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

[David Freedman]

Hi - wouldn't it be possible to bootstrap the difference between the fit of
the 2 models?  For example, if one had a *linear* regression problem, the
following script could be used (although I'm sure that it could be
improved):

library(MASS); library(boot)
#create intercorrelated data
Sigma <- matrix(c(1,.5,.4,  .5,1,.8,  .4,.8,1),3,3)
Sigma
dframe<-as.data.frame(mvrnorm(n<-200, rep(0, 3), Sigma))
names(dframe)<-c('disease','age','ht') #age and ht are predictors of
'disease'
head(dframe); cor(dframe)

#bootstrap the difference between models containing the 2 predictors
model.fun <- function(data, indices) {
     dsub<-dframe[indices,]
     m1se<-summary(lm(disease~age,data=dsub))$sigma; 
     m2se<-summary(lm(disease~ht,da=dsub))$sigma; 
     diff<-m1se-m2se;  #diff is the difference in the SEs of the 2 models
     }
eye <- boot(dframe,model.fun, R=200);  class(eye); names(eye);
des(an(eye$t))
boot.ci(eye,conf=c(.95,.99),type=c('norm'))
 


Ben Bolker wrote:
> 
> 
> 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
> 
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