[R-sig-ME] Rules of thumb for model complexity with small sample size in lme()

Thierry Onkelinx thierry.onkelinx at inbo.be
Wed Apr 4 17:10:41 CEST 2018

Dear John,

Since you don't have replication at the transect level, you should
omit that from the random effects structure.

I tend to strive for at least 10 observations per parameter. More is
better of course. Assuming that Nitrogen and Phosphorus are factors
with two levels, then Regulated + Light + Nitrogen + Phosphorus +
Nitrogen:Phosphorus requires 5 parameters. Add 1 for the random effect
and you have 6 parameters or at least 60 observations. So this model
might work with N = 66. However you will need to carefully check the

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel

To call in the statistician after the experiment is done may be no
more than asking him to perform a post-mortem examination: he may be
able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does
not ensure that a reasonable answer can be extracted from a given body
of data. ~ John Tukey

2018-04-04 15:55 GMT+02:00 John Ludlam <jludlam at fitchburgstate.edu>:
> Hello,
> I have an experiment with six streams in two groups (regulated and control).  At each stream there were five sites (Transect).  At each site there were unreplicated nutrient treatments (N, P, N+P, C).  Light was measured at each site.
> Stream  Regulated       Transect        Nitrogen        Phosphorus      R       Light
> Cranberry       Regulated       30      C       C       -0.102512563    2042.266667
> Cranberry       Regulated       30      C       P       -0.08877551     2042.266667
> Cranberry       Regulated       50      C       C       -0.107142857    1283.3
> Cranberry       Regulated       50      N       C       -0.059375       1283.3
> Cranberry       Regulated       70      C       C       -0.067346939    1336.6
> Cranberry       Regulated       70      N       C       -0.063636364    1336.6
> ...
> I would like to know if the response differs among groups (regulated vs control) or is related to light or nutrient treatment.  I have two separate analyses, N = 107 and N = 66 with different numbers of missing values (N = 120 before missing values).
> I think the appropriate model structure is:
> lme(Response ~ Regulated + Light + Nitrogen + Phosphorus + Nitrogen:Phosphorus), random=~1|Stream/Transect, data=data, method="ML"))
> However, I'm concerned that the model is far too complex for my sample size.  Any advice would be appreciated!
> Thanks!
> John P. Ludlam, Ph.D. - Fitchburg State University
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