Hi,Oksanen,

Thanks for your reply.

I agree with you at the point  that if we misjudge none-zero intercept to be
zero, there will be loss still or even great loss as you and Venables
emphasized in your practical research work. If there won't be any loss when
we misjudge
zero intercept to be none-zero, and we don't care the possible improvement
on predictive ability, the strategy that always including intercept will be
OK. Otherwise, even though the cases that true intercept is none-zero are
very rare, I think in some special cases, my strategy is worthy to be
concerned.

In fact, to your example, my strategy gives correct result at a very high
possibility, shown by the following code:

> library(leaps)
> n.sim=1000
> result=matrix(rep(NA,2*n.sim),ncol=2)
>
> for(i.sim in 1:n.sim){
+ mass <- runif(100, 10, 500) # typical range for plant biomass/m^2
+ spno <- rpois(100, 12) # Moderate number of species independent of mass
+
+ var.selection=leaps(cbind(rep(1,length(mass)),mass),spno,int=F,method="adjr2")

+ temp=var.selection$which[var.selection$adjr2==max(var.selection$adjr2),]
+ names(temp)=c("intercept","mass")
+ result[i.sim,]=temp ########## This is the result given by my strategy
+ }
>
> apply(result,2,sum)/n.sim ########## This is the frequencies that
intercept and mass are selected respectively
[1] 1.000 0.314



2007/5/22, Jari Oksanen <jari.oksanen@oulu.fi>:
>
> 쟀에쌤 <klijunjie <at> gmail.com> writes:
>
> >
> > Hi, Lynch,
> >
> > Thank you for attention first.
> >
> > I am also not a statistician and have just taken several statistics
> classes.
> > So it is natral for us to ask some question seeming naive to
> statisticans.
> >
> > I am sorry that I cannot agree with your point that we must always
> include
> > intercept in our model. becaus if true intercept is zero, the strategy
> of
> > you or your textbook will be have 2 losses. First, there will be
> > explaination problem. If true intercept is zero and your estimate of it
> is
> > not zero, the result of regression is misleading. However, it might be
> not
> > so serious as we judge those coefficients which are actually zeros to be
> > none-zeros, but the misjudge here is still a loss in some
> > extent. Secondly, if true intercept is zero, your strategy's predictive
> > ability is often lower than other strategies which do not always include
> > intercept.
> >
> I'm not a statistician, but I've seen much damage done with regression
> forced
> through zero in my field (ecology). This technique is tought in many
> statistical
> textbooks  popular among ecologists. The key problem here is: how do you
> *know*
> that the intercept is zero? Even in logically compelling cases it is very
> easy
> to reach false certainty of zero intercept. A typical case in ecology is
> where
> people study  the number of species against biomass, and argue that there
> *must*
> be zero species when biomass = 0 (if there is nothing, then there is
> nothing).
> The conclusion is that you must fit a model with no intercept. Let's see a
> typical example (and I'm so confident that I won't put any random number
> seed
> for this):
>
> mass <- runif(100, 10, 500) # typical range for plant biomass/m^2
> spno <- rpois(100, 12) # Moderate number of species independent of mass
> summary(lm(spno ~ mass - 1)) # WRONG!
> summary(lm(spno ~ mass)) # More or less correct
>
> It is not sufficient to know that the value must be zero in a certain
> point, you
> also should know how that point is scaled: it may make sense to say that
> spno =
> 0 at log(mass) = -Inf, but then it does not make sense to force regression
> through that point. In particular, when the zero-point is extrapolated
> from the
> data, it is dangerous to force regression through the origin. Further, if
> your x
> does not have a really natural scale, but you can replace x with x -
> constant
> (like x - mean(x)), then it hardly makes sense to play with zero
> intercepts.
>
> There may be cases where forcing regression through zero makes sense, but
> they
> seem to be very rare. I've seen them very rarely.
>
> There is an exegetic text on the issue at
> http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf which also touches this
> issue
> (page 3) and makes a nice reading anyhow.
>
> Cheers, Jari Oksanen
>
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>



-- 
Junjie Li,                  klijunjie@gmail.com
Undergranduate in DEP of Tsinghua University,

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