truncated regressor

On Sun, 14 May 2000, Troels Ring wrote:

Dear friends. I have the problem of assessing the importance of bleeding 
times censored at 20 minutes for predicting blood loss incurred after a 
liver biopsy. How would I use the knowledge that the censored values were 
20 minutes or more ?

This is a (partially) missing-value problem.  Are values > 20 mins 
always censored?  If so I would group the times and use an ordered factor
as a regressor.  If you really want a linear effect on, say `bt' you can
use

... + bt + I(bt==20) + ...

which allows a separate value of bt==20 over and above a linear model.

I am trying to understand this. The help for ?I says:

...
     To avoid this confusion, the function `I()' can be used to bracket
     those portions of a model formula where the operators are used in
     their arithmetic sense.  For example, in the formula `y ~ a +
     I(b+c)', the term `b+c' is to be interpreted as the sum of `b' and
     `c'.
...

which is clear to me: doing lm(y ~ a + I(b+c)) is similar to

	d <- b + c
	lm(y ~ a + d)

But what if the expression in I() is a logical? After playing a moment, I
found out that a formula can include a logical variable, and treats it as a
factor:

x <- runif(50, 0, 50)
y <- 2*x + rnorm(50, 0, 5)
lm(y ~ x < 25)

Call:
lm(formula = y ~ x < 25)

Coefficients:
(Intercept)       x < 25  
      78.24       -53.92

lm(y ~ x > 25)

Call:
lm(formula = y ~ x > 25)

Coefficients:
(Intercept)       x > 25  
      24.32        53.92  


Is it worth adding a few lines in this help file on the use of logical
variables in formula? (also characters can be included but must be
converted into factors before)

Emmanuel Paradis
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