[R] Adding regression lines to each factor on a plot when using ANCOVA

[Peter Ehlers]

Steve,

Thanks for providing an example (which does, however need a bit of
tweaking; BTW, it's usually not a good idea to cbind your data
when what you really want is a data.frame).

Your guess about some clever way of using abline() is unfortunately
not correct - as the help page indicates, the slope and intercept
must be given as single values. So you will have to extract each
(intercept, slope) pair from the model coefficients and call abline()
on them. A convenient way to do this is to specify the model as

  mod <- lm(y ~ f/x + 0)

(which I first learned from MASS, the book).
Here f is your grouping variable.  As the book says,
this gives "separate regression models of the type 1 + x within
the levels of f".  The "+ 0" removes the usual intercept which is
replaced by individual intercepts for each level of f.

For your example this will give 12 intercepts as
the first 12 coefficients and 12 slopes as the remaining coefs.

Then you can use

  cof <- coef(mod)
  for(i in 1:12) abline(a=cof[i], b=cof[12 + i])

to plot the 12 lines.

  -Peter Ehlers

On 2010-04-01 16:21, Steven Worthington wrote:
>
> Dear R users,
>
> i'm using a custom function to fit ancova models to a dataset. The data are
> divided into 12 groups, with one dependent variable and one covariate. When
> plotting the data, i'd like to add separate regression lines for each group
> (so, 12 lines, each with their respective individual slopes). My 'model1'
> uses the group*covariate interaction term, and so the coefficients to plot
> these lines should be contained within the 'model1' object (there are 25
> coefficients and it looks like I need the last 12). The problem is I can't
> figure out how to extract the relevant coefficients from 'model1' and add
> them using abline. I imagine there's some way of using the relevant slopes
>
> abline(model1$coef[14:25])
>
> together with the intercept, but I can't quite get it right. Can anyone
> offer a suggestion as to how to go about this? Ideally, What i'd like is to
> plot each regression line in the same color as the group to which it
> belongs.
>
> I've provided an example with dummy data below
>
> best,
>
> Steve
>
>
> # ===========================================================
> # hypothetical data
> species<-
> c(1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,7,7,7,8,8,8,8,9,9,9,9,9,10,10,10,11,11,11,11,12,12,12,12,12)
> beak.lgth<-
> c(2.3,4.2,2.7,3.4,4.2,4.8,1.9,2.2,1.7,2.5,15,16.5,14.7,9.6,8.5,9.1,9.4,17.7,15.6,14,6.8,8.5,9.4,10.5,10.9,11.2,11.5,19,17.2,18.9,19.5,19.9,12.6,12.1,12.9,14.1,12.5,15,14.8,4.3,5.7,2.4,3.5,2.9)
> mass<-
> c(45.9,47.1,47.6,17.2,17.9,17.7,44.9,44.8,45.3,44.9,39,39.7,41.2,84.8,79.2,78.3,82.8,102.8,107.2,104.1,51.7,45.5,50.6,27.5,26.6,27.5,26.9,25.4,23.7,21.7,22.2,23.8,46.9,51.5,49.4,33.4,33.1,33.2,34.7,39.3,41.7,40.5,42.7,41.8)
> dataset<- cbind(groups, beak.lgth, mass)
>
> # ANCOVA function
> anc<- function(variable, covariate, group){
> 	# transform data
> 	lgVar<- log10(variable)
> 	lgCov<- log10(covariate)
> 	# separate regression lines for each group
> 	model1<- lm(lgVar ~ lgCov + group + lgCov:group)
> 		model1.summ<- summary(model1)
> 		model1.anv<- anova(model1)
> 	# separate regression lines for each group, but with the same slope
> 	model2<- lm(lgVar ~ lgCov + group)
> 		model2.summ<- summary(model2)
> 		model2.anv<- anova(model2)
> 	# same regression line for all groups
> 	model3<- lm(lgVar ~ lgCov)
> 		model3.summ<- summary(model3)
> 		model3.anv<- anova(model3)
> 	compare<- anova(model1, model2, model3) # compare all models
> 	# plots
> 	par(mfcol=c(1,2))
> 	boxplot(lgVar ~ group, col="darkgoldenrod1")
> 	# plot the variate and covariate by group
> 	plot(lgVar ~ lgCov, pch=as.numeric(group), col=as.numeric(group))
> 		legend("topleft", inset=0, legend=as.character(unique(group)),
> col=as.numeric(unique(group)),
> 		pch=as.numeric(unique(group)), pt.cex=1.5)
> 		abline(model1) # Need separate regression lines here
> 	list(model_1_summary=model1.summ, model_1_ANOVA=model1.anv,
> model_2_summary=model2.summ,
> 		model_2_ANOVA=model2.anv, model_3_summary=model3.summ,
> model_3_ANOVA=model3.anv, model_comparison=compare)
> }
>
> # call function
> anc(beak.lgth, mass, species)
> # ===========================================================
>

-- 
Peter Ehlers
University of Calgary