[R-SIG-Mac] How to compare two regression line slopes

[Kasper Daniel Hansen]

Ask on R-help, but note that this is more of a statistics question  
that a R question.\

Kasper

On Jan 27, 2009, at 6:08 , Etienne Toffin wrote:

> Hi,
>
> I've made a research about how to compare two regression line slopes  
> (of y versus x for 2 groups, "group" being a factor ) using R.
>
> I knew the method based on the following statement :
> t = (b1 - b2) / sb1,b2
> where b1 and b2 are the two slope coefficients and sb1,b2 the pooled  
> standard error of the slope (b)
>
> which can be calculated in R this way:
> > df1 <- data.frame(x=1:3, y=1:3+rnorm(3))
> > df2 <- data.frame(x=1:3, y=1:3+rnorm(3))
> > fit1 <- lm(y~x, df1)
> > s1 <- summary(fit1)$coefficients
> > fit2 <- lm(y~x, df2)
> > s2 <- summary(fit2)$coefficients
> > db <- (s2[2,1]-s1[2,1])
> > sd <- sqrt(s2[2,2]^2+s1[2,2]^2)
> > df <- (fit1$df.residual+fit2$df.residual)
> > td <- db/sd
> > 2*pt(-abs(td), df)
> [1] 0.9510506
>
> However, I also found a procedure in Wonnacott & Wonnacott, that is  
> based on the use of a mute variable D that will have a binary value  
> according to the group to which a given point belongs (group : D=0;  
> group 2: D=1). Then the equation that is computed is as follow:
> y = b0 + b1.x + D.b2.x
>
> which can be computed in R with:
> > fit <- lm(y ~ group + x + x:group)
> where y is the response of the 2 groups.
> The p-value of x:group gives the probability for the two slopes to  
> be different, and the estimated values of parameters are these of  
> both populations.
>
> These two methods have already been described in the mailing list  
> but not confronted and discussed.
> So, my questions are:
> - are these methods different ?
> - which one should be preferentially used ?
>
> I don't think I'm really clear and I know I'm not rigorous at all in  
> my descriptions, but I hope someone will understand me.
>
> Thanks,
>
> Etienne
>
> -------------------------------------------------------------------
> Etienne Toffin, PhD Student
> Unit of Social Ecology
> Université Libre de Bruxelles, CP 231
> Boulevard du Triomphe
> B-1050 Brussels
> Belgium
>
> Tel: +32(0)2/650.55.30
> Fax: +32(0)/650.59.87
> Skype: etienne_titou
> http://www.ulb.ac.be/sciences/use/toffin.html
>
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