anova.lme: Compare Likelihoods of Fitted Objects
In nlme: Linear and Nonlinear Mixed Effects Models
Description
Usage
Arguments
Value
Note
Author(s)
References
See Also
Examples
Description
When only one fitted model object is present, a data frame with the
numerator degrees of freedom, denominator degrees of
freedom, F-values, and P-values for Wald tests for the terms in the
model (when Terms and L are NULL), a combination
of model terms (when Terms in not NULL), or linear
combinations of the model coefficients (when L is not
NULL). Otherwise, when multiple fitted objects are being
compared, a data frame with the degrees of freedom, the (restricted)
log-likelihood, the Akaike Information Criterion (AIC), and the
Bayesian Information Criterion (BIC) of each object is returned. If
test=TRUE, whenever two consecutive objects have different
number of degrees of freedom, a likelihood ratio statistic with the
associated p-value is included in the returned data frame.
Usage
1
2
3
4
Arguments
object
an object inheriting from class "lme",
representing a fitted linear mixed-effects model.
...
other optional fitted model objects inheriting from
classes "gls", "gnls", "lm", "lme",
"lmList", "nlme", "nlsList", or "nls".
test
an optional logical value controlling whether likelihood
ratio tests should be used to compare the fitted models represented
by object and the objects in .... Defaults to
TRUE.
type
an optional character string specifying the type of sum of
squares to be used in F-tests for the terms in the model. If
"sequential", the sequential sum of squares obtained by
including the terms in the order they appear in the model is used;
else, if "marginal", the marginal sum of squares
obtained by deleting a term from the model at a time is used. This
argument is only used when a single fitted object is passed to the
function. Partial matching of arguments is used, so only the first
character needs to be provided. Defaults to "sequential".
adjustSigma
an optional logical value. If TRUE and the
estimation method used to obtain object was maximum
likelihood, the residual standard error is multiplied by
sqrt(nobs/(nobs - npar)),
converting it to a REML-like estimate. This argument is only used
when a single fitted object is passed to the function. Default is
TRUE.
Terms
an optional integer or character vector specifying which
terms in the model should be jointly tested to be zero using a Wald
F-test. If given as a character vector, its elements must correspond
to term names; else, if given as an integer vector, its elements must
correspond to the order in which terms are included in the
model. This argument is only used when a single fitted object is
passed to the function. Default is NULL.
L
an optional numeric vector or array specifying linear
combinations of the coefficients in the model that should be tested
to be zero. If given as an array, its rows define the linear
combinations to be tested. If names are assigned to the vector
elements (array columns), they must correspond to coefficients
names and will be used to map the linear combination(s) to the
coefficients; else, if no names are available, the vector elements
(array columns) are assumed in the same order as the coefficients
appear in the model. This argument is only used when a single fitted
object is passed to the function. Default is NULL.
x
an object inheriting from class "anova.lme"
verbose
an optional logical value. If TRUE, the calling
sequences for each fitted model object are printed with the rest of
the output, being omitted if verbose = FALSE. Defaults to
FALSE.
Value
a data frame inheriting from class "anova.lme".
Note
Likelihood comparisons are not meaningful for objects fit using
restricted maximum likelihood and with different fixed effects.
Author(s)
José Pinheiro and Douglas Bates bates@stat.wisc.edu
References
Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models
in S and S-PLUS", Springer.
See Also
gls, gnls, nlme,
lme, AIC, BIC,
print.anova.lme,
logLik.lme,
Examples
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fm1 <- lme(distance ~ age, Orthodont, random = ~ age | Subject)
anova(fm1)
fm2 <- update(fm1, random = pdDiag(~age))
anova(fm1, fm2)
## Pinheiro and Bates, pp. 251-254 ------------------------------------------
fm1Orth.gls <- gls(distance ~ Sex * I(age - 11), Orthodont,
correlation = corSymm(form = ~ 1 | Subject),
weights = varIdent(form = ~ 1 | age))
fm2Orth.gls <- update(fm1Orth.gls,
corr = corCompSymm(form = ~ 1 | Subject))
## anova.gls examples:
anova(fm1Orth.gls, fm2Orth.gls)
fm3Orth.gls <- update(fm2Orth.gls, weights = NULL)
anova(fm2Orth.gls, fm3Orth.gls)
fm4Orth.gls <- update(fm3Orth.gls, weights = varIdent(form = ~ 1 | Sex))
anova(fm3Orth.gls, fm4Orth.gls)
# not in book but needed for the following command
fm3Orth.lme <- lme(distance ~ Sex*I(age-11), data = Orthodont,
random = ~ I(age-11) | Subject,
weights = varIdent(form = ~ 1 | Sex))
# Compare an "lme" object with a "gls" object (test would be non-sensical!)
anova(fm3Orth.lme, fm4Orth.gls, test = FALSE)
## Pinheiro and Bates, pp. 222-225 ------------------------------------------
op <- options(contrasts = c("contr.treatment", "contr.poly"))
fm1BW.lme <- lme(weight ~ Time * Diet, BodyWeight, random = ~ Time)
fm2BW.lme <- update(fm1BW.lme, weights = varPower())
# Test a specific contrast
anova(fm2BW.lme, L = c("Time:Diet2" = 1, "Time:Diet3" = -1))
## Pinheiro and Bates, pp. 352-365 ------------------------------------------
fm1Theo.lis <- nlsList(
conc ~ SSfol(Dose, Time, lKe, lKa, lCl), data=Theoph)
fm1Theo.lis
fm1Theo.nlme <- nlme(fm1Theo.lis)
fm2Theo.nlme <- update(fm1Theo.nlme, random= pdDiag(lKe+lKa+lCl~1) )
fm3Theo.nlme <- update(fm2Theo.nlme, random= pdDiag( lKa+lCl~1) )
# Comparing the 3 nlme models
anova(fm1Theo.nlme, fm3Theo.nlme, fm2Theo.nlme)
options(op) # (set back to previous state)
Example output
numDF denDF F-value p-value
(Intercept) 1 80 3096.4871 <.0001
age 1 80 85.8464 <.0001
Model df AIC BIC logLik Test L.Ratio p-value
fm1 1 6 454.6367 470.6173 -221.3183
fm2 2 5 453.3146 466.6318 -221.6573 1 vs 2 0.6778943 0.4103
Model df AIC BIC logLik Test L.Ratio p-value
fm1Orth.gls 1 14 452.5468 489.5683 -212.2734
fm2Orth.gls 2 9 449.9724 473.7719 -215.9862 1 vs 2 7.425576 0.1909
Model df AIC BIC logLik Test L.Ratio p-value
fm2Orth.gls 1 9 449.9724 473.7719 -215.9862
fm3Orth.gls 2 6 445.7572 461.6236 -216.8786 1 vs 2 1.784873 0.6182
Model df AIC BIC logLik Test L.Ratio p-value
fm3Orth.gls 1 6 445.7572 461.6236 -216.8786
fm4Orth.gls 2 7 436.1887 454.6994 -211.0943 1 vs 2 11.56859 7e-04
Model df AIC BIC logLik
fm3Orth.lme 1 9 429.5225 453.3220 -205.7612
fm4Orth.gls 2 7 436.1887 454.6994 -211.0943
F-test for linear combination(s)
Time:Diet2 Time:Diet3
1 -1
numDF denDF F-value p-value
1 1 157 2.862607 0.0926
Call:
Model: conc ~ SSfol(Dose, Time, lKe, lKa, lCl) | Subject
Data: Theoph
Coefficients:
lKe lKa lCl
6 -2.307332 0.1516234 -2.973242
7 -2.280370 -0.3860511 -2.964335
8 -2.386437 0.3188339 -3.069111
11 -2.321530 1.3478239 -2.860397
3 -2.508073 0.8975422 -3.229965
2 -2.286108 0.6640568 -3.106317
4 -2.436494 0.1582638 -3.286087
9 -2.446088 2.1821879 -3.420774
12 -2.248326 -0.1828442 -3.170158
10 -2.604148 -0.3631216 -3.428271
1 -2.919614 0.5751612 -3.915857
5 -2.425486 0.3862853 -3.132600
Degrees of freedom: 132 total; 96 residual
Residual standard error: 0.7001921
Warning message:
In (function (model, data = sys.frame(sys.parent()), fixed, random, :
Iteration 2, LME step: nlminb() did not converge (code = 1). Do increase 'msMaxIter'!
Model df AIC BIC logLik Test L.Ratio p-value
fm1Theo.nlme 1 10 366.6421 395.4702 -173.3211
fm3Theo.nlme 2 6 366.0429 383.3397 -177.0214 1 vs 2 7.400746 0.1162
fm2Theo.nlme 3 7 368.0470 388.2266 -177.0235 2 vs 3 0.004123 0.9488
nlme documentation built on Feb. 4, 2021, 9:06 a.m.
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Description Usage Arguments Value Note Author(s) References See Also Examples
Description
When only one fitted model object is present, a data frame with the
numerator degrees of freedom, denominator degrees of
freedom, F-values, and P-values for Wald tests for the terms in the
model (when Terms and L are NULL), a combination
of model terms (when Terms in not NULL), or linear
combinations of the model coefficients (when L is not
NULL). Otherwise, when multiple fitted objects are being
compared, a data frame with the degrees of freedom, the (restricted)
log-likelihood, the Akaike Information Criterion (AIC), and the
Bayesian Information Criterion (BIC) of each object is returned. If
test=TRUE, whenever two consecutive objects have different
number of degrees of freedom, a likelihood ratio statistic with the
associated p-value is included in the returned data frame.
Usage
1 2 3 4 |
Arguments
object |
an object inheriting from class |
... |
other optional fitted model objects inheriting from
classes |
test |
an optional logical value controlling whether likelihood
ratio tests should be used to compare the fitted models represented
by |
type |
an optional character string specifying the type of sum of
squares to be used in F-tests for the terms in the model. If
|
adjustSigma |
an optional logical value. If |
Terms |
an optional integer or character vector specifying which
terms in the model should be jointly tested to be zero using a Wald
F-test. If given as a character vector, its elements must correspond
to term names; else, if given as an integer vector, its elements must
correspond to the order in which terms are included in the
model. This argument is only used when a single fitted object is
passed to the function. Default is |
L |
an optional numeric vector or array specifying linear
combinations of the coefficients in the model that should be tested
to be zero. If given as an array, its rows define the linear
combinations to be tested. If names are assigned to the vector
elements (array columns), they must correspond to coefficients
names and will be used to map the linear combination(s) to the
coefficients; else, if no names are available, the vector elements
(array columns) are assumed in the same order as the coefficients
appear in the model. This argument is only used when a single fitted
object is passed to the function. Default is |
x |
an object inheriting from class |
verbose |
an optional logical value. If |
Value
a data frame inheriting from class "anova.lme".
Note
Likelihood comparisons are not meaningful for objects fit using restricted maximum likelihood and with different fixed effects.
Author(s)
José Pinheiro and Douglas Bates bates@stat.wisc.edu
References
Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.
See Also
gls, gnls, nlme,
lme, AIC, BIC,
print.anova.lme,
logLik.lme,
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | fm1 <- lme(distance ~ age, Orthodont, random = ~ age | Subject)
anova(fm1)
fm2 <- update(fm1, random = pdDiag(~age))
anova(fm1, fm2)
## Pinheiro and Bates, pp. 251-254 ------------------------------------------
fm1Orth.gls <- gls(distance ~ Sex * I(age - 11), Orthodont,
correlation = corSymm(form = ~ 1 | Subject),
weights = varIdent(form = ~ 1 | age))
fm2Orth.gls <- update(fm1Orth.gls,
corr = corCompSymm(form = ~ 1 | Subject))
## anova.gls examples:
anova(fm1Orth.gls, fm2Orth.gls)
fm3Orth.gls <- update(fm2Orth.gls, weights = NULL)
anova(fm2Orth.gls, fm3Orth.gls)
fm4Orth.gls <- update(fm3Orth.gls, weights = varIdent(form = ~ 1 | Sex))
anova(fm3Orth.gls, fm4Orth.gls)
# not in book but needed for the following command
fm3Orth.lme <- lme(distance ~ Sex*I(age-11), data = Orthodont,
random = ~ I(age-11) | Subject,
weights = varIdent(form = ~ 1 | Sex))
# Compare an "lme" object with a "gls" object (test would be non-sensical!)
anova(fm3Orth.lme, fm4Orth.gls, test = FALSE)
## Pinheiro and Bates, pp. 222-225 ------------------------------------------
op <- options(contrasts = c("contr.treatment", "contr.poly"))
fm1BW.lme <- lme(weight ~ Time * Diet, BodyWeight, random = ~ Time)
fm2BW.lme <- update(fm1BW.lme, weights = varPower())
# Test a specific contrast
anova(fm2BW.lme, L = c("Time:Diet2" = 1, "Time:Diet3" = -1))
## Pinheiro and Bates, pp. 352-365 ------------------------------------------
fm1Theo.lis <- nlsList(
conc ~ SSfol(Dose, Time, lKe, lKa, lCl), data=Theoph)
fm1Theo.lis
fm1Theo.nlme <- nlme(fm1Theo.lis)
fm2Theo.nlme <- update(fm1Theo.nlme, random= pdDiag(lKe+lKa+lCl~1) )
fm3Theo.nlme <- update(fm2Theo.nlme, random= pdDiag( lKa+lCl~1) )
# Comparing the 3 nlme models
anova(fm1Theo.nlme, fm3Theo.nlme, fm2Theo.nlme)
options(op) # (set back to previous state)
|
Example output
numDF denDF F-value p-value
(Intercept) 1 80 3096.4871 <.0001
age 1 80 85.8464 <.0001
Model df AIC BIC logLik Test L.Ratio p-value
fm1 1 6 454.6367 470.6173 -221.3183
fm2 2 5 453.3146 466.6318 -221.6573 1 vs 2 0.6778943 0.4103
Model df AIC BIC logLik Test L.Ratio p-value
fm1Orth.gls 1 14 452.5468 489.5683 -212.2734
fm2Orth.gls 2 9 449.9724 473.7719 -215.9862 1 vs 2 7.425576 0.1909
Model df AIC BIC logLik Test L.Ratio p-value
fm2Orth.gls 1 9 449.9724 473.7719 -215.9862
fm3Orth.gls 2 6 445.7572 461.6236 -216.8786 1 vs 2 1.784873 0.6182
Model df AIC BIC logLik Test L.Ratio p-value
fm3Orth.gls 1 6 445.7572 461.6236 -216.8786
fm4Orth.gls 2 7 436.1887 454.6994 -211.0943 1 vs 2 11.56859 7e-04
Model df AIC BIC logLik
fm3Orth.lme 1 9 429.5225 453.3220 -205.7612
fm4Orth.gls 2 7 436.1887 454.6994 -211.0943
F-test for linear combination(s)
Time:Diet2 Time:Diet3
1 -1
numDF denDF F-value p-value
1 1 157 2.862607 0.0926
Call:
Model: conc ~ SSfol(Dose, Time, lKe, lKa, lCl) | Subject
Data: Theoph
Coefficients:
lKe lKa lCl
6 -2.307332 0.1516234 -2.973242
7 -2.280370 -0.3860511 -2.964335
8 -2.386437 0.3188339 -3.069111
11 -2.321530 1.3478239 -2.860397
3 -2.508073 0.8975422 -3.229965
2 -2.286108 0.6640568 -3.106317
4 -2.436494 0.1582638 -3.286087
9 -2.446088 2.1821879 -3.420774
12 -2.248326 -0.1828442 -3.170158
10 -2.604148 -0.3631216 -3.428271
1 -2.919614 0.5751612 -3.915857
5 -2.425486 0.3862853 -3.132600
Degrees of freedom: 132 total; 96 residual
Residual standard error: 0.7001921
Warning message:
In (function (model, data = sys.frame(sys.parent()), fixed, random, :
Iteration 2, LME step: nlminb() did not converge (code = 1). Do increase 'msMaxIter'!
Model df AIC BIC logLik Test L.Ratio p-value
fm1Theo.nlme 1 10 366.6421 395.4702 -173.3211
fm3Theo.nlme 2 6 366.0429 383.3397 -177.0214 1 vs 2 7.400746 0.1162
fm2Theo.nlme 3 7 368.0470 388.2266 -177.0235 2 vs 3 0.004123 0.9488
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