Variable confounds with residual

[#1]

Hi,

l am attempting to analyse data for an interlab study with a mixed model, its a nested design with 5 variables, the dependant variable is titers, the structure of my analysis is as follows

Fixed Effect

Sample (30 of)

Random Effects

Sample*Lab (3 levels)
Sample*Day (3 Levels)
Sample*Run (2 Levels)
Replicate[Sample,Lab,Day,Run] (replicate has 2 levels)
Sample*Lab*Day

l get the error message that Replicate[Sample,Lab,Day,Run] confounds with residual, this is the first time i have encountered this message and i am not sure what its telling me, has anyone encountered this before and how did they overcome it??

Thanks

Mick

[#2]

Thought l would reply to my own post, i think i have over complicated things, l have retried with a simplified model

Sample  Fixed Effect

Sample*Lab & Random Lab Variance

Run[Sample,Lab,Day] & Random Run Variance

Sample*Lab*Day & Random Interaction between Lab and Day

Sample*Day & Random Day Variance

the R2 is great, no convergence issues, no confounding, and is easy to explain.

Any input would be appreciated

[#3]

The residual is automatically the lowest random effect. If residual of each observation is actually the same as the replicate level of random effect, then they are confounded. Leave replicate out of the model. The residual estimate is the replicate estimate.

[#4]

OK, got you

[#5]

Are you also including the main random effects of Lab, Run, and Day?

[#6]

l am Interpreting the interaction of sample*Lab, sample*Day, and Run[Sample,Lab,Day] as my main effects of Lab, Day and Run, so for lab, by including the random slopes and intercept l want to see the devaition for each lab from the average effect of sample, and this i will interepret as my main effect. 

[#7]

The deviation of each level from the mean is the simple main effect Sample, Lab, Day, and Run. Not the cross-products with Sample. The interaction terms capture how the effect of one variable depends on the level of another factor. So the term Day represents the average deviation of each day while the Sample*Day term represents how the average deviation of each day depends on the sample.

The nesting of levels like Run in Day, for example, might prevent you from estimating interaction effects.

[#8]

Thanks for your assistance @Mark_Bailey, its greatly appreciated, its interesting, and i guess it depends on the research question l want to answer and "how the average deviation of each day depends on the sample" is one of them, as the samples were sent from the one source so the variance should all be the same (foolish thinking ?) 

The data structure is per the attached excel file, X 3 labs, so the correct syntax for the mixed model to estimate each levels % proportion of variation explained should look like this, all as random effects

Lab

Day[Lab]

Run[Day, Lab]

if i then wanted to include sample to see the % proportion of variation explained by sample l would then include sample as Random effect, drop it as a fixed effect and the syntax would look like this, all as random effects

Sample

Lab
Day[Lab]
Run[Day, Lab]

As sample doesnt fit into the data structure is just a main effect as well as Lab???

This intuitively feels correct to me, but any advice would be appreciated.

Thanks very much

[#9]

l might be overstating the number of levels in the data, if i wished to include the lowest level of data, replicate these would be correlated and the same could be said of run, not so for day therefore

Sample

Lab

Day

Run[Lab, Day]

Replicate[Lab,Day,Run]

So Sample, Lab and Day as main effects makes sense, and due to the clustering in Replicate and Run, they would need to specified as nested??

Does this sound right?

[#10 · Accepted solution]

No.

Yes, the replicates are correlated, but the correlation is accounted for by the other terms in the model. I would not include explicitly replicate in model. It is implicitly included as the residual variance. The assumption of the usual linear regression model is that the residual variance is independent of the response level. Be sure to carefully perform residual analysis to verify this and other assumptions.

In other words, the structure you defined, including the nesting, is correct, but it is unnecessary to include the lowest level of the structure in the terms of the model.