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

[Frank E Harrell Jr]

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...
> 
> Previous 	Next 	| 	Save 	| 	Delete 	| 	Reply 	|
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 


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