comparing slopes for significant difference

From: Ben (benjamin.kenward_at_zoology.ox.ac.uk)
Date: 03/11/05 

Date: Fri, 11 Mar 2005 14:20:25 +0000 (UTC)

Hi there,

I have data for four individuals. This consists of measurements of a
certain parameter over time, and the parameter tends to increase. I want
to work out if the rate of increase is significantly different in
different individuals. So the easy way to do it would be a GLM with time
as a covariate and individual as a factor. Unfortunately there is a
complication. One of the individuals is missing a lot of data at the
start of the period, which causes its regression line not to pass
through the origin (and therefore creates an artifactual significant
difference). For this particular parameter, it should by nature have
value 0 at time 0 (and the intercepts of the regression for the other
individuals do go pretty much right through 0). I would like therefore
like to constrain the regression to pass through the origin. This is
easy to do in genstat or minitab when calculating a regression for one
individual, but there is no option to do this with a GLM with factors. I
don't know if this is just because the option is missing or because
there is a fundamental way why a GLM like this would not be valid.

By the way, I realise that the fact that missing data causes a change in
the slope implies that the rate of change is not constant, so in theory
I should fit a squared term for time. But I think this adds extra
complication which I could do without, as the data doesn't seem to be
very different from linear.

So one way I thought of to do it is to work out the regression
coefficients for each individual separately, and you can then calculate
the t statistic to see if the slope from one individual differs
significantly from another slope like this:

t = ( Estimate of slope - comparison slope ) / s.e. estimated slope

and using the error d.f. as the d.f. for looking up the P value.

The problem with this way is that I get different P values depending
which way round I compare two slopes (because they have different s.e.
and d.f.). This makes me think this method is a little dodgy, and I
wonder if anyone can suggest an improvement?

Alternatively can anyone suggest any other way of approaching this?

Thanks a lot,

Ben

Ben Kenward
Department of Zoology, Oxford University
http://users.ox.ac.uk/~kgroup/ben.html

Relevant Pages

  • Re: comparing slopes for significant difference
    ... One of the individuals is missing a lot of data at the ... > like to constrain the regression to pass through the origin. ... but there is no option to do this with a GLM with factors. ... > the slope implies that the rate of change is not constant, ...
    (sci.stat.math)
  • Re: comparing slopes for significant difference
    ... One of the individuals is missing a lot of data at the ... > like to constrain the regression to pass through the origin. ... but there is no option to do this with a GLM with factors. ... > the slope implies that the rate of change is not constant, ...
    (sci.stat.edu)
  • Re: comparing slopes for significant difference
    ... So the easy way to do it would be a GLM with ... One of the individuals is missing a lot of data at the ... > like to constrain the regression to pass through the origin. ... > the t statistic to see if the slope from one individual differs ...
    (sci.stat.math)
  • Re: comparing slopes for significant difference
    ... So the easy way to do it would be a GLM with ... One of the individuals is missing a lot of data at the ... > like to constrain the regression to pass through the origin. ... > the t statistic to see if the slope from one individual differs ...
    (sci.stat.edu)
  • comparing slopes for significant difference
    ... One of the individuals is missing a lot of data at the ... value 0 at time 0 (and the intercepts of the regression for the other ... but there is no option to do this with a GLM with factors. ... the slope implies that the rate of change is not constant, ...
    (sci.stat.edu)
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