R help - Mar 2008 - difference between lrm's "Model L.R." and anova's "Chi-Square"

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...

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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...

johnson4 at babel.ling.upenn.edu wrote:
> 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?
anova (anova.Design) computes Wald statistics.  When the log-likelihood 
is very quadratic, these statistics will be very close to log-likelihood 
ratio chi-square statistics.  In general LR chi-square tests are better; 
we use Wald tests for speed.  It's best to take the time and do 
lrtest(fit1,fit2) in Design, where one of the two fits is a subset of 
the other.

Frank Harrell
> 
> 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...
> 
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> 
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> 

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University