Compute Model-averaged Effect Sizes (Multimodel Inference on Group Differences)
Description
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).
a list storing each of the models in the candidate model set.
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.
newdata
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').
second.ord
logical. If TRUE, the function returns the second-order Akaike
information criterion (i.e., AICc).
nobs
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.
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. To obtain confidence intervals
corrected for multiple comparisons between pairs of treatments, it is
possible to adjust the α level according to various
strategies such as the Bonferroni correction (Dunn 1961).
type
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).
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 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.
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 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, rlm, survreg, as well as
unmarkedFitOccu, unmarkedFitColExt,
unmarkedFitOccuFP, unmarkedFitOccuRN,
unmarkedFitPCount, unmarkedFitPCO, unmarkedFitDS,
unmarkedFitGDS, unmarkedFitMPois, unmarkedFitGMM,
and unmarkedFitGPC classes.
Value
The result is an object of class modavgEffect with the following
components:
Group.variable
the grouping variable defining the two groups
compared
Group1
the first group considered in the comparison
Group2
the second group considered in the comparison
Type
the scale on which the model-averaged effect size was
computed (e.g., response or link)
Mod.avg.table
the full model selection table including the
entire set of candidate models
Mod.avg.eff
the model-averaged effect size based on the entire
candidate model set
Uncond.SE
the unconditional standard error for the model-averaged
effect size
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. Biometrics53, 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 Research33, 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
Sociobiology65, 23–25.
Dail, D., Madsen, L. (2011) Models for estimating abundance from
repeated counts of an open population. Biometrics67,
577–587.
Dunn, O. J. (1961) Multiple comparisons among means. Journal of the
American Statistical Association56, 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. Ecology83,
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. Ecology84, 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-Reptilia27, 169–180.
Royle, J. A. (2004) N-mixture models for estimating population
size from spatially replicated counts. Biometrics60,
108–115.