[R] lm(y ~ x1) vs. lm(y ~ x0 + x1 - 1) with x0 <- rep(1, length(y))

[Bert Gunter]

Well ... as x1 is continuous(numeric), it has no levels. So ...??

Note that the fits are identical for both models. The issue is only
what is the Null that you are testing in the two cases. In the first
case, it is just y = constant, so you are testing the 1 df for x1. In
the second, it is y = 0 (which rarely makes any sense) and you are
testing the 2 df for the two terms (x0 and x1). Etc. etc.

-- Bert

On Fri, Jan 21, 2011 at 7:48 PM, David Winsemius <dwinsemius at comcast.net> wrote:
>
> On Jan 21, 2011, at 9:03 PM, jochen laubrock wrote:
>
>> Dear list,
>>
>> the following came up in an introductory class. Please help me understand
>> the -1 (or 0+) syntax in formulae: Why do the enumerator dfs, F-statisics
>> etc. differ between the models lm(y ~ x1) and lm(y ~ x0 + x1 - 1), if x0 is
>> a vector containing simply ones?
>
> You are testing something different. In the first case you are testing the
> difference between the baseline and the second level of x1 (so there is only
> one d.f.), while in the second case you are testing for both of the
> coefficients being zero (so the numerator has 2 d.f.). It would be easier to
> see if you did print() on the fit object. The first model would give you an
> estimate for an "Intercept", which is really an estimate for the first level
> of x1.  Having been taught to think of anova as just a special case of
> regression is helpful here. Look at the model first  and only then look at
> the anova table.
>
>
>>
>> Example:
>>
>> N  <- 40
>> x0 <- rep(1,N)
>> x1 <- 1:N
>> vare <- N/8
>> set.seed(4)
>> e <- rnorm(N, 0, vare^2)
>>
>> X <- cbind(x0, x1)
>> beta <- c(.4, 1)
>> y <- X %*% beta + e
>>
>> summary(lm(y ~ x1))
>> # [...]
>> # Residual standard error: 20.92 on 38 degrees of freedom
>> # Multiple R-squared: 0.1151,   Adjusted R-squared: 0.09182
>> # F-statistic: 4.943 on 1 and 38 DF,  p-value: 0.03222
>>
>> summary(lm(y ~ x0 + x1 - 1))        # or summary(lm(y ~ 0 + x0 + x1))
>> # [...]
>> # Residual standard error: 20.92 on 38 degrees of freedom
>> # Multiple R-squared: 0.6888,   Adjusted R-squared: 0.6724
>> # F-statistic: 42.05 on 2 and 38 DF,  p-value: 2.338e-10
>>
>>
>> Thanks in advance,
>> Jochen
>>
>>
>> ----
>> Jochen Laubrock, Dept. of Psychology, University of Potsdam,
>> Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
>> phone: +49-331-977-2346, fax: +49-331-977-2793
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius, MD
> West Hartford, CT
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>



-- 
Bert Gunter
Genentech Nonclinical Biostatistics
467-7374
http://devo.gene.com/groups/devo/depts/ncb/home.shtml