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

Guelman, Leo leo.guelman at rbc.com
Mon Jan 18 17:22:42 CET 2016

```Thanks Peter. That make sense. Nevertheless, what comes at a surprise to me (and maybe to others) is that one can potentially get different fits by simply swapping the terms in the model formula.

Best,
Leo.

-----Original Message-----
From: peter dalgaard [mailto:pdalgd at gmail.com]
Sent: 2016, January, 18 11:16 AM
To: Guelman, Leo
Cc: r-help at r-project.org; Charles C. Berry
Subject: Re: [R] Order of formula terms in model.matrix

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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```