infoCriteria.asreml: Computes AIC and BIC for models.
In asremlPlus: Augments 'ASReml-R' in Fitting Mixed Models and Packages Generally in Exploring Prediction Differences
infoCriteria R Documentation
Computes AIC and BIC for models.
Description
Computes Akiake and Bayesian (Schwarz) Information Criteria for models.
Either the Restricted Maximum likelihood (REML) or the full likelihood
(full) can be used. The full likelihood, evaluated using REML estimates
is used when it is desired to compare models that differ in their fixed models.
Usage
## S3 method for class 'asreml'
infoCriteria(object, DF = NULL,
bound.exclusions = c("F","B","S","C"),
IClikelihood = "REML", fixedDF = NULL, varDF = NULL, ...)
## S3 method for class 'list'
infoCriteria(object, bound.exclusions = c("F","B","S","C"),
IClikelihood = "REML", fixedDF = NULL, varDF = NULL, ...)
Arguments
object
An asreml object resulting from the fitting of a model using REML
or a list of asreml objects. If the components of the
list are named, then those names will be used as the
rownames for the returned data.frame.
DF
A numeric giving the number of estimated variance parameters. If
NULL then this is determined from the information in
object. This argument has been replaced by varDF,
but is retained for compatibility with legacy code. It is not
available with the list method.
bound.exclusions
A character specifying the bound (constraint) codes that
will result in a variance parameter being excluded from the count of
estimated variance parameters. If set to NULL then none will
be excluded.
IClikelihood
A character specifying whether Restricted Maximum Likelihood
(REML) or the full likelihood, evaluated using REML estimates,
(full) are to be used in calculating the information criteria
for family set to asr_gaussian.
For family set to asr_binomial
or asr_poisson and with dispersion set to 1, the
deviance is extracted from object and used to calculate
the AIC and BIC (as suggested by Damian Collins); the setting of
IClikelihood is ignored and the log-likelihood set to NA.
The information criteria are not valid for other settings of
family and dispersion.
fixedDF
A numeric giving the number of estimated fixed parameters. If
NULL then this is determined from the information in
object. For object a list only a single value
that is used for all components of the list has been
implemented.
varDF
A numeric giving the number of estimated variance parameters. If
NULL then this is determined from the information in
object. It replaces the DF argument.
For object a list only a single value
that is used for all components of the list has been
implemented.
...
Provision for passsing arguments to functions called internally -
not used at present.
Details
The variance degrees of freedom (varDF) are the number of number of variance parameters that
have been estimated, excluding those whose estimates have a code for bound
specified in bound.exclusions. If varDF is not NULL, the supplied value
is used. Otherwise varDF is determined from the information in object,
i.e. if object is an asreml object then from it, or if object is a
list then from each asreml object in the list.
Similarly, the fixed degrees of freedom (fixedDF) are the number of number of fixed parameters
that have been estimated, any coefficients that have the value NA being excluded.
If fixedDF is not NULL, the supplied value is used. Otherwise fixedDF
is determined from the information in object.
If ASReml-R version 4 is being used then the codes specified in bound.exclusions are
not restricted to a subset of the default codes, but a warning is issued if a code other
than these is specified.
For ASReml-R version 3, only a subset of the default codes are allowed:
F (Fixed), B (Boundary), C (Constrained) and
S (Singular).
The calculation of the information criteria is an adaption of the code supplied in File S1
of Verbyla (2019). The log-likeliood is calculated as
loglik = log(REML) - log(|C|)/2,
where C is the inverse coefficient matrix; the term involving C is omitted for REML.
The AIC is calculated as - 2 * loglik + 2 * (varDF + fixedDF)
and the BIC as - 2 * loglik + (fixedDF + varDF) * log(n - r + fixedDF),
where n is the number of observations and r is the rank of the fixed effects
design matrix. For REML, fixedDF = 0.
Value
A data.frame containing the numbers of estimated fixed (fixedDF) and variance (varDF)
parameters, the number of bound parameters (NBound), AIC, BIC and the value of the
log-likelihood (loglik). All elements of the data.frame will be set to NA
for the invalid combinations of family and dispersion as noted in the IClikelihood argument.
If object is a list and its components are named, then those names will be used to
set the rownames of the data.frame.
Author(s)
Chris Brien
References
Verbyla, A. P. (2019). A note on model selection using information criteria for general
linear models estimated using REML. Australian & New Zealand Journal of Statistics,
61, 39–50. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/anzs.12254")}.
See Also
REMLRT.asreml, changeTerms.asrtests, changeModelOnIC.asrtests
Examples
## Not run:
data(Wheat.dat)
## Fit several models to the wheat data and caclulate their ICs
# Fit initial model
m.max <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column + units,
residual = ~ ar1(Row):ar1(Column),
data=Wheat.dat)
infoCriteria(m.max.asr, IClikelihood = "full")
#Drop term for within Column pairs
m1 <- asreml(yield ~ Rep + Variety,
random = ~ Row + Column + units,
residual = ~ ar1(Row):ar1(Column),
data=Wheat.dat)
#Drop nugget term
m2 <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column,
residual = ~ ar1(Row):ar1(Column),
data=Wheat.dat)
#Drop Row autocorrelation
m3 <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column + units,
residual = ~ Row:ar1(Column),
data=Wheat.dat)
#Drop Col autocorrelation
m4 <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column + units,
residual = ~ ar1(Row):Column,
data=Wheat.dat)
mods.asr <- list(m.max, m1, m2, m3, m4)
infoCriteria(mods.asr, IClikelihood = "full")
## End(Not run)
asremlPlus documentation built on Nov. 5, 2023, 5:07 p.m.
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| infoCriteria | R Documentation |
Computes AIC and BIC for models.
Description
Computes Akiake and Bayesian (Schwarz) Information Criteria for models.
Either the Restricted Maximum likelihood (REML) or the full likelihood
(full) can be used. The full likelihood, evaluated using REML estimates
is used when it is desired to compare models that differ in their fixed models.
Usage
## S3 method for class 'asreml'
infoCriteria(object, DF = NULL,
bound.exclusions = c("F","B","S","C"),
IClikelihood = "REML", fixedDF = NULL, varDF = NULL, ...)
## S3 method for class 'list'
infoCriteria(object, bound.exclusions = c("F","B","S","C"),
IClikelihood = "REML", fixedDF = NULL, varDF = NULL, ...)
Arguments
object |
An |
DF |
A |
bound.exclusions |
A |
IClikelihood |
A |
fixedDF |
A |
varDF |
A |
... |
Provision for passsing arguments to functions called internally - not used at present. |
Details
The variance degrees of freedom (varDF) are the number of number of variance parameters that
have been estimated, excluding those whose estimates have a code for bound
specified in bound.exclusions. If varDF is not NULL, the supplied value
is used. Otherwise varDF is determined from the information in object,
i.e. if object is an asreml object then from it, or if object is a
list then from each asreml object in the list.
Similarly, the fixed degrees of freedom (fixedDF) are the number of number of fixed parameters
that have been estimated, any coefficients that have the value NA being excluded.
If fixedDF is not NULL, the supplied value is used. Otherwise fixedDF
is determined from the information in object.
If ASReml-R version 4 is being used then the codes specified in bound.exclusions are
not restricted to a subset of the default codes, but a warning is issued if a code other
than these is specified.
For ASReml-R version 3, only a subset of the default codes are allowed:
F (Fixed), B (Boundary), C (Constrained) and
S (Singular).
The calculation of the information criteria is an adaption of the code supplied in File S1
of Verbyla (2019). The log-likeliood is calculated as
loglik = log(REML) - log(|C|)/2,
where C is the inverse coefficient matrix; the term involving C is omitted for REML.
The AIC is calculated as - 2 * loglik + 2 * (varDF + fixedDF)
and the BIC as - 2 * loglik + (fixedDF + varDF) * log(n - r + fixedDF),
where n is the number of observations and r is the rank of the fixed effects
design matrix. For REML, fixedDF = 0.
Value
A data.frame containing the numbers of estimated fixed (fixedDF) and variance (varDF)
parameters, the number of bound parameters (NBound), AIC, BIC and the value of the
log-likelihood (loglik). All elements of the data.frame will be set to NA
for the invalid combinations of family and dispersion as noted in the IClikelihood argument.
If object is a list and its components are named, then those names will be used to
set the rownames of the data.frame.
Author(s)
Chris Brien
References
Verbyla, A. P. (2019). A note on model selection using information criteria for general linear models estimated using REML. Australian & New Zealand Journal of Statistics, 61, 39–50. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/anzs.12254")}.
See Also
REMLRT.asreml, changeTerms.asrtests, changeModelOnIC.asrtests
Examples
## Not run:
data(Wheat.dat)
## Fit several models to the wheat data and caclulate their ICs
# Fit initial model
m.max <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column + units,
residual = ~ ar1(Row):ar1(Column),
data=Wheat.dat)
infoCriteria(m.max.asr, IClikelihood = "full")
#Drop term for within Column pairs
m1 <- asreml(yield ~ Rep + Variety,
random = ~ Row + Column + units,
residual = ~ ar1(Row):ar1(Column),
data=Wheat.dat)
#Drop nugget term
m2 <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column,
residual = ~ ar1(Row):ar1(Column),
data=Wheat.dat)
#Drop Row autocorrelation
m3 <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column + units,
residual = ~ Row:ar1(Column),
data=Wheat.dat)
#Drop Col autocorrelation
m4 <- asreml(yield ~ Rep + WithinColPairs + Variety,
random = ~ Row + Column + units,
residual = ~ ar1(Row):Column,
data=Wheat.dat)
mods.asr <- list(m.max, m1, m2, m3, m4)
infoCriteria(mods.asr, IClikelihood = "full")
## End(Not run)R Package Documentation
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