Is it really the same model?

Following the example provided by Lars:

set.seed(1)
x1 <- rnorm(100)
f1 <- factor(sample(letters[1:3], 100, replace = TRUE))
trt <- sample(c(-1,1), 100, replace = TRUE)
y <- factor(sample(c(0,1), 100, T))
df <- data.frame(y=y, x1=x1, f1=f1, trt=trt)

fit1 <- glm(y ~ x1:trt + f1:trt, data = df, family = binomial)
coef(fit1)

fit2 <- glm(y ~ f1:trt + x1:trt, data = df, family = binomial)
coef(fit2)

identical(fitted(fit1), fitted(fit2))
[1] FALSE



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