# [R] glm(y ~ -1 + c, "binomial") question

Yuelin Li yuelin at pandora.outcomes.chop.edu
Thu May 16 21:03:12 CEST 2002

```This is a question about removing the intercept in a binomial
glm() model with categorical predictors.  V&R (3rd Ed. Ch7) and
Chambers & Hastie (1993) were very helpful but I wasn't sure I
got all the answers.

In a simplistic example suppose I want to explore how disability
(3 levels, profound, severe, and mild) affects the dichotomized
outcome.  The glm1 model (see below) is the same as glm2 (2 dummy
variables coding sever and mild).  In both models the reference
level is profound disability.

My questions are:

1. How do I interpret the coefficients in the third model (the
intercept is removed)?

2. Does glm3 make sense?  Does anyone ever want to construct a
model like glm3?  If so, when?

3. What is the algebraic specification of glm3?

Many thanks,

-- Yuelin Li.

-------------------

categ <- factor(rep(c(1, 2, 3), times=c(20, 20, 20)),
labels=c("P", "S", "M"))
Y <- c(1,1,1,1,1,1,2,1,2,1,2,1,1,1,1,1,1,2,2,
1,2,2,1,2,2,1,2,1,2,1,1,2,2,2,2,2,2,2,2,1,
2,2,2,2,2,1,2,1,1,1,2,2,2,2,1,2,1,1,1,2)
Y <- Y == 2

glm1 <- glm(Y ~ categ, family="binomial")
glm2 <- glm(Y ~ c(categ == "S") + c(categ == "M"), "binomial")
glm3 <- glm(Y ~ -1 + categ, "binomial")

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