This function model-averages the effect size between two groups defined by a categorical variable based on the entire model set and computes the unconditional standard error and unconditional confidence intervals as described in Buckland et al. (1997) and Burnham and Anderson (2002). This can be particularly useful when dealing with data from an experiment (e.g., ANOVA) and when the focus is to determine the effect of a given factor. This is an information-theoretic alternative to multiple comparisons (e.g., Burnham et al. 2011).
modavgEffect(cand.set, modnames = NULL, newdata, second.ord = TRUE,
nobs = NULL, uncond.se = "revised", conf.level = 0.95,
...)# S3 method for AICaov.lm
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AICglm.lm
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", c.hat = 1, gamdisp = NULL,
...)
# S3 method for AICgls
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AIClm
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AIClme
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AICmer
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", ...)
# S3 method for AICglmerMod
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", ...)
# S3 method for AIClmerMod
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AIClmerModLmerTest
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AICnegbin.glm.lm
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", ...)
# S3 method for AICrlm.lm
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, ...)
# S3 method for AICsurvreg
modavgEffect(cand.set, modnames = NULL, newdata,
second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", ...)
# S3 method for AICunmarkedFitOccu
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", c.hat = 1,
parm.type = NULL, ...)
# S3 method for AICunmarkedFitColExt
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitOccuRN
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitPCount
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitPCO
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", c.hat = 1,
parm.type = NULL, ...)
# S3 method for AICunmarkedFitDS
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", c.hat = 1,
parm.type = NULL, ...)
# S3 method for AICunmarkedFitGDS
modavgEffect(cand.set, modnames = NULL,
newdata, second.ord = TRUE, nobs = NULL, uncond.se = "revised",
conf.level = 0.95, type = "response", c.hat = 1,
parm.type = NULL, ...)
# S3 method for AICunmarkedFitOccuFP
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitMPois
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitGMM
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitGPC
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitOccuTTD
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitMMO
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitDSO
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitOccuMS
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitOccuMulti
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitGOccu
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
# S3 method for AICunmarkedFitOccuComm
modavgEffect(cand.set, modnames =
NULL, newdata, second.ord = TRUE, nobs = NULL, uncond.se =
"revised", conf.level = 0.95, type = "response",
c.hat = 1, parm.type = NULL, ...)
The result is an object of class modavgEffect with the following
components:
the grouping variable defining the two groups compared.
the first group considered in the comparison.
the second group considered in the comparison.
the scale on which the model-averaged effect size was computed (e.g., response or link).
the full model selection table including the entire set of candidate models.
the model-averaged effect size based on the entire candidate model set.
the unconditional standard error for the model-averaged effect size.
the confidence level used to compute the confidence interval.
the lower confidence limit.
the upper confidence limit.
a matrix containing the model-averaged effect size, the unconditional standard error, and the lower and upper confidence limits.
a list storing each of the models in the candidate model set.
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.
a data frame with two rows and where the columns correspond to the
explanatory variables specified in the candidate models. Note that this
data set must have the same structure as that of the original data frame
for which we want to make predictions, specifically, the same variable
type and names that appear in the original data set. Each row of the
data set defines one of the two groups compared. The first row in
newdata defines the first group, whereas the second row defines
the second group. The effect size is computed as the prediction in the
first row minus the prediction in the second row (first row - second
row). Only the column relating to the grouping variable can change value
and all others must be held constant for the comparison (see
'Details'). For community occupancy models of unmarkedFitOccuComm
classes, the newdata data frame must include a column specifying
the name of the species for which each prediction is requested (see
'Examples' below).
logical. If TRUE, the function returns the second-order Akaike
information criterion (i.e., AICc).
this argument allows the specification of 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.
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.
the confidence level (\(1 - \alpha\)) requested for the computation of unconditional confidence intervals. To obtain confidence intervals corrected for multiple comparisons between pairs of treatments, it is possible to adjust the \(\alpha\) level according to various strategies such as the Bonferroni correction (Dunn 1961).
the scale of prediction requested, one of "response" or
"link" (only relevant for glm, mer, and
unmarkedFit classes). Note that the value "terms" is not
defined for modavgEffect).
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 and dynamic occupancy models (MacKenzie et
al. 2002, 2003), or N-mixture models (Royle 2004, Dail and Madsen
2011). If c.hat > 1, modavgEffect 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 class.
if gamma GLM is used, the dispersion parameter should be specified here to apply the same value to each model.
this argument specifies the parameter type on which the effect size
will be computed and is only relevant for models of unmarkedFit
classes. The character strings supported vary with the type of model
fitted. For unmarkedFitOccu, unmarkedFitOccuMulti, and
unmarkedFitOccuComm 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
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. For
unmarkedFitOccuMS objects, psi, phi, and
detect denote occupancy, transition, and detection probability,
respectively. For unmarkedFitGOccu objects, possible values
are psi, phi, or detect, denoting occupancy,
availability, and detection probabilities, respectively.
additional arguments passed to the function.
Marc J. Mazerolle
The strategy used here to compute effect sizes is to work from the
newdata object to create two predictions from a given model and
compute the differences and standard errors between both values. This
step is executed for each model in the candidate model set, to obtain a
model-averaged estimate of the effect size and unconditional standard
error. As a result, the newdata argument is restricted to two
rows, each for a given prediction. To specify each group, the values
entered in the column for each explanatory variable can be identical,
except for the grouping variable. In such a case, the function will
identify the variable and the assign group names based on the values of
the variable. If more than a single variable has different values in
its respective column, the function will print generic names in the
output to identify the two groups. A sensible choice of value for the
explanatory variables to be held constant is the average of the
variable.
Model-averaging effect sizes is most useful in true experiments (e.g., ANOVA-type designs), where one wants to obtain the best estimate of effect size given the support of each candidate model. This can be considered as a information-theoretic analog of traditional multiple comparisons, except that the information contained in the entire model set is used instead of being restricted to a single model. See 'Examples' below for applications.
modavgEffect calls the appropriate method depending on the class
of objects in the list. The current classes supported include
aov, glm, gls, lm, lme, mer,
glmerMod, lmerMod, lmerModLmerTest, rlm,
survreg, as well as models of unmarkedFitOccu,
unmarkedFitColExt, unmarkedFitOccuFP,
unmarkedFitOccuRN, unmarkedFitOccuTTD,
unmarkedFitPCount, unmarkedFitPCO, unmarkedFitDS,
unmarkedFitDSO, unmarkedFitGDS, unmarkedFitMPois,
unmarkedFitGMM, unmarkedFitMMO, unmarkedFitGPC,
unmarkedFitOccuMS, unmarkedFitOccuMulti,
unmarkedFitGOccu, and unmarkedFitOccuComm classes.
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.
Burnham, K. P., Anderson, D. R., Huyvaert, K. P. (2011) AIC model selection and multimodel inference in behaviorial ecology: some background, observations and comparisons. Behavioral Ecology and Sociobiology 65, 23--25.
Dail, D., Madsen, L. (2011) Models for estimating abundance from repeated counts of an open population. Biometrics 67, 577--587.
Dunn, O. J. (1961) Multiple comparisons among means. Journal of the American Statistical Association 56, 52--64.
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.
AICc, aictab, c_hat,
confset, evidence, importance,
modavgShrink, modavgPred