Display Model Summary Corrected for Overdispersion
This function displays the estimates of a model with standard errors corrected for overdispersion for a variety of model classes. The output includes either confidence intervals based on the normal approximation or Wald hypothesis tests corrected for overdispersion. 1.1
summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'glm' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccu' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitColExt' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccuRN' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitPCount' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitPCO' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitDS' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitGDS' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccuFP' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitMPois' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitGMM' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitGPC' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccuMulti' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccuMS' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccuTTD' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitMMO' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitDSO' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitGOccu' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'unmarkedFitOccuComm' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'glmerMod' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'maxlikeFit' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'multinom' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...) ## S3 method for class 'vglm' summaryOD(mod, c.hat = 1, conf.level = 0.95, out.type = "confint", ...)
mod: an object of class glm, glmmTMB, maxlikeFit, mer, merMod, multinom, vglm, and various unmarkedFit classes containing the output of a model.c.hat: value of overdispersion parameter (i.e., variance inflation factor) such as that obtained from c_hat, mb.gof.test, or Nmix.gof.test.conf.level: the confidence level () requested for the computation of confidence intervals.out.type: the type of summary requested for each parameter estimate. If out.type = "confint", computes confidence intervals corrected for overdispersion, whereas out.type = "nhst" conducts null-hypothesis statistical testing corrected for overdispersion....: additional arguments passed to the function.Overdispersion occurs when the variance in the data exceeds that expected from a theoretical distribution such as the Poisson or binomial (McCullagh and Nelder 1989, Burnham and Anderson 2002). When the model is correct, small values of c-hat (1 < c-hat < 4) can reflect minor deviations from model assumptions (Burnham and Anderson 2002). In such cases, it is possible to adjust standard errors of parameter estimates by multiplying with sqrt(c.hat) (McCullagh and Nelder 1989). This is the correction applied by summaryOD.
Depending on the type of summary requested, i.e., out.type = "confint" or out.type = "nhst", summaryOD will return either confidence intervals based on the normal approximation or Wald tests for each parameter estimate (Agresti 1990).
For binomial distributions, note that values of c.hat > 1 are only appropriate with trials > 1 (i.e., success/trial or cbind(success, failure) syntax). The function supports different model types such as Poisson GLM's and GLMM'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).
summaryOD returns an object of class summaryOD as a list with the following components:
out.type: the type of output requested by the user.
c.hat: the c.hat estimate used to adjust standard errors.
conf.level: the confidence level used to compute confidence intervals around the estimates.
outMat: the output of the model corrected for overdispersion organized in a matrix.
Agresti, A. (2002) Categorical Data Analysis. Second edition. John Wiley and Sons: New Jersey.
Burnham, K. P., 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.
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.
McCullagh, P., Nelder, J. A. (1989) Generalized Linear Models. Second edition. Chapman and Hall: New York.
Royle, J. A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60 , 108--115.
Marc J. Mazerolle
c_hat, mb.gof.test, Nmix.gof.test, anovaOD
##anuran larvae example from Mazerolle (2006) data(min.trap) ##assign "UPLAND" as the reference level as in Mazerolle (2006) min.trap$Type <- relevel(min.trap$Type, ref = "UPLAND") ##run model m1 <- glm(Num_anura ~ Type + log.Perimeter + Num_ranatra, family = poisson, offset = log(Effort), data = min.trap) ##check c-hat for global model c_hat(m1) #uses Pearson's chi-square/df ##display results corrected for overdispersion summaryOD(m1, c_hat(m1)) summaryOD(m1, c_hat(m1), out.type = "nhst") ##example with occupancy model ## Not run: ##load unmarked package if(require(unmarked)){ data(bullfrog) ##detection data detections <- bullfrog[, 3:9] ##assemble in unmarkedFrameOccu bfrog <- unmarkedFrameOccu(y = detections) ##run model fm <- occu(~ 1 ~ 1, data = bfrog) ##check GOF ##GOF <- mb.gof.test(fm, nsim = 1000) ##estimate of c-hat: 1.89 ##display results after overdispersion adjustment summaryOD(fm, c.hat = 1.89) summaryOD(fm, c.hat = 1.89, out.type = "nhst") detach(package:unmarked) } ## End(Not run)
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