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I have an experiment with 3 biological factors (dev, dev_stage; reg, brain_region; gen, gen_type) plus a batch factor (bat, batch). Unfortunately I have only rather superficial understanding of ANOVA or other statistics, so I'm not sure what is the right formula for my data (I'd consider all 3 biological factors plus their higher interactions with batch effect as an additive factor.). So I hope some luck with the right ANOVA formula here :)

As you can see below,

  1. dev could not be separated from bat;
  2. At dev P28, gen and bat are unbalanced.

So based on many discussions among others seen on the web (mainly here), I guess that bat should be treated as a random effect, and the formula is 

aov( x ~ dev * reg * gen, random = ~1|bat)

However, it seems that random = ~1|bat was not working since R returned a warning

Warning message:
In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
  extra arguments random are just disregarded.

Futhermore, I am not sure how to deal with the unbalance between gen and bat at dev P28...

Also, I am not sure if the gen and reg factors could/should be treated as repeated measures from each batch. Repeated measures are meant to be from the same subject, but to me subject and batch are similar to each other in the sense that they both "shift" the measures in a systematic way, although hidden factors are meant to be controlled within subject and are biasing among batches. But I'm not sure if it's reasonable to compare different levels of gen within bat. Anyway, I tried this formula: 

aov( x ~ dev*reg*gen + Error( bat / (reg*gen)))

Then dev became much less significant compared to that of aov( x ~ dev * reg * gen, random = ~1|bat) or aov( x ~ dev * reg * gen + bat), and affected less genes than did reg.

But according to PCA plot, dev is the strongest factor, much stronger than bat, and reg is the second. Also I don't know how to do multiple comparisons in this case, since Tuckey's HSD could not handle the returned values of aov when Error is used.

..........brain_region.gen_type.dev_stage....batch
.anteromedial_thalamus........1.....E15.5.11/17/06
.anteromedial_thalamus.......22.....E15.5.11/17/06
........frontal_cortex........1.....E15.5.11/17/06
........frontal_cortex.......22.....E15.5.11/17/06
..somatosensory_cortex........1.....E15.5.11/17/06
..somatosensory_cortex.......22.....E15.5.11/17/06
..ventrobasal_thalamus........1.....E15.5.11/17/06
..ventrobasal_thalamus.......22.....E15.5.11/17/06
.anteromedial_thalamus........1.....E15.5..5/10/07
.anteromedial_thalamus.......22.....E15.5..5/10/07
........frontal_cortex........1.....E15.5..5/10/07
........frontal_cortex.......22.....E15.5..5/10/07
..somatosensory_cortex........1.....E15.5..5/10/07
..somatosensory_cortex.......22.....E15.5..5/10/07
..ventrobasal_thalamus........1.....E15.5..5/10/07
..ventrobasal_thalamus.......22.....E15.5..5/10/07
.anteromedial_thalamus........1.....E15.5...6/1/07
.anteromedial_thalamus.......22.....E15.5...6/1/07
........frontal_cortex........1.....E15.5...6/1/07
........frontal_cortex.......22.....E15.5...6/1/07
..somatosensory_cortex........1.....E15.5...6/1/07
..somatosensory_cortex.......22.....E15.5...6/1/07
..ventrobasal_thalamus........1.....E15.5...6/1/07
..ventrobasal_thalamus.......22.....E15.5...6/1/07
.anteromedial_thalamus........1.......P28.10/19/07
.anteromedial_thalamus.......22.......P28.10/19/07
.anteromedial_thalamus.......22.......P28.10/19/07
........frontal_cortex........1.......P28.10/19/07
........frontal_cortex.......22.......P28.10/19/07
........frontal_cortex.......22.......P28.10/19/07
..somatosensory_cortex........1.......P28.10/19/07
..somatosensory_cortex.......22.......P28.10/19/07
..somatosensory_cortex.......22.......P28.10/19/07
..ventrobasal_thalamus........1.......P28.10/19/07
..ventrobasal_thalamus.......22.......P28.10/19/07
..ventrobasal_thalamus.......22.......P28.10/19/07
.anteromedial_thalamus........1.......P28.11/30/07
.anteromedial_thalamus........1.......P28.11/30/07
.anteromedial_thalamus.......22.......P28.11/30/07
........frontal_cortex........1.......P28.11/30/07
........frontal_cortex........1.......P28.11/30/07
........frontal_cortex.......22.......P28.11/30/07
..somatosensory_cortex........1.......P28.11/30/07
..somatosensory_cortex........1.......P28.11/30/07
..somatosensory_cortex.......22.......P28.11/30/07
..ventrobasal_thalamus........1.......P28.11/30/07
..ventrobasal_thalamus........1.......P28.11/30/07
..ventrobasal_thalamus.......22.......P28.11/30/07.

I'm looking forward to your help!

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  • 1
    $\begingroup$ You can use Markdown syntax to format your post. There's a lot of stuff here: ANOVA with random effects, PCA, post-hoc comparisons; it would help if you could specify your working hypotheses and give some background on your research study. (Ah, and the title is rather uninformative but I have no idea on how to make it more attractive -- it should certainly depend on the aforementioned points.) $\endgroup$
    – chl
    Commented Sep 10, 2011 at 10:46
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    $\begingroup$ I think your problem is very solvable, but we need to understand your data better. Let's see if I understood you correctly: i. there are three factors (trt) of interest -- development, region, and genotype. ii. there is a batch effect also, about which you don't care. iii. I still don't understand the design (confusing to me at least). Could you tell us in plain English what is your experiment, how do you go about measuring the variables of interest, and how does batch effect creep in. Given this info, modeling will follow. $\endgroup$
    – suncoolsu
    Commented Sep 10, 2011 at 18:36

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