[R] Fwd: 2 way ANOVA with possible pseudoreplication

Andrew Dolman andydolman at gmail.com
Fri May 1 16:04:32 CEST 2009

Hi Natalie,

The fact that there's a non-linear relationship between frequency and power
does not matter if you treat power as a categorical variable rather than

So like Steve suggested above:

Using the lme4 package

lmer(power~freq*short+(1|animal), data=...)

would seem a good starting point. Make sure that frequency and shortening
are treated as factors.

Alternatively the nlme package

lme(power~freq*short, random=1|animal, data=...)


---------- Forwarded message ----------
From: Natalie Holt <fbsnch at leeds.ac.uk>
Date: 2009/5/1
Subject: Re: [R] 2 way ANOVA with possible pseudoreplication
To: Andrew Dolman <andydolman at gmail.com>

Hi Andy,

Thanks ever so much for your reply. I have attached the general layout of my
data with some more infomation on how it was collected. If you have any
ideas they would be much appreciated.

Many thanks,

 So I’ve measured muscle power output (continuous) for 3 different shapes of
contraction cycle (25, 50 and 75% shortening) at 3 different frequencies. So
I have 9 possible combinations. I have several replicates of each treatment.
I randomized the order in which I did all 9 treatments and did as many as
possible on one animal before moving on to the next. There are between 1 and
4 treatments on any one animal. There is only ever 1 replicate of any 1
treatment on a single animal.

I could do a mixed effect model however it is well established that the
power frequency relationship is non-liner with an optimum value at around 5.
I believe it is possible to do a non-linear mixed effects model. However I
do not have an equation describing this non-linear relationship. Is this
still possible to do??

Quoting Andrew Dolman <andydolman at gmail.com>:

 Hi Natalie,
> It sounds like a mixed model might be appropriate but it's not completely
> clear what your data are like. How many levels are there of each factor? Or
> is each factor just binary (treatment or no treatment)? What did you
> measure
> as the response? It's a good idea to post a sample of your data, or at
> least
> some dummy data with the same structure, so that we can see what it's like.
> It sounds like you don't have pseudo replication but you do have repeated
> measures (same animal used for more that 1 observation) and missing
> observations (not all treatment / treatment combinations measured for each
> animal). A mixed effects model with a random effect for animal might be
> appropriate but it would depend on how many animals you have, how many
> treatment combos there were and how many treatment combos each animal got
> on
> average. Also knowing the order treatments were given to each animal might
> help.
> Andy.
> andydolman at gmail.com
> 2009/4/29 nat_h <fbsnch at leeds.ac.uk>
>> Hi,
>> I have an experiment with 2 independant factors which I have been trying
>> to
>> analyse in R. The problem is that there are several data points recorded
>> on
>> the same animal. However, no combination of treatments  is repeated on the
>> same animal. All possible combinations of treatments are done in a random
>> order with as many points as possible being done on 1 animal before moving
>> onto the next.
>> The suggested way to remove pseudoreplication is to average the points
>> from
>> the same animal. However, as my measures on the same animal are of
>> different
>> treatment combinations so this makes no sense. It is also suggested that
>> as
>> I have random and fixed effects I should use a mixed effects model.
>> However,
>> given that my independant variables are factorial I am not sure how to
>> incorporate this. I would be very grateful for any advice on methods of
>> getting round this problem or whether I have sufficiently accounted from
>> my
>> none independant measures experimentally.
>> Many thanks,
>> Natalie
>> --
>> View this message in context:
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>> Sent from the R help mailing list archive at Nabble.com.
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