# [R] Order of formula terms in model.matrix

peter dalgaard pdalgd at gmail.com
Mon Jan 18 17:15:56 CET 2016

```On 18 Jan 2016, at 16:49 , Guelman, Leo <leo.guelman at rbc.com> wrote:

> Is it really the same model?

No, and I didn't say that they would be. I did say that they would be in the all-factor case, which does seem to be right:

> df\$trt <- factor(df\$trt)
> fit1 <- glm(y ~ x1:trt + f1:trt, data = df, family = binomial)
> fit2 <- glm(y ~ f1:trt + x1:trt, data = df, family = binomial)
> plot(fitted(fit1), fitted(fit2)) # still differs
> df\$x1 <- factor(sample(c(-1,1), 100, replace = TRUE))
> fit1 <- glm(y ~ x1:trt + f1:trt, data = df, family = binomial)
> fit2 <- glm(y ~ f1:trt + x1:trt, data = df, family = binomial)
> plot(fitted(fit1), fitted(fit2)) # looks like it's on diagonal
> identical(fitted(fit1), fitted(fit2)) # wrong check
[1] FALSE
> all.equal(fitted(fit1), fitted(fit2)) # better
[1] TRUE

-pd

>
> 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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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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