R help - Nov 2007 - fit linear regression with multiple predictor and constrained intercept

Hi group,

I have this type of data
x(predictor), y(response), factor (grouping x into many groups, with 6-20
obs/group)

I want to fit a linear regression with one common intercept. 'factor'
should only modify the slopes, not the intercept. The intercept is expected
to be >0.

If I use
y~ x + factor, I get a different intercept for each factor level, but one
slope only

if I use
y~ x * factor, I get the interaction term I want, but the intercept is not
kept constant.
Also, if I constrain teh intercept in the regression model (y~a+x*factor),
I get estimates both for slope and intercept of each factor level.

Robert




----------------------------------------------------------------------------------------------------------------------
NIVAs hovedkontor har flyttet til nye lokaler i CIENS - Forskningssenter
for milj? og samfunn; Gaustadall?en 21, 0349 Oslo. Meld deg p? v?rt
nyhetsbrev p? www.niva.no

robert.ptacnik at niva.no wrote:
> Hi group,
>
> I have this type of data
> x(predictor), y(response), factor (grouping x into many groups, with 6-20
> obs/group)
>
> I want to fit a linear regression with one common intercept.
'factor'
> should only modify the slopes, not the intercept. The intercept is expected
> to be >0.
>
> If I use
> y~ x + factor, I get a different intercept for each factor level, but one
> slope only
>
> if I use
> y~ x * factor, I get the interaction term I want, but the intercept is not
> kept constant.
> Also, if I constrain teh intercept in the regression model (y~a+x*factor),
> I get estimates both for slope and intercept of each factor level.
>
> Robert
>
>
>
>   
You seem to be looking for the colon operator. In R, unlike certain
other statistical packages, the star implies inclusion of main effects:
a*b is a + b + a:b. There is some trickery about when you get factors
contrast coded in interaction terms (as far as I remember x:factor and
x+x:factor are two different parametrizations of the same model), but
you should be able to find that out by a little experimenting.

-- 
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

I think you are looking for y ~ x + x:factor   E.g.
> library(car)
> lm(repwt ~ repht + repht:sex, data=Davis)
Coefficients:
(Intercept)        repht   repht:sexM
   -59.30865      0.71412      0.05694

where the third term is the difference in slope between males and females.
> lm(repwt ~ repht:sex, data=Davis)
Coefficients:
(Intercept)   repht:sexF   repht:sexM
    -59.3086       0.7141       0.7711

for separately reported slopes.

If you want to constrain the intercept, fit with and without and take the 
better fit (or look into package nnls, but that would be overkill here).


On Wed, 28 Nov 2007, robert.ptacnik at niva.no wrote:
> Hi group,
>
> I have this type of data
> x(predictor), y(response), factor (grouping x into many groups, with 6-20
> obs/group)
>
> I want to fit a linear regression with one common intercept.
'factor'
> should only modify the slopes, not the intercept. The intercept is expected
> to be >0.
>
> If I use
> y~ x + factor, I get a different intercept for each factor level, but one
> slope only
>
> if I use
> y~ x * factor, I get the interaction term I want, but the intercept is not
> kept constant.
> Also, if I constrain teh intercept in the regression model (y~a+x*factor),
> I get estimates both for slope and intercept of each factor level.
>
> Robert
>
>
>
>
>
----------------------------------------------------------------------------------------------------------------------
> NIVAs hovedkontor har flyttet til nye lokaler i CIENS - Forskningssenter
> for milj? og samfunn; Gaustadall?en 21, 0349 Oslo. Meld deg p? v?rt
> nyhetsbrev p? www.niva.no
> ______________________________________________
> 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.
>
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595