Mixed design nightmare I hope you can steer me in the right direction.
I'm helping a colleague analysing a dataset that consists of:

*

*one dependent variable (value) measured 3 times (observation) by 3 people (evaluator) on the 2 sides (side - right/left) of an individual (~150 individuals)


*several independent variables: one continuous (age), and 2 discrete (sex, ancestry).


*the data also has NA has some evaluators skipped over a few individuals in one or more of the observation points.

His main questions concern the reproducibility of measurements and effect of independent variables:

*

*for reproducibility I used intraclass correlation coefficients with relative success;

*to look at the effect of independent variables, I would normally use some form of a linear model (ANOVA/ANCOVA).

However, I'm worried about the lack of independence between observations, basically the first assumption of a lot of these tests. I tried looking at mixed models (e.g. using 1 between subjects factor (sex) and 2 within subjects factors (evaluator & observation) ), but I couldn't find good examples of this application (particularly using R), and mixed models seem to focus on evaluating the impact of these within subject factors, when in fact I mostly just want to control for these and focus on the effect of the independent factors.
Questions: (1) Could I assume independence? (2) What would be an appropriate design model (@RobertLong 's correction)? (3 - slightly off topic) Any R pointers are welcome.

Update
Following Robert Long's answer, I'm now working with a mixed model that looks like this lme(value ~  sex * side + age + ancestry + evaluator, data = L, random = ~1|individual, method = "ML", na.action = na.exclude) (using Andy Field's book)
However, now I have more questions:
(1) How to follow up (especially considering that I want to understand the effect of sex while controlling for the effect of ´evaluator´. Would contrast be a good option?
(2) Reading on this, I realised that lack of independence will also be an issue for the ICC I calculated. Could I calculate them from the mixed model? (Based on this: Computing repeatability of effects from an lmer model)


(1) Could I assume independence?

No, because you have repeated measurements. Observations within one individual are more likely to be similar to other observations within the same individual than observations on other individuals. One way to handle this is to fit random intercepts for individuals in a mixed model. It also seems that evaluator is crossed with individual, but you don't have enough evaluators to justify fitting random intercepts for that, so you will need to fit fixed effects for evaluator.

(2) What would be an appropriate design?

Perhaps you mean model, not design ? The (study) design is the experiment itself which apparently has already been done. As for the model, a mixed model may be appropriate.

3 - (slightly off topic) Any R pointers are welcome.

I would start with a model such as:
value ~ age + sex + ancestry + side + evaluator + (1 | individual)

You could use the lmer function in the lme4 package for that.
