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, hurdle, 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), beta regression models (betareg class), parametric survival models (survreg class), nonlinear models (nls and gnls classes), nonlinear mixed models (nlme and nlmerMod classes), univariate models (fitdist and fitdistr classes), and certain types of latent variable models (lavaan class). 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. Objects following model selection and multimodel inference can be formatted to LaTeX using xtable methods included in the package.

Details

Package: AICcmodavg
Type: Package
Version: 2.1-0
Date: 2016-11-17
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.

  • bictab Constructs model selection tables with number of parameters, BIC, delta BIC, BIC weights for a set of candidate models.

  • boot.wt Computes summary statistics from detection histories.

  • 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.

  • importance Computes importance values (w+) for the support of a given parameter among set of candidate models.

  • 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 entire set of candidate models.

  • modavgPred Computes model-average predictions, unconditional SE's, and confidence intervals among entire set of candidate models.

  • multComp Performs multiple comparisons across levels of a factor in a model selection framework.

  • useBIC Computes BIC or a quasi-likelihood counterparts (QBIC).

A number of functions for model diagnostics are available:

  • c_hat Estimates variance inflation factor for binomial or Poisson GLM's based on various estimators.

  • checkConv Checks the convergence information of the algorithm for the model.

  • checkParms Checks the occurrence of parameter estimates with high standard errors in a model.

  • countDist Computes summary statistics from distance sampling data.

  • countHist Computes summary statistics from count history data.

  • covDiag Computes covariance diagnostics for lambda in N-mixture models.

  • detHist Computes summary statistics from detection histories.

  • extractCN Extracts condition number from models of certain classes.

  • mb.gof.test Computes the MacKenzie and Bailey goodness-of-fit test for single season and dynamic occupancy models using the Pearson chi-square statistic.

  • Nmix.gof.test Computes goodness-of-fit test for N-mixture models based on the Pearson chi-square statistic.

Other utility functions include:

  • 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.

  • predictSE Computes predictions and associated standard errors models of certain classes.

  • xtable Formats various objects resulting from model selection and multimodel inference to LaTeX or HTML tables.

Author(s)

Marc J. Mazerolle <marc.mazerolle@uqat.ca>.

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

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##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]], method = "pearson") #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, type = "response")

##compute model-averaged effect size between two groups
##works when data set has two rows
modavgEffect(cand.set = Cand.mod, modnames = Modnames,
             newdata = dat.pred, type = "link")


##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))) 

##check detection history data from data object
detHist(pferUMF)

##set up candidate model set
fm1 <- occu(~ obsvar1 ~ sitevar1, pferUMF)
##check detection history data from model object
detHist(fm1) 

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)

## End(Not run)

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