# [Rd] y ~ X -1 , X a matrix

(Ted Harding) Ted.Harding at manchester.ac.uk
Thu Mar 18 01:57:23 CET 2010

```On 17-Mar-10 23:32:41, Ross Boylan wrote:
> While browsing some code I discovered a call to lm that used
> a formula y ~ X - 1, where X was a matrix.
>
> Looking through the documentation of formula, lm, model.matrix
> and maybe some others I couldn't find this useage (R 2.10.1).
> Is it anything I can count on in future versions?  Is there
> documentation I've overlooked?
>
> For the curious: model.frame on the above equation returns a
> data.frame with 2 columns.  The second "column" is the whole X
> matrix. model.matrix on that object returns the expected matrix,
> with the transition from the odd model.frame to the regular
> matrix happening in an .Internal call.
>
> Thanks.
> Ross
>
> P.S. I would appreciate cc's, since mail problems are preventing
> me from seeing list mail.

Hmmm ... I'm not sure what is the problem with what you describe.
Code:

set.seed(54321)
X  <- matrix(rnorm(50),ncol=2)
Y  <- 1*X[,1] + 2*X[,2] + 0.25*rnorm(25)
LM <- lm(Y ~ X-1)

summary(LM)
# Call:
# lm(formula = Y ~ X - 1)
# Residuals:
#      Min       1Q   Median       3Q      Max
# -0.39942 -0.13143 -0.02249  0.11662  0.61661
# Coefficients:
#    Estimate Std. Error t value Pr(>|t|)
# X1  0.97707    0.04159   23.49   <2e-16 ***
# X2  2.09152    0.06714   31.15   <2e-16 ***
# ---
# Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
# Residual standard error: 0.2658 on 23 degrees of freedom
# Multiple R-squared: 0.9863,     Adjusted R-squared: 0.9851
# F-statistic: 826.6 on 2 and 23 DF,  p-value: < 2.2e-16

model.frame(LM)
#              Y          X.1          X.2
# 1   0.04936244 -0.178900750  0.051420078
# 2  -0.54224173 -0.928044132 -0.027963292
# [...]
# 24  1.54196979  0.312332806  0.602009497
# 25 -0.16928420 -1.285559427  0.394790358

str(model.frame(LM))
#  \$ Y: num  0.0494 -0.5422 -0.7295 -3.4422 -3.1296 ...
#  \$ X: num [1:25, 1:2] -0.179 -0.928 -0.784 -1.651 -0.408 ...
# [...]

model.frame(Y ~ X-1)
#              Y          X.1          X.2
# 1   0.04936244 -0.178900750  0.051420078
# 2  -0.54224173 -0.928044132 -0.027963292
# [...]
# 24  1.54196979  0.312332806  0.602009497
# 25 -0.16928420 -1.285559427  0.394790358
## (Identical to above)

str(model.frame(Y ~ X-1))
# \$ Y: num  0.0494 -0.5422 -0.7295 -3.4422 -3.1296 ...
# \$ X: num [1:25, 1:2] -0.179 -0.928 -0.784 -1.651 -0.408 ...
# [...]
## (Identical to above)

Maybe the clue (admittedly somewhat obtuse( can be found in ?lm:

lm(formula, data, subset, weights, na.action,
method = "qr", model = TRUE, x = FALSE, y = FALSE, qr = TRUE,
singular.ok = TRUE, contrasts = NULL, offset, ...)
[...]

data: an optional data frame, list or environment (or object
coercible by 'as.data.frame' to a data frame) containing the
are taken from 'environment(formula)', typically the
environment from which ?lm? is called.

So, in the example the variables are taken from X, "coercible
by 'as.data.frame' ... taken from 'environment(formula)'".

Hence (I guess) X is found in the environment and is coerced
into a dataframe with 2 columns, and X.1, X.2 are taken from there.

R Gurus: Please comment! (I'm only guessing by plausibility).
Ted.

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Date: 18-Mar-10                                       Time: 00:57:20
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