Hi there!

My question is not necessarily specific to R, bit I still hope that I 
can find help here. I appreciate any suggestions; how to do/improve my 
analysis, what stuff to read more on etc...

I am interested in a dependent variable A. I measured A of 10 
individuals at 7 different levels of an explanatory variable B. The 
levels of B represent a magnitude of force, so in theory, are 
continuous. I however controlled the exact magnitude of the force and 
therefore assume it to have 7 discrete levels. The numerical difference 
between the levels is not equal either; the values are 0, 0.5, 1, 2, 4, 
6 and 8.
I also measured another continuous variable C of each of the 10 
individuals at each of the 7 different levels of B.
I am now interested in the following questions:

a) To what extend does B influence A?
b) To what extend does B influence C?
c) To what extend does C influence A?

My main problem is that I have several ideas of how to do this analysis, 
but not the sufficient knowledge to decide which is most appropriate. In 
a very first step, I simply did a linear regression with B~A and then 
looked at the residuals of that regression plotted against C. I would 
guess however, that there is a better way of doing a similar analysis 
that also allows to account for my repeated measures design and to 
remove the influence of B on C - maybe an ANCOVA, setting B as a factor 
and C  as a covariate:

A~as.factor(B)*C

As far as I understand it, I have to account for my repeated measures 
design, thus include an error term:

A~as.factor(B)*C+Error(Individual/as.factor(B))

Now this cannot be quite it, as my repeated measures is also affecting 
C. C is a continuous variable measured from each of the 10 individuals 
at each of the 7 levels of B. I am however entirely unsure about how to 
phrase the error term correctly. Would the corresponding syntax be

A~as.factor(B)*C+Error(Individual/C/as.factor(B))

or

A~as.factor(B)*C+Error(Individual/(C*as.factor(B)))

or maybe something completely different?

Then again, maybe that is the wrong way of modelling my data in the 
first place. I reckon one could argue, that I should model both A and C 
as dependent variables and do a MANOVA:

y <- cbind(A, C)
fit <- manova(y~B)

Here, however, I don't account for repeated measures and don't know how 
to extract information about the influence of C on A. Others might 
argue, that I have to do a mixed effect ANOVA, modelling C as random 
factor. Or maybe that is wrong, too, and I should in fact do a multiple 
linear regression, and don't model /B/ as a factor - but how to account 
for repeated measures here?
I read several replies to similar questions, but now am a bit confused 
about all the stuff I find people recommending in similar situations in 
the web. What is the correct and best way to do the analysis in my 
situation? I would really appreciate your help.

Best,
David


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