[R] difference between lrm's "Model L.R." and anova's "Chi-Square"

[johnson4 at babel.ling.upenn.edu]

I am running lrm() with a single factor. I then run anova() on the fitted
model to obtain a p-value associated with having that factor in the model.

I am noticing that the "Model L.R." in the lrm results is almost the same
as the "Chi-Square" in the anova results, but not quite; the latter value
is always slightly smaller.

anova() calculates the p-value based on "Chi-Square", but I have
independent evidence that "Model L.R." is the actual -2*log(LR), so should
I be using that?

Why are the values different?

prob_a <- inv.logit(rnorm(1,0,1))
prob_b <- inv.logit(rnorm(1,0,1))
data <- data.frame(
factor=c(rep("a",500),rep("b",500)),
outcome=c(sample(c(1,0),100,replace=T,prob=c(prob_a,1-prob_a)),
          sample(c(1,0),100,replace=T,prob=c(prob_b,1-prob_b))))
fit <- lrm(outcome~factor,data)

fit           # gives "Model L.R." e.g. 8.23, 11.76, 6.89...
anova(fit)    # gives "Chi-Square" e.g. 8.19, 11.69, 6.85...