Likelihood Ratio Test of Nested Models
lrtest
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)
object |
a |
... |
further object specifications passed to methods. See below for details. |
no.warning |
logical; if |
name |
a function for extracting a suitable name/description from
a fitted model object.
By default the name is queried by calling |
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.
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
.
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.
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.
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, data = pneumo) fit2 <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, data = pneumo) fit3 <- vglm(cbind(normal, mild, severe) ~ let , cumulative, data = pneumo) # Various equivalent specifications of the LR test for testing x3 (ans1 <- lrtest(fit2, fit1)) ans2 <- lrtest(fit2, 2) ans3 <- lrtest(fit2, "x3") ans4 <- lrtest(fit2, . ~ . - x3) c(all.equal(ans1, ans2), all.equal(ans1, ans3), all.equal(ans1, ans4)) # Doing it manually (testStatistic <- 2 * (logLik(fit2) - logLik(fit1))) (mypval <- pchisq(testStatistic, df = length(coef(fit2)) - length(coef(fit1)), lower.tail = FALSE)) (ans4 <- lrtest(fit3, fit1)) # Test proportional odds (parallelism) assumption
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