AICcmodavg (version 2.00)

AICcmodavg-package: Model Selection and Multimodel Inference Based on (Q)AIC(c)

Description

Description: This package includes functions to create model selection tables based on Akaike's information criterion (AIC) and the second-order AIC (AICc), as well as their quasi-likelihood counterparts (QAIC, QAICc). The package also features functions to conduct classic model averaging (multimodel inference) for a given parameter of interest or predicted values, as well as a shrinkage version of model averaging parameter estimates. Other handy functions enable the computation of relative variable importance, evidence ratios, and confidence sets for the best model. The present version works with Cox proportional hazards models and conditional logistic regression (coxph and coxme classes), linear models (lm class), generalized linear models (glm, vglm, and zeroinfl classes), linear models fit by generalized least squares (gls class), linear mixed models (lme class), generalized linear mixed models (mer and merMod classes), multinomial and ordinal logistic regressions (multinom, polr, clm, and clmm classes), robust regression models (rlm class), nonlinear models (nls class), and nonlinear mixed models (nlme and nlmerMod classes). The package also supports various models of unmarkedFit and maxLikeFit classes estimating demographic parameters after accounting for imperfect detection probabilities. Some functions also allow the creation of model selection tables for Bayesian models of the bugs and rjags classes.

Details

ll{ Package: AICcmodavg Type: Package Version: 2.00 Date: 2014-07-14 License: GPL (>=2 ) LazyLoad: yes } This package contains several useful functions for model selection and multimodel inference:

• AICc

{Computes AIC, AICc, and their quasi-likelihood counterparts (QAIC, QAICc).} aictab {Constructs model selection tables with number of parameters, AIC, delta AIC, Akaike weights or variants based on other AICc, QAIC, and QAICc for a set of candidate models.} boot.wt {Computes model selection relative frequencies based on the bootstrap.} c_hat {Computes an estimate of variance inflation factor for binomial or Poisson GLM's based on Pearson's chi-square.} confset {Determines the confidence set for the best model based on one of three criteria.} DIC {Extracts DIC.} dictab {Constructs model selection tables with number of parameters, DIC, delta DIC, DIC weights for a set of candidate models.} evidence {Computes the evidence ratio between the highest-ranked model based on the information criteria selected and a lower-ranked model.} extractLL {Extracts log-likelihood from models of certain classes.} extractSE {Extracts standard errors from models of certain classes and adds the labels.} fam.link.mer {Extracts the distribution family and link function from a generalized linear mixed model of classes mer and merMod.} importance {Computes importance values (w+) for the support of a given parameter among set of candidate models.} mb.gof.test {Computes the MacKenzie and Bailey goodness-of-fit test for single season occupancy models using the Pearson chi-square statistic.} modavg {Computes model-averaged estimate, unconditional standard error, and unconditional confidence interval of a parameter of interest among a set of candidate models.} modavgEffect {Computes model-averaged effect sizes between groups based on the entire candidate model set.} modavgShrink {Computes shrinkage version of model-averaged estimate, unconditional standard error, and unconditional confidence interval of a parameter of interest among a set of candidate models.} modavgPred {Computes model-average predictions and unconditional SE's among entire set of candidate models.} multComp {Performs multiple comparisons in a model selection framework.} Nmix.gof.test {Computes goodness-of-fit test for N-mixture models based on the Pearson chi-square statistic.} predictSE {Computes predictions and associated standard errors models of certain classes.}

References

Anderson, D. R. (2008) Model-based inference in the life sciences: a primer on evidence. Springer: New York.

Burnham, K. P., and 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.

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.

Examples

##anuran larvae example from Mazerolle (2006) - Poisson GLM with offset
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 + Num_ranatra,
                     family = poisson, offset = log(Effort),
                     data = min.trap) 
Cand.mod[[2]] <- glm(Num_anura ~ Type + log.Perimeter, family = poisson,
                     offset = log(Effort), data = min.trap) 
Cand.mod[[3]] <- glm(Num_anura ~ Type + Num_ranatra, family = poisson,
                     offset = log(Effort), data = min.trap) 
Cand.mod[[4]] <- glm(Num_anura ~ Type, family = poisson,
                     offset = log(Effort), data = min.trap) 
Cand.mod[[5]] <- glm(Num_anura ~ log.Perimeter + Num_ranatra,
                     family = poisson, offset = log(Effort),
                     data = min.trap) 
Cand.mod[[6]] <- glm(Num_anura ~ log.Perimeter, family = poisson,
                     offset = log(Effort), data = min.trap) 
Cand.mod[[7]] <- glm(Num_anura ~ Num_ranatra, family = poisson,
                     offset = log(Effort), data = min.trap) 
Cand.mod[[8]] <- glm(Num_anura ~ 1, 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("type + logperim + invertpred", "type + logperim",
              "type + invertpred", "type", "logperim + invertpred",
              "logperim", "invertpred", "intercept only") 

##model selection table based on AICc
aictab(cand.set = Cand.mod, modnames = Modnames)

##compute evidence ratio
evidence(aictab(cand.set = Cand.mod, modnames = Modnames))

##compute confidence set based on 'raw' method
confset(cand.set = Cand.mod, modnames = Modnames, second.ord = TRUE,
        method = "raw")  

##compute importance value for "TypeBOG" - same number of models
##with vs without variable
importance(cand.set = Cand.mod, modnames = Modnames, parm = "TypeBOG") 

##compute model-averaged estimate of "TypeBOG"
modavg(cand.set = Cand.mod, modnames = Modnames, parm = "TypeBOG")

##compute model-averaged estimate of "TypeBOG" with shrinkage
##same number of models with vs without variable
modavgShrink(cand.set = Cand.mod, modnames = Modnames,
             parm = "TypeBOG")

##compute model-average predictions for two types of ponds
##create a data set for predictions
dat.pred <- data.frame(Type = factor(c("BOG", "UPLAND")),
                       log.Perimeter = mean(min.trap$log.Perimeter),
                       Num_ranatra = mean(min.trap$Num_ranatra),
                       Effort = mean(min.trap$Effort))

##model-averaged predictions across entire model set
modavgPred(cand.set = Cand.mod, modnames = Modnames,
           newdata = dat.pred)


##single-season occupancy model example modified from ?occu
if(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.models <- list(fm1, fm2, fm3, fm4)
Modnames <- c("fm1", "fm2", "fm3", "fm4")

##compute table
print(aictab(cand.set = Cand.models, modnames = Modnames,
       second.ord = TRUE), digits = 4)

##compute evidence ratio
evidence(aictab(cand.set = Cand.models, modnames = Modnames))
##evidence ratio between top model vs lowest-ranked model
evidence(aictab(cand.set = Cand.models, modnames = Modnames), model.high = "fm2", model.low = "fm3")

##compute confidence set based on 'raw' method
confset(cand.set = Cand.models, modnames = Modnames, second.ord = TRUE,
        method = "raw")  

##compute importance value for "sitevar1" on occupancy
##same number of models with vs without variable
importance(cand.set = Cand.models, modnames = Modnames, parm = "sitevar1",
           parm.type = "psi") 

##compute model-averaged estimate of "sitevar1" on occupancy
modavg(cand.set = Cand.models, modnames = Modnames, parm = "sitevar1",
       parm.type = "psi")

##compute model-averaged estimate of "sitevar1" with shrinkage
##same number of models with vs without variable
modavgShrink(cand.set = Cand.models, modnames = Modnames,
             parm = "sitevar1", parm.type = "psi")

##compute model-average predictions for two types of ponds
##create a data set for predictions
dat.pred <- data.frame(sitevar1 = seq(from = min(siteCovs(pferUMF)$sitevar1),
                         to = max(siteCovs(pferUMF)$sitevar1), by = 0.5),
                       sitevar2 = mean(siteCovs(pferUMF)$sitevar2))

##model-averaged predictions of psi across range of values
##of sitevar1 and entire model set
modavgPred(cand.set = Cand.models, modnames = Modnames,
           newdata = dat.pred, parm.type = "psi")
detach(package:unmarked)
}