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

[Kim Pearce]

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).



Consider the syntax:



Model1<-lmer(Y~Groupf+(1|Subject/Cell),REML=FALSE,data=file1)



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.



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) ?



Model1<-lmer(Y~Groupf+(1|Cell),REML=FALSE,data=file1)



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.



Model1<-lmer(Y~Groupf+(1|Subject),REML=FALSE,data=file1)



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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