[R-sig-ME] repeated measure in partially crossed design

ONKELINX, Thierry Thierry.ONKELINX at inbo.be
Tue Jan 31 13:02:22 CET 2012

Dear Matteo,

You want to know the effect of treatment and season: then you should use them as fixed effect. Here a some models

V1 ~ treatment * season + V2 + (1|subject)
V1 ~ treatment * season + V2 + (1 + V2|subject) #interaction between subject and V2
V1 ~ treatment * season + V2 + (1|subject/season) #interaction between subject and season

You way want to do some reading on mixed models. E.g. Zuur et al (2009)

Best regards,


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be

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

-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] Namens matteo dossena
Verzonden: maandag 30 januari 2012 21:05
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] repeated measure in partially crossed design

Dear All,

I'm having a some doubts on how to properly specify the random effect  in lmer for the following experiment:

I have 10 subject assigned to treatment A and 10 assigned to treatment B. For each subject I measured 2 variables, V1 and V2, and these measures were repeated in season A and season B.

I'm interested in assessing the effect of treatment, season and their interaction on the relationship between the two variables. 

I'm a little confused on how I have to specify the random structure.

According to the design  I identified the following random structure

(1 + V2 | treatment/subject) + (1 + V2 | season)

where the first term account for the nested design and temporal pseudorplication and the second term for the other unmeasured variable that covary with season and could affect the within season relationship between V1 and V2


Then i performed a model selection procedure, to investigate which would be the best random structure. To do so I subsequently removed each term from the random structure, and  compared the AIC score.
>From this procedure it turned out that the best random structure is:  (1 + var2 | season).

My concern here is, if subject is no longer included in the random structure, i'm no longer accounting for the pseudorplication, am I?

Is the fact that the term (1 + V2 | treatment/subject) does not improve the model fit telling that in fact there is no significant correlation between measures on the same subject?

To further explore the issue, i also analysed the following random structure:

(1 + V2 | subject) + (1 + V2 | season)

and in this case the model selection procedure identified this as the best random structure.

So here is where i got confused.
My question is how do i properly specify the random structure?

Searching for an answer to my doubt in the literature, in Crawley 2007, i came across a further way to account  for temporal pseudoreplication (in lme: random = ~ season | subject) translated in lmer would it be

(season | subject) ? 

at this stage I had to give up and ask for help.
Could anyone give me some advice? is my strategy somehow wrong?

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