lrtest is a generic function for carrying out likelihood ratio tests.
The default method can be employed for comparing nested VGLMs
(see details below).
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further object specifications passed to methods. See below for details.
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
.... Instead of passing the fitted model
..., 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
method is assumed.
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
methods) is compared with a Chi-squared distribution.
An object of class
"VGAManova" which contains a slot
log-likelihood, degrees of freedom, the difference in
degrees of freedom, likelihood ratio Chi-squared statistic
and corresponding p value.
These are printed by
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.
Approximate LRTs might be applied to VGAMs, as
vgam, but it is probably better in inference
vglm with regression splines
This methods function should not be applied to other models such as
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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
Loading required package: stats4 Loading required package: splines 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  TRUE TRUE TRUE  0.007619612  0.9304407 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
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