[R-sig-ME] Singularity and the 3 Level Hierarchy

[kalman.toth]

Hi Kim,

I am just a scientist who often works with repeated measures data and not a statistician but I would like to add a few comments and others might amend those or add more.

1) I don’t see any reason to use REML = FALSE in your case. Given what you described, I’d definitely stick with REML = TRUE—it’s the better choice when you want to properly account for the random effect structure.
2) A work example would help.
3) What model you use should be primarily based on your experimental design and your scientific knowledge of the field.
4) That singular fit warning probably means that one of your parameters is estimated at (or very close to) zero. In most cases, it’s fine to just drop that parameter—unless you have a strong scientific reason to keep it. Also, if your experimental design is fully nested, you might want to try adding the interaction term ('Subject:Cell') instead of just 'Cell'.
5) anova() or AIC() can be used to compare models with different random effect structures. 

Best Regards,
Kalman Toth  


On Thursday, February 20th, 2025 at 1:14 PM, Kim Pearce via R-sig-mixed-models <r-sig-mixed-models using r-project.org> wrote:

> Hello everyone,
> 
> 
> 
> If I may, I would like to ask about the appropriateness of a particular model when the original design takes on a 3 level hierarchical structure.
> 
> 
> 
> Say we have N subjects and each of these subjects has several cells. Within each cell there are mitochondria and a continuous measurement (Y) is recorded for each mitochondrion. In this design, mitochondria (level 1) are nested within cells (level 2) and cells are nested within subjects (level 3).
> 
> 
> 
> For ease, say we are interested in establishing if patient disease group is related to Y. There are 3 patient disease groups recorded in the factor variable "Groupf". In addition, variable "Subject" identifies each of the N subjects and variable "Cell" identifies the cells (within the subjects).
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> Consider the syntax:
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> Model1<-lmer(Y~Groupf+(1|Subject/Cell),REML=FALSE,data=file1)
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> The above would give us a fixed effect for Groupf as well as intercepts for the N subjects and intercepts for the Subject x Cell combinations.
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> Hypothetically, say we found evidence of singularity (i.e. the estimated random intercept variance was near zero at the Subject and Subject x Cell levels), however, singularity was not flagged for a 2 level hierarchy (where mitochondria are nested within cells). Would it be valid to report such a 2 level model (i.e. where the "top level" was Cell) ?
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> Model1<-lmer(Y~Groupf+(1|Cell),REML=FALSE,data=file1)
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> or would it be more preferable to always consider Subject as the "top level" if singularity was not flagged in such a model i.e.
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> Model1<-lmer(Y~Groupf+(1|Subject),REML=FALSE,data=file1)
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> Many thanks for your appreciated views on this issue in advance.
> 
> Kind regards,
> 
> Kim
> 
> 
> 
> Dr Kim Pearce PhD, CStat, Fellow HEA
> Senior Statistician
> Faculty of Medical Sciences Graduate School
> Room 3.14
> 3rd Floor Ridley Building 1
> Newcastle University
> Queen Victoria Road
> Newcastle Upon Tyne
> NE1 7RU
> 
> Tel: (0044) (0)191 208 8142
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