lrtest.Rdlrtest is a generic function for carrying out
likelihood ratio tests.
The default method can be employed for comparing nested VGLMs
(see details below).
lrtest(object, ...)
lrtest_vglm(object, ..., no.warning = FALSE, name = NULL)a vglm object.
See below for details.
further object specifications passed to methods. See below for details.
logical; if TRUE then no warning is issued.
For example, setting TRUE might be a good idea when testing
for linearity of a variable for a "pvgam" object.
a function for extracting a suitable name/description from
a fitted model object.
By default the name is queried by calling formula.
lrtest is intended to be a generic function for
comparisons of models via asymptotic likelihood ratio
tests. The default method consecutively compares the
fitted model object object with the models passed
in .... Instead of passing the fitted model
objects in ..., several other specifications
are possible. The updating mechanism is the same as for
waldtest() in lmtest:
the models in ...
can be specified as integers, characters (both for terms
that should be eliminated from the previous model),
update formulas or fitted model objects. Except for
the last case, the existence of an update
method is assumed.
See waldtest() in lmtest for details.
Subsequently, an asymptotic likelihood ratio test for each
two consecutive models is carried out: Twice the difference
in log-likelihoods (as derived by the logLik
methods) is compared with a Chi-squared distribution.
The code was adapted directly from lmtest (written by T. Hothorn, A. Zeileis, G. Millo, D. Mitchell) and made to work for VGLMs and S4. This help file also was adapted from lmtest.
Approximate LRTs might be applied to VGAMs, as
produced by vgam, but it is probably better in
inference to use vglm with regression splines
(bs and
ns).
This methods function should not be applied to other models
such as those produced
by rrvglm,
by cqo,
by cao.
Several VGAM family functions implement distributions which do not satisfying the usual regularity conditions needed for the LRT to work. No checking or warning is given for these.
An object of class "VGAManova" which contains a slot
with the
log-likelihood, degrees of freedom, the difference in
degrees of freedom, likelihood ratio Chi-squared statistic
and corresponding p value.
These are printed by stats:::print.anova();
see anova.
lmtest,
vglm,
lrt.stat.vlm,
score.stat.vlm,
wald.stat.vlm,
anova.vglm.
set.seed(1)
pneumo <- transform(pneumo, let = log(exposure.time),
x3 = runif(nrow(pneumo)))
fit1 <- vglm(cbind(normal, mild, severe) ~ let , propodds, pneumo)
fit2 <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo)
fit3 <- vglm(cbind(normal, mild, severe) ~ let , cumulative, pneumo)
# Various equivalent specifications of the LR test for testing x3
(ans1 <- lrtest(fit2, fit1))
#> Likelihood ratio test
#>
#> Model 1: cbind(normal, mild, severe) ~ let + x3
#> Model 2: cbind(normal, mild, severe) ~ let
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 12 -25.087
#> 2 13 -25.090 1 0.0076 0.9304
ans2 <- lrtest(fit2, 2)
#> Error in eval(predvars, data, env): object 'let' not found
ans3 <- lrtest(fit2, "x3")
#> Error in eval(predvars, data, env): object 'let' not found
ans4 <- lrtest(fit2, . ~ . - x3)
#> Error in eval(predvars, data, env): object 'let' not found
c(all.equal(ans1, ans2), all.equal(ans1, ans3), all.equal(ans1, ans4))
#> Error: object 'ans2' not found
# Doing it manually
(testStatistic <- 2 * (logLik(fit2) - logLik(fit1)))
#> [1] 0.007619612
(pval <- pchisq(testStatistic, df = df.residual(fit1) - df.residual(fit2),
lower.tail = FALSE))
#> [1] 0.9304407
(ans4 <- lrtest(fit3, fit1)) # Test PO (parallelism) assumption
#> Likelihood ratio test
#>
#> Model 1: cbind(normal, mild, severe) ~ let
#> Model 2: cbind(normal, mild, severe) ~ let
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 12 -25.019
#> 2 13 -25.090 1 0.1424 0.7059