[R] Is there any function can be used to compare two probit models made from same data?

[Ben Bolker]

jingjiang yan <jingjiangyan <at> gmail.com> writes:

> 
> hi, people
>     How can we compare two probit models brought out from the same data?
>     Let me use the example used in "An Introduction to R".
>     "Consider a small, artificial example, from Silvey (1970).
> 
> On the Aegean island of Kalythos the male inhabitants suffer from a
> congenital eye disease, the effects of which become more marked with
> increasing age. Samples of islander males of various ages were tested for
> blindness and the results recorded. The data is shown below:
> 
> Age: 20 35 45 55 70
> No. tested: 50 50 50 50 50
> No. blind: 6 17 26 37 44
> "
> 
> now, we can use the age and the blind percentage to produce a probit model
> and get their coefficients by using glm function as was did in "An
> Introduction to R"
> 
> My question is, let say there is another potential factor instead of age
> affected the blindness percentage.
> for example, the height of these males. Using their height, and their
> relevant blindness we can introduce another probit model.
> 
> If I want to determine which is significantly better, which function can I
> use to compare both models? and, in addition, compared with the Null
> hypothesis(i.e. the same blindness for all age/height) to prove this model
> is effective?
>

  You can use a likelihood ratio test (i.e.
anova(model1,model0) to compare either model
to the null model (blindness is independent of
both age and height).  The age model and height
model are non-nested, and of equal complexity.
You can tell which one is *better* by comparing
log-likelihoods/deviances, but cannot test
a null hypothesis of significance. Most (but
not all) statisticians would say you can compare 
non-nested models by using AIC, but you don't
get a hypothesis-test/p-value in this way.


  Ben Bolker