[R] nested model with random factors

Ben Bolker bolker at ufl.edu
Thu Jul 9 01:50:02 CEST 2009




Jeff DaCosta wrote:
> 
> I am really having trouble with getting the right syntax for my  
> model.  Here is a truncated version of my data:
> 
>  > data
>      Ind Treatment Order      Date        PC1
> 1 PER14        SC   3rd  4-May-09  0.5704611
> 2 PER14        SH   1st 26-Apr-09  0.5329025
> 3 PER14        AC   2nd 29-Apr-09  2.1392279
> 4 PER25        SC   2nd 29-Apr-09 -0.2083382
> 5 PER25        SH   3rd  3-May-09  3.7818356
> 6 PER25        AC   1st 26-Apr-09 -1.9689733
> 7 PER30        SC   1st 24-Apr-09 -0.1255970
> 8 PER30        SH   2nd 27-Apr-09  2.1474393
> 9 PER30        AC   3rd 30-Apr-09 -1.8683396
> 
>  > str(data)
> 'data.frame':	9 obs. of  5 variables:
>   $ Ind      : Factor w/ 3 levels "PER14","PER25",..: 1 1 1 2 2 2 3 3 3
>   $ Treatment: Factor w/ 3 levels "AC","SC","SH": 2 3 1 2 3 1 2 3 1
>   $ Order    : Factor w/ 3 levels "1st","2nd","3rd": 3 1 2 2 3 1 1 2 3
>   $ Date     : Factor w/ 7 levels "24-Apr-09","26-Apr-09",..: 7 2 4 4  
> 5 2 1 3 6
>   $ PC1      : num  0.57 0.533 2.139 -0.208 3.782 ...
> 
>  > factor(Order, ordered=TRUE)
> [1] 3rd 1st 2nd 2nd 3rd 1st 1st 2nd 3rd
> Levels: 1st < 2nd < 3rd
> 
>  > factor(Date,ordered=TRUE)
> [1] 4-May-09  26-Apr-09 29-Apr-09 29-Apr-09 3-May-09  26-Apr-09 24- 
> Apr-09 27-Apr-09 30-Apr-09
> Levels: 24-Apr-09 < 26-Apr-09 < 27-Apr-09 < 29-Apr-09 < 3-May-09 < 30- 
> Apr-09 < 4-May-09
> 
> "Ind" are different individuals in the study, each of which received  
> three "Treatment"s (SC, SH, and AC). The "Order" (ordered=TRUE) in  
> which each individual received a treatment was systematically  
> shuffled in the study, and the "Date" (ordered=TRUE) is simply when  
> each treatment was completed.  The response variable are scores from  
> a principal components analysis ("PC1").
> 
> So I want to run a model where "PC1" is the response variable and  
> "Ind" is nested within "Treatment", and I also want to include  
> "Order" and "Date" as random factors.
> 
> I have been struggling to describe the model with aov, lm, lme, and  
> lmer, and don't think I'm getting the syntax right.  Suggestions?
> 
> 

I suggest you forward to the r-sig-mixed-models list, where the
question is less likely to get lost in the noise.

A few other thoughts:

* "Order" might as well be treated as fixed, you probably won't be able to
get a reliable estimate of its associated variance.

* I'm not sure that you'll be able to make very much use of the ordering of
the factors (unless you want to be extreme and treat them as continuous
covariates, i.e. fit a linear trend) in the aov/lme/lmer world.

* I would think that

lmer(PC1 ~ Treatment*Order+(1|Ind)+(1|Date),data=data)

would be a good start.

Have you read Pinheiro and Bates 2000?

  Ben Bolker


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