Frank,
I don't think there is any way to "fix" your problem except the way that I
did it.
library(survival)
tdata <- data.frame(y=c(1,3,3,5, 5,7, 7,9, 9,13),
x1=factor(letters[c(1,1,1,1,1,2,2,2,2,2)]),
x2= c(1,2,1,2,1,2,1,2,1,2))
fit1 <- lm( y ~ x1 * strata(x2) - strata(x2), tdata)
coef(fit1)
(Intercept) x1b x1a:strata(x2)x2=2 x1b:strata(x2)x2=2
3.000000 5.000000 1.000000 1.666667
Your code is calling model.matrix with the same model frame and terms structure as the lm
call above (I checked). In your case you know that the underlying model has 2 intercepts
(strata), one for the group with x2=1 and another for the group with x2=2, but how is the
model.matrix routine supposed to guess that? It can't, so model.matrix returns the proper
result for the lm call. As seen above the result is not singular, while for the Cox model
it is singular due to the extra intercept.
This is simply an extension of leaving the "intercept" term in the model and then removing
that column from the returned X matrix, which is necessary to have the correct coding for
ordinary factor variables, something we've both done since day 1. In order for
model.matrix to do the right thing with interactions, it has to know how many intercepts
there actually are.
I've come to the conclusion that the entire thrust of 'contrasts' in S was wrong headed,
i.e., the "remove redundant columns from the X matrix ahead of time" logic. It is simply
not possible for the model.matrix routine to guess correctly for all y and x combinations,
something that been acknowledged in R by changing the default for "singular.ok" to TRUE.
Dealing with this after the fact via a good contrast function (a la SAS -- heresy!) would
have been a much better design choice. But as long as I'm in R the coxph routine tries to
be a good citizen.
Terry T.
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