Likelihood Ratio Test Statistics Evaluated at the Null Values
Generic function that computes likelihood ratio test (LRT) statistics evaluated at the null values (consequently they do not suffer from the Hauck-Donner effect).
lrt.stat(object, ...)
lrt.stat.vlm(object, values0 = 0, subset = NULL, omit1s = TRUE,
all.out = FALSE, trace = FALSE, ...)object, values0, subset |
Same as in |
omit1s, all.out, trace |
Same as in |
... |
Ignored for now. |
When summary() is applied to a vglm object
a 4-column Wald table is produced.
The corresponding p-values are generally viewed as inferior to
those from a likelihood ratio test (LRT).
For example, the Hauck and Donner (1977) effect (HDE) produces
p-values that are biased upwards (see hdeff).
Other reasons are that the Wald test is often less accurate
(especially in small samples) and is not invariant to
parameterization.
By default, this function returns p-values based on the LRT by
deleting one column at a time from the big VLM matrix
and then restarting IRLS to obtain convergence (hopefully).
Twice the difference between the log-likelihoods
(or equivalently, the difference in the deviances if they are defined)
is asymptotically chi-squared with 1 degree of freedom.
One might expect the p-values from this function
therefore to be more accurate
and not suffer from the HDE.
Thus this function is a recommended
alternative (if it works) to summaryvglm
for testing for the significance of a regression coefficient.
By default, a vector of signed square root of the LRT statistics;
these are asymptotically standard normal under the null hypotheses.
If all.out = TRUE then a list is returned with the
following components:
lrt.stat the signed LRT statistics,
pvalues the 2-sided p-values,
Lrt.stat2 the usual LRT statistic,
values0 the null values.
See wald.stat.vlm.
T. W. Yee.
set.seed(1)
pneumo <- transform(pneumo, let = log(exposure.time),
x3 = rnorm(nrow(pneumo)))
fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, pneumo)
cbind(coef(summary(fit)),
"signed LRT stat" = lrt.stat(fit, omit1s = FALSE))
summary(fit, lrt0 = TRUE) # Easy way to get itPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.