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Analysis of linear mixed effect model

I have a hard time analyze my results from using the nlme package in R.

This is the scenario:

I got a repeated measures analysis (7 timepoints within each of the 20 subjects). I got three response variables, which might affect each other: Having a higher responsevariable1 (the length of a protein) might be correlated to responsevariable2 (the size of the gene expressing this protein). I have three factors (one is age, one is genotype and the third one is the application of a drug), which might interact (the drug for example might only work in old subjects and thus only there the protein and gene size increase).

As a summary:
factor of 2: factor1 (age: young or old)
factor of 2: factor2 (genotype: genotype1 or genotype2)
factor of 2: factor3 (drug: yes or no)
factor of 7: time (timepoint 1, 2, 3, 4, 5, 6 or 7)
subject: 1 to 20
formula: rv1*rv2*rv3 ~ time*f1*f2*f3 random = ~1|subject method = "ML"
rv = response variable and f = factor

Now i wanted to describe this interaction, which you can see in the picture:

How can i interpret the p-value 
time:factor1(6m) (p = 0.0437), 
time:factor3nvns (p = 0.0012) and 
time:factor16m:factor3nVNS (p = 0.0236)??

Does it mean that for example the three response variables change over time is dependent on factor 1 (= age)? Or what would be a better interpretation?

And how to interpret the time:factor1:factor3 positive p-value?

Thanks a lot in advance!

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I don't know what you expect but I don't think lme does what you expect. These are the same models:

lme(Sepal.Length * Sepal.Width ~ Petal.Length, random = ~1|Species, data = iris)

iris <- within(iris, y <- Sepal.Length * Sepal.Width)
lme(y ~ Petal.Length, random = ~1|Species, data = iris)

If you need a multivariate mixed model, you need different software.

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