ANCOVA for linear regressions without intercept

See inline.
Thanks Bert.

I have read "?formula" again and again, and I'm still struggling;

lm(body_length ~ head_length-1)
This removes intercept from each individual regression (for male, female, unknown).

When they are taken together,

lm(body_length ~ sex*head_length)
This shows differences in slopes and intercepts between the regressions (but I want to compare the slopes of the regressions WITHOUT intercepts).

If I put

lm(body_length ~ sex:head_length-1)
This shows slopes for each sex without intercepts, but NOT differences in the slope between the regressions.
You probably want:

  lm(body_length ~ head_length + sex:head_length-1)

or, in short form:

  lm(body_length ~ head_length/sex-1)

You might then compare the model 'without intercepts'
(i.e. with intercepts forced to zero) with a model that
includes intercepts. If the intercepts turn out to
be significantly nonzero, what will you do?

Peter Ehlers
I also tried

lm(body_length ~ sex*head_length-1)
lm(body_length ~ sex*head_length-sex-1)
But none of them worked.

Would anyone be able to help me? All I want to do is to compare the slopes of three linear regressions that go through the origin (0,0) so that I can say if their difference is significant or not.

Thanks for your help.

________________________________________
From: Bert Gunter [mailto:gunter.berton at gene.com]
Sent: Friday, 1 April 2011 12:56 AM
To: Yusuke Fukuda
Cc: r-help at r-project.org
Subject: Re: [R] ANCOVA for linear regressions without intercept

If you haven't already received an answer, a careful reading of

?formula

will provide it.

-- Bert
On Wed, Mar 30, 2011 at 11:42 PM, Yusuke Fukuda<Yusuke.Fukuda at nt.gov.au>  wrote:

Hello R experts

I have two linear regressions for sexes (Male, Female, Unknown). All have a good correlation between body length (response variable) and head length (explanatory variable). I know it is not recommended, but for a good practical reason (the purpose of study is to find a single conversion factor from head length to body length), the regressions need to go through the origin (0 intercept).

Is it possible to do ANCOVA for these regressions without intercepts? When I do

summary(lm(body length ~ sex*head length))

this will include the intercepts as below

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)
(Intercept)            -6.49697    1.68497  -3.856 0.000118 ***
sexMale                -9.39340    1.97760  -4.750 2.14e-06 ***
sexUnknown             -1.33791    2.35453  -0.568 0.569927
head_length             7.12307    0.05503 129.443<  2e-16 ***
sexMale:head_length     0.31631    0.06246   5.064 4.37e-07 ***
sexUnknown:head_length  0.19937    0.07022   2.839 0.004556 **
---

Is there any way I can remove the intercepts so that I can simply compare the slopes with no intercept taken into account?

Thanks for help in advance.

Yusuke Fukuda

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ANCOVA for linear regressions without intercept

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