[R-sig-ME] How to handle measurement uncertainities with lmer

[Frömmel, Ulrike]

Dear list members,


a result set obtained from an automated video microscope contains
adhesion density values of a particular bacterial isolate per cell
surface area (germs/mm^2). Because the device determines this density
several times, the result set also contains an associated measurement
uncertainity, given as coefficient of variation Cv = sd/µ (standard deviation / mean).

In addition, each isolate was determined repeatedly on the same plate,
and also on different plates.

Independently from these experiments, the presence or absence of around 40
genes had been determined for each of the 316 bacterial isolates.

To investigate how much a particular gene influences bacterial adhesion,
the following lmer model was used:


   lmer(log(`Germs/mm^2`+1) ~ -1 + GeneA + GeneB + .... GeneZ + (1|Isolate) + (1|Plate), data=df)


> str(df):

'data.frame':   4101 obs. of  67 variables:
 $ Adhesion    : num  5.67 5.55 5.33 6.85 6.94 ...
 $ Isolate     : Factor w/ 316 levels "2164","2166",..: 183 183 183 12 12 107 107 107 246 76 ...
 $ Plate       : Factor w/ 59 levels "5637 BP01 m1",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ Germs/mm^2  : num  288 256 206 946 1031 ...
 $ Germs_cv    : num  48.49 5.51 4.56 9.07 6.78 ...
 $ GeneA       : Factor w/ 2 levels "-","+": 1 1 1 1 1 1 1 1 1 1 ...
 $ GeneB       : Factor w/ 2 levels "-","+": 1 1 1 1 1 1 1 1 1 1 ...
 $ GeneC       : Factor w/ 2 levels "-","+": 2 2 2 1 1 1 1 1 1 1 ...
 [...] <- ~ 40 Genes plus some other data)


The log transformation was applied because the residual vs. fitted diagram
strongly indicated heteroscedasticity. With the log transformation applied,
the density values are approximately normal distributed.


My questions are:

 1/ How to feed the uncertainity measures into lmer?

 2/ What would an effect of zero actually mean, considering that the
    data had to be log transformed in order to cope with
    heteroscedascity?

 3/ How can I do the inverse transform of the effects?



Best regards