MCMCglmm rcov term

Hi Fiona,

us(trait):units in the rcov term is fitting a 3x3 covariance matrix  
for the residuals of the three PC scores. It makes sense that the  
covariances are close to zero and the variances get smaller given they  
are PC scores, but this doe not have to be the case because the PC's  
are defined at the level of the raw data rather than the residuals.

The term us(trait):units:isoline is equivalent because each unit (row  
of the data frame) belongs to a single isoline so there is a on to one  
mapping between units and  units:isoline.

The remaining parts of the model (fixed and random) are at the moment  
a little odd, because you don't form interactions between trait and  
other terms.  This means that the effect of food and temperature in  
the fixed effects are constrained to be the same across the three  
PCs.   The isoline effects within a treatment/temperature are assumed  
to be equivalent across the three PC's (i.e. the correlations between  
isoline effects within a treatment/temperature on the three PC's are  
assumed to be 1  - they are probably closer to zero given they're  
PC's, and they are assumed to have the same variance). They are are  
allowed to differ across food/temperature treatments although the  
assumption is that the correlation between isoline effects on PC1 (for  
example) in different treatments is zero (I would expect it to be  
positive, but perhaps not 1).

  When forming interactions with random effects I always try and  
determine what this means in terms of covariance matrices  - its  
easier this way. Table 3.1 (p 70) of the CourseNotes and Chapter 5 on  
multi-response models may be helpful. With 60 isoline effects you need  
to be cautious about over-fitting/prior sensitivity with parameter- 
rich multi-response models.

Cheers,

Jarrod

MCMCglmm rcov term

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