1)
mass2 <- mass^2
age <- rpois(n = 40, lambda = 3.2)
agecorr <- rpois(n = 40, lambda = 2) 
sizecat <- rep(c("a", "ab"), times = 20)
data1 <- data.frame(resp = resp, size = size, sizecat = sizecat,
                    mass = mass, mass2 = mass2, age = age,
                    agecorr = agecorr)

##set up models in list
Cand <- list( )
Cand[[1]] <- lm(resp ~ size + agecorr, data = data1)
Cand[[2]] <- lm(resp ~ size + mass + agecorr, data = data1)
Cand[[3]] <- lm(resp ~ age + mass, data = data1)
Cand[[4]] <- lm(resp ~ age + mass + mass2, data = data1)
Cand[[5]] <- lm(resp ~ mass + mass2 + size, data = data1)
Cand[[6]] <- lm(resp ~ mass + mass2 + sizecat, data = data1)
Cand[[7]] <- lm(resp ~ sizecat, data = data1)
Cand[[8]] <- lm(resp ~ sizecat + mass + sizecat:mass, data = data1)
Cand[[9]] <- lm(resp ~ agecorr + sizecat + mass + sizecat:mass,
                 data = data1) 

##create vector of model names
Modnames <- paste("mod", 1:length(Cand), sep = "")

aictab(cand.set = Cand, modnames = Modnames, sort = TRUE) #correct

##as expected, issues warning as mass occurs sometimes with "mass2" or
##"sizecatab:mass" in some of the models
## Not run: modavg(cand.set = Cand, parm = "mass", modnames = Modnames)

##no warning issued, because "age" and "agecorr" never appear in same model
modavg(cand.set = Cand, parm = "age", modnames = Modnames)

##as expected, issues warning because warn=FALSE, but it is a very bad
##idea in this example since "mass" occurs with "mass2" and "sizecat:mass"
##in some of the models - results are INCORRECT
## Not run: modavg(cand.set = Cand, parm = "mass", modnames = Modnames,
                warn = FALSE)
## End(Not run)

##correctly excludes models with quadratic term and interaction term
##results are CORRECT
modavg(cand.set = Cand, parm = "mass", modnames = Modnames,
       exclude = list("mass2", "sizecat:mass")) 

##correctly computes model-averaged estimate because no other parameter
##occurs simultaneously in any of the models
modavg(cand.set = Cand, parm = "sizesmall", modnames = Modnames) #correct

##as expected, issues a warning because "sizecatab" occurs sometimes in
##an interaction in some models
## Not run: modavg(cand.set = Cand, parm = "sizecatab",
                modnames = Modnames) 
## End(Not run)

##exclude models with "sizecat:mass" interaction - results are CORRECT
modavg(cand.set = Cand, parm = "sizecatab", modnames = Modnames,
       exclude = list("sizecat:mass"))



##example with multiple-season occupancy model modified from ?colext
##this is a bit longer
## Not run: 
require(unmarked)
data(frogs)
umf <- formatMult(masspcru)
obsCovs(umf) <- scale(obsCovs(umf))
siteCovs(umf) <- rnorm(numSites(umf))
yearlySiteCovs(umf) <- data.frame(year = factor(rep(1:7,
                                    numSites(umf))))

##set up model with constant transition rates
fm <- colext(psiformula = ~ 1, gammaformula = ~ 1, epsilonformula = ~ 1,
             pformula = ~ JulianDate + I(JulianDate^2), data = umf,
             control = list(trace=1, maxit=1e4))

##model with with year-dependent transition rates
fm.yearly <- colext(psiformula = ~ 1, gammaformula = ~ year,
                    epsilonformula = ~ year,
                    pformula = ~ JulianDate + I(JulianDate^2),
                    data = umf)

##store in list and assign model names
Cand.mods <- list(fm, fm.yearly)
Modnames <- c("psi1(.)gam(.)eps(.)p(Date + Date2)",
              "psi1(.)gam(Year)eps(Year)p(Date + Date2)")

##compute model-averaged estimate of occupancy in the first year
modavg(cand.set = Cand.mods, modnames = Modnames, parm = "(Intercept)",
       parm.type = "psi")

##compute model-averaged estimate of Julian Day squared on detectability
modavg(cand.set = Cand.mods, modnames = Modnames,
       parm = "I(JulianDate^2)", parm.type = "detect")

## End(Not run)


##example of model-averaged estimate of area from distance model
##this is a bit longer
## Not run: 
data(linetran) #example modified from ?distsamp
     
ltUMF <- with(linetran, {
  unmarkedFrameDS(y = cbind(dc1, dc2, dc3, dc4),
                  siteCovs = data.frame(Length, area, habitat),
                  dist.breaks = c(0, 5, 10, 15, 20),
                  tlength = linetran$Length * 1000, survey = "line", unitsIn = "m")
})
     
## Half-normal detection function. Density output (log scale). No covariates.
fm1 <- distsamp(~ 1 ~ 1, ltUMF)
     
## Halfnormal. Covariates affecting both density and detection.
fm2 <- distsamp(~ area + habitat ~ area + habitat, ltUMF)

## Hazard function. Covariates affecting both density and detection.
fm3 <- distsamp(~ habitat ~ area + habitat, ltUMF, keyfun="hazard")

##assemble model list
Cands <- list(fm1, fm2, fm3)
Modnames <- paste("mod", 1:length(Cands), sep = "")

##model-average estimate of area on abundance
modavg(cand.set = Cands, modnames = Modnames, parm = "area", parm.type = "lambda")
detach(package:unmarked)

## End(Not run)

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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