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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> PLEASE do read the posting guide
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> and provide commented, minimal, self-contained, reproducible code.
>
>
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