[R] Log transformed values and contrasts in LME

[Francisco J. Zagmutt Vergara]

Dear All

This is probably a very basic question for this list but I just wanted to 
make sure that I am doing things right:

I have an LME model with 4 categorical variables and 2 continuous variables 
(analysis of covariance model).  I had to use a log transformation on the 
data to achieve normality (log(x)-.1) and then I used contrast treatment to 
compare differences between a baseline level and the other level of the same 
categorical variable (as far as I understand R picks automatically the level 
with the smaller marginal mean to make these comparisons).  When I want to 
interpret my coefficients in terms of the original (non-transformed data) is 
not as simple as using:

>exp(beta)-.1

since (I believe) the hypotheses testing with the contrasts is 
log(Beta1)-Log(beta2)=0

So I though that a way to go around this is to remove the intercept from the 
original model to get a "cell-means" model which would  basically give me 
the average log transformed value of the outcome variable for each category:

log(beta1) +log(beta2)+...log(betan)

and then transform those values to the original data form and subtract the 
means to obtain an estimate of the difference between the means that I 
tested with the contrast:

>b1<-exp(beta) -.1
>b2<-exp(beta)-.1
>b1-b2

Is this conceptually right? I would not be making any hypothesis testing 
with the new model, just getting an estimate of the actual difference 
between the level means so I think that his could be a valid approach.  I 
would still report the test statistics and significance values for the 
contrasts from the original model but just would include the estimation of 
the means from the second model.  Am I in the right path?


Many thanks for your help!!

Francisco

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