Thanks for the illustrative example. In my project actually my supervisor
wanted to estimate the probabilities using a "conditional MLE" approach,
which happens to be the case that *uses clogit() while trying to achieve
aim b in your words*.

I learned that clogit() is based on the sufficient statistic which is
usually the sum over all positive responses in each stratum. However since
we are supposed to not knowing the responses when trying to predict a new
sample, it can be impossible to do this "out-of-sample" prediction right?

Now what I suggested is to use clogit() to estimate beta (ppl say this beta
is better than betas from unconditional MLE, why??) and derive the linear
predictor for any new sample by multiplying new predictors with this beta,
then

1) if there is only one obs each strata, use the traditional unconditional
formula

phat = exp(xbeta)/(1+exp(xbeta))

to get the so-called predicted probability;

2) if there is a lot of obs each strata, use

phat = exp(xbeta)/sum(exp(xbeta))

to get the so-called predicted probabilities.

My case has only 1 obs per stratum so I used method 1. Though I am not sure
if it is reasonable. Would like to hear opinions from all of you guy. ;P

On Mon, Mar 4, 2013 at 10:04 PM, Terry Therneau <therneau@mayo.edu> wrote:

> I'm late to this discussion, but let me try to put it in another context.
>   Assume that I wanted to know whether kids who live west of their school
> or east of their shool are more likely to be early (some hypothesis about
> walking slower if the sun is in their eyes).  So I create a 0/1 variable
> east/west and get samples of 10 student arrival times at each of 100
> different schools.  Fit the model
>
>    lm(arrive ~ factor(school) + east.west)
>
> where "arrive" is in some common scale like "minutes since midnight".
>  Since different schools could have different starting times for their
> first class we need an intercept per school.
>
>   Two questions:
>      1. Incremental effect: the coefficient of east/west measures the
> incredmental effect across all schools.  With n of 1000 it is likely
> estimated with high precision.
>      2. Absolute: predict the average arrival time (on the clock) for
> students.
>
> Conditional logistic is very like this.  We have a large number of strata
> ("schools") with a small number of observations in each (often only 2 per
> strata).  One can ask incremental questions about variables common to all
> strata, but absolute prediction is pretty worthless.  a. You can only do it
> for schools (strata) that have already been seen and b. there are so few
> subjects in each of them that the estimates are very noisy.
>   The default prediction from clogit is focused on questions of type 1.
>  The documentation doesn't even bother to mention predictions of type 2,
> which would be probabilities of events.  I can think of a way to extract
> such output from the routine (being the author gives some insight), but why
> would I want to?
>
> Terry Therneau
>
>

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