[BioC] limma warning: Coefficients not estimable

Fri Feb 12 00:09:43 CET 2010

Dear Karl,

You are trying to do the impossible.

The essential thing to appreciate is that your experiment has two levels 
of variability, within and between animals.

You have two samples from each animal, tissues R and C.  Therefore tissue 
is your within-animal factor.  Your other two factors, Rperiod and Time 
are between-animal factors.

If you include Animal as a term in your design matrix formula, then you 
are comparing treatments within animal, and you can only test 
within-animal hypotheses.  Therefore you cannot include Pperiod or Time in 
your model.

You have two choices.  One is to do all your analysis within animal. 
Therefore you fit the model (~Tissue + Animal) and test only the tissue 
effect.  This fully adjusts for any Period or Time effects, but does not 
allow you to test for them.

If you wish to recover information about Period and Time from the 
between-animal error strata, then you need to treat Animal as a random 
effect.  This you do by:

    design <- model.matrix(~Tissue * Pperiod + Time)
    dupfit <- duplicateCorrelation(rma.pp, design, ndups=1, block=Animal)
    fit <- lmFit(rma.pp, design, correlation=dupfit$consensus,
           block=Animal)

remembering to check that dupfit$consensus is positive.

James has given you good advice about consulting a good biostatistician. 
(There are plenty of questions that could be asked.  Do you really need to 
adjust for a Time variable with 16 levels etc.)

Best wishes
Gordon

> Date: Wed, 10 Feb 2010 22:37:27 +0100
> From: Karl Brand <k.brand at erasmusmc.nl>
> To: "James W. MacDonald" <jmacdon at med.umich.edu>
> Cc: bioconductor at stat.math.ethz.ch
> Subject: Re: [BioC] limma warning: Coefficients not estimable
> Message-ID: <4B732717.5080708 at erasmusmc.nl>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
> Cheers Jim,
>
> On 2/10/2010 5:57 PM, James W. MacDonald wrote:
>> Hi Karl,
>>
>> Karl Brand wrote:
>>> Dear BioC,
>>>
>>> Using limma, when fitting the model:
>>> model.matrix(~Tissue * Pperiod + Time + Animal)
>>>
>>> I get this warning:
>>>> fit <- lmFit(rma.pp, design)
>>> Coefficients not estimable: Animal32 Animal33 Animal34 Animal35
>>> Animal36 Animal37 Animal38 Animal39 Animal40 Animal41 Animal42
>>> Animal43 Animal44 Animal45 Animal46 Animal47 Animal48
>>> Warning message:
>>> Partial NA coefficients for 45101 probe(s)
>>>
>>> In addition, the reuslting number or DE genes for my contrasts of
>>> interest (which are different than the 'not estimable' ones listed in
>>> teh warning above) are mcuh lower than expected; & furthermore, the
>>> contrast-coefficents (log2FCs) and simply wrong.
>>>
>>> When fitting a similar model, merely lacking the 'pairing' factor
>>> ("Animal"):
>>> model.matrix(~Tissue * Pperiod + Time)
>>>
>>> I don't get this error. My question:
>>>
>>> Is it me? Or am i attempting the impossible, ie., by including a
>>> factor for pairing (Animal) trying to fit more factors than my
>>> measurements can support and this is limma's way of telling me? Raw
>>> script and targets file below.
>>
>> You may be attempting the impossible, or you may just be doing something
>> incorrectly. You are certainly trying to estimate more parameters than
>> you have data with which to do so.
>
> Right. This helps me alot, some confirmation of what i can and cant
> achieve with my data.
>>
>> It looks like you have a fairly complex experimental design, so I would
>> recommend finding a local statistician who can help you with the analysis.
>>
>>>
>>> I really hope an experienced limma user can enlighten me on this, or
>>> point me to a resource suitable for a biologists level of understanding.
>>
>> Pretty much any basic linear modeling textbook would be helpful.
>> However, it looks like you might have a timecourse experiment with
>> perhaps repeated measures, which may require a non-trivial analysis
>> method. As a Biologist, you might have jumped into the deep end of the
>> pool, so finding somebody local to help is not a bad idea.
>
> Unfortunately learning to swim has been faster....along with your (and
> several other non-local statisticians) 'flotation aids'.
>
> sincere thanks for your thoughts,
>
> Karl
>
>>
>> Best,
>>
>> Jim
>>
>>
>>>
>>> Thanks in advance,
>>>
>>> Karl
>>>
>>>
>>>> targets <- read.delim("RNA_Targets.txt")
>>>
>>>> Tissue <- factor(targets$Tissue, levels = c("R", "C"))
>>>
>>>> Pperiod <- factor(targets$Pperiod, levels = c("E", "L", "S"))
>>>
>>>> Time <- factor(targets$Time, levels = c("1", "2", "3", "4",
>>> + "5", "6", "7", "8",
>>> + .... [TRUNCATED]
>>>
>>>> Animal <- factor(targets$Animal, levels = c("1", "2", "3", "4",
>>> + "5", "6", "7", "8",
>>> + .... [TRUNCATED]
>>>
>>>> design <- model.matrix(~Tissue * Pperiod + Time + Animal)
>>>
>>>> colnames(design)
>>> [1] "(Intercept)" "TissueC" "PperiodL" "PperiodS" "Time2" "Time3"
>>> "Time4" "Time5" "Time6" "Time7"
>>> [11] "Time8" "Time9" "Time10" "Time11" "Time12" "Time13" "Time14"
>>> "Time15" "Time16" "Animal2"
>>> [21] "Animal3" "Animal4" "Animal5" "Animal6" "Animal7" "Animal8"
>>> "Animal9" "Animal10" "Animal11" "Animal12"
>>> [31] "Animal13" "Animal14" "Animal15" "Animal16" "Animal17" "Animal18"
>>> "Animal19" "Animal20" "Animal21" "Animal22"
>>> [41] "Animal23" "Animal24" "Animal25" "Animal26" "Animal27" "Animal28"
>>> "Animal29" "Animal30" "Animal31" "Animal32"
>>> [51] "Animal33" "Animal34" "Animal35" "Animal36" "Animal37" "Animal38"
>>> "Animal39" "Animal40" "Animal41" "Animal42"
>>> [61] "Animal43" "Animal44" "Animal45" "Animal46" "Animal47" "Animal48"
>>> "TissueC:PperiodL" "TissueC:PperiodS"
>>>> source(.trPaths[5], echo=TRUE, max.deparse.length=150)
>>>
>>>> fit <- lmFit(rma.pp, design)
>>> Coefficients not estimable: Animal32 Animal33 Animal34 Animal35
>>> Animal36 Animal37 Animal38 Animal39 Animal40 Animal41 Animal42
>>> Animal43 Animal44 Animal45 Animal46 Animal47 Animal48
>>> Warning message:
>>> Partial NA coefficients for 45101 probe(s)
>>>>
>>>
>>>
>>> FileName Tissue Pperiod Time Animal
>>> 01-PPL3-sample02.CEL R S 1 1
>>> 02-PPL3-sample03.CEL C S 1 1
>>> 03-PPL5-sample02.CEL R S 2 2
>>> 04-PPL5-sample03.CEL C S 2 2
>>> 05-PPL3-sample04.CEL R S 3 3
>>> 06-PPL3-sample05.CEL C S 3 3
>>> 07-PPL5-sample04.CEL R S 4 4
>>> 08-PPL5-sample05.CEL C S 4 4
>>> 09-PPL3-sample06.CEL R S 5 5
>>> 10-PPL3-sample07.CEL C S 5 5
>>> 11-PPL5-sample06.CEL R S 6 6
>>> 12-PPL5-sample07.CEL C S 6 6
>>> 13-PPL3-sample08.CEL R S 7 7
>>> 14-PPL3-sample09.CEL C S 7 7
>>> 15-PPL5-sample08.CEL R S 8 8
>>> 16-PPL5-sample09.CEL C S 8 8
>>> 17-PPL3-sample10.CEL R S 9 9
>>> 18-PPL3-sample11.CEL C S 9 9
>>> 19-PPL5-sample10.CEL R S 10 10
>>> 20-PPL5-sample11.CEL C S 10 10
>>> 21-PPL3-sample12.CEL R S 11 11
>>> 22-PPL3-sample13.CEL C S 11 11
>>> 23-PPL5-sample12.CEL R S 12 12
>>> 24-PPL5-sample13.CEL C S 12 12
>>> 25-PPL3-sample14.CEL R S 13 13
>>> 26-PPL3-sample15.CEL C S 13 13
>>> 27-PPL5-sample14.CEL R S 14 14
>>> 28-PPL5-sample15.CEL C S 14 14
>>> 29-PPL3-sample16.CEL R S 15 15
>>> 30-PPL3-sample17.CEL C S 15 15
>>> 31-PPL5-sample16.CEL R S 16 16
>>> 32-PPL5-sample17.CEL C S 16 16
>>> 33-PPL1-sample02.CEL R E 1 17
>>> 34-PPL1-sample03.CEL C E 1 17
>>> 35-PPL6-sample02.CEL R E 2 18
>>> 36-PPL6-sample03.CEL C E 2 18
>>> 37-PPL1-sample04.CEL R E 3 19
>>> 38-PPL1-sample05.CEL C E 3 19
>>> 39-PPL6-sample04.CEL R E 4 20
>>> 40-PPL6-sample05.CEL C E 4 20
>>> 41-PPL1-sample06.CEL R E 5 21
>>> 42-PPL1-sample07.CEL C E 5 21
>>> 43-PPL6-sample06.CEL R E 6 22
>>> 44-PPL6-sample07.CEL C E 6 22
>>> 45-PPL1-sample08.CEL R E 7 23
>>> 46-PPL1-sample09.CEL C E 7 23
>>> 47-PPL6-sample08.CEL R E 8 24
>>> 48-PPL6-sample09.CEL C E 8 24
>>> 49-PPL1-sample10.CEL R E 9 25
>>> 50-PPL1-sample11.CEL C E 9 25
>>> 51-PPL6-sample10.CEL R E 10 26
>>> 52-PPL6-sample11.CEL C E 10 26
>>> 53-PPL1-sample12.CEL R E 11 27
>>> 54-PPL1-sample13.CEL C E 11 27
>>> 55-PPL6-sample12.CEL R E 12 28
>>> 56-PPL6-sample13.CEL C E 12 28
>>> 57-PPL1-sample14.CEL R E 13 29
>>> 58-PPL1-sample15.CEL C E 13 29
>>> 59-PPL6-sample14.CEL R E 14 30
>>> 60-PPL6-sample15.CEL C E 14 30
>>> 61-PPL1-sample16.CEL R E 15 31
>>> 62-PPL1-sample17.CEL C E 15 31
>>> 63-PPL6-sample16.CEL R E 16 32
>>> 64-PPL6-sample17.CEL C E 16 32
>>> 65-PPL2-sample02.CEL R L 1 33
>>> 66-PPL2-sample03.CEL C L 1 33
>>> 67-PPL4-sample02.CEL R L 2 34
>>> 68-PPL4-sample03.CEL C L 2 34
>>> 69-PPL2-sample04.CEL R L 3 35
>>> 70-PPL2-sample05.CEL C L 3 35
>>> 71-PPL4-sample04.CEL R L 4 36
>>> 72-PPL4-sample05.CEL C L 4 36
>>> 73-PPL2-sample06.CEL R L 5 37
>>> 74-PPL2-sample07.CEL C L 5 37
>>> 75-PPL4-sample06.CEL R L 6 38
>>> 76-PPL4-sample07.CEL C L 6 38
>>> 77-PPL2-sample08.CEL R L 7 39
>>> 78-PPL2-sample09.CEL C L 7 39
>>> 79-PPL4-sample08.CEL R L 8 40
>>> 80-PPL4-sample09.CEL C L 8 40
>>> 81-PPL2-sample10.CEL R L 9 41
>>> 82-PPL2-sample11.CEL C L 9 41
>>> 83-PPL4-sample10.CEL R L 10 42
>>> 84-PPL4-sample11.CEL C L 10 42
>>> 85-PPL2-sample12.CEL R L 11 43
>>> 86-PPL2-sample13.CEL C L 11 43
>>> 87-PPL4-sample12.CEL R L 12 44
>>> 88-PPL4-sample13.CEL C L 12 44
>>> 89-PPL2-sample14.CEL R L 13 45
>>> 90-PPL2-sample15.CEL C L 13 45
>>> 91-PPL4-sample14.CEL R L 14 46
>>> 92-PPL4-sample15.CEL C L 14 46
>>> 93-PPL2-sample16.CEL R L 15 47
>>> 94-PPL2-sample17.CEL C L 15 47
>>> 95-PPL4-sample16.CEL R L 16 48
>>> 96-PPL4-sample17.CEL C L 16 48
>>>
>> **********************************************************
>> Electronic Mail is not secure, may not be read every day, and should not
>> be used for urgent or sensitive issues
>
> -- 
> Karl Brand <k.brand at erasmusmc.nl>
> Department of Genetics
> Erasmus MC
> Dr Molewaterplein 50
> 3015 GE Rotterdam
> lab +31 (0)10 704 3409 fax +31 (0)10 704 4743 mob +31 (0)642 777 268

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