[R-sig-ME] R-sig-mixed-models Digest, Vol 36, Issue 3

Malcolm Fairbrother m.fairbrother at bristol.ac.uk
Thu Dec 3 13:08:05 CET 2009

Dear Stephen,

If I understand correctly, you're trying to estimate the unique effect of group for each specific region, while also taking into account what you know about overall differences across individuals (since, I presume, individuals with a large region 1 will also tend to have larger regions 2-30, etc.).

To me, that implies:

lmer(y ~ group + (group | region) + (1 | subject))

This will get you a random (unique) intercept for each subject and each region, and a unique effect of (each level of) group for each separate region, net of the average effect of group across all regions, captured by the fixed effect. The unique effect is your primary interest, as I take it.

Hope that's useful.


Dr Malcolm Fairbrother
Lecturer in Global Policy and Politics
School of Geographical Sciences
University of Bristol

> Message: 3
> Date: Wed, 2 Dec 2009 17:36:57 -0600
> From: Stephen Weigand <weigand.stephen at gmail.com>
> Subject: [R-sig-ME] Analyzing hierarchical MRI data
> To: r-sig-mixed-models at r-project.org
> Message-ID:
> 	<bc47d3330912021536i833d285ue7c1a07cd9909c0 at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
> Hello,
> I'd like to explore ways to analyze data from brain MRIs using lmer.
> My data are typically of the following form:
> * There are a small number of groups (e.g., disease 1, disease 2,
> control) with from 10 to 50 human subjects in each group.
> * Each subject has had an MRI of the head. From the MRI I get one
> value at each of 30 different regions of the brain (e.g., a value for
> the amygdala, a value for the hippocampus, etc.). This value is
> typically an estimate of the region size. So I get 30 values for each
> subject. These values are typically conditionally Gaussian. My data
> frame may look like this
> group subject region y
> A Subj1 Amygdala 2.5
> A Subj1 Hippocampus 2.8
> A Subj2 Amygdala 3.2
> A Subj2 Hippocampus 4.8
> ...
> B Subj3 Amygdala 1.7
> B Subj3 Hippocampus 4.9
> B Subj4 Amygdala 2.2
> B Subj4 Hippocampus 3.5
> ...
> The question is, In which regions do the groups differ and by how much?
> I can treat group and region as fixed effects by arguing that they are
> the only groups and regions of interest and fit a random intercept
> model with a group by region interaction of the form:
> lmer(y ~ group*region + (1 | subject))
> But I would like to take advantage of pooling/penalization/shrinkage
> to get more reliable estimates of the differences between groups at
> each region.  So I think I want to turn region (and maybe group?) into
> random effects.
> I want to try
> lmer(y ~ (1 | group) + (1 | region) + (1 | subject))
> but is that ignoring the nested structure of the data? I would greatly
> appreciate suggestions.
> Thank you,
> Stephen
> PS I'm OK with ignoring spatial correlation for now although I expect
> that regions that are close to one another in the brain are going to
> be more correlated than regions at opposite sides of the brain.
> PPS I would guess that to the experts these questions seem all the
> same but to the uninitiated, every problem seems like a unique case!!
> -- 
> Rochester, Minn. USA

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