Hi:

The split-plot analogy works for the most part; I think there's a little
more complexity within mouse than you've suggested thus far. Certainly, each
mouse represents a block, with treatment the whole plot treatment. The whole
plot part of the experiment seems clear.

My perception is that there are three replicate sets of trials within mouse;
within each replicate, a mouse traverses each of the three beams. I would
consider each replicate set of trials as a within subject block (i.e., at
the split-plot level). Within a replicate set, there are three subtrials,
one per beam, and here is where the confounding between beam and subtrial
occurs. The beams/subtrials are the within-subblock treatments, but the
complication is that the trials are run in systematic rather than random
order, so at this level you may want to consider serial correlation.

It appears to me this is an RCB experiment at the whole plot level and a
replicated RCB experiment at the split plot level.
The whole plot treatment is the treatment condition, whereas the split-plot
treatment factor within replicate set is the beams. This would mean that you
would need to construct a factor for replicate sets in your data frame.
Considering there are only three replicate sets, this should be a fixed
factor in your model.

Does that make sense to you?

HTH,
Dennis

On Wed, Sep 29, 2010 at 1:21 PM, Nicholas Lewin-Koh <nikko@hailmail.net>wrote:

> I was thinking of it more like a split-plot, where each mouse gets a
> treatment (whole plot),
> and within each mouse  there is a set of treatments, beams and the trials
> are the replicates. So yes I can see that the beams are fixed, and all
> mice are tested on the same beams ie crossed. Each mouse gets three
> trials on each beam, 9 trials altogether. I could average the trials on
> each beam
> by mouse, which would make the model easier to fit. So that would be
>
> lmer(latency.s.~ Treatment*BeamSize + (1|ID),data=dat,na.action=na.omit)
>
> But I would still like to understand how to fit the full model in R. My
> data is structured
> as follows:
>  dat[1:10,]
>            newID     falls      footslips Sex  GT Treatment       ID.
> BB.age
> 1  2596-1802.L.1     0         0 M     pos         V  2596-1802   17.1
> 2  2596-1802.L.2     0         0 M     pos         V  2596-1802   17.1
> 3  2596-1802.L.3     0         1 M     pos         V  2596-1802   17.1
> 4  2596-1802.M.1     0         1 M     pos        V  2596-1802   17.1
> 5  2596-1802.M.2     0         2 M     pos        V  2596-1802   17.1
> 6  2596-1802.M.3     0        13 M     pos       V  2596-1802   17.1
> 7  2596-1802.S.1     0        15 M     pos        V  2596-1802   17.1
> 8  2596-1802.S.2     0         7 M     pos         V  2596-1802   17.1
> 9  2596-1802.S.3     0         5 M     pos         V  2596-1802   17.1
> 10 2596-1804.L.1     0         0 F     pos         T  2596-1804   17.4
>    traverses.beam BeamSize latency.s. TrialNo
> 1         on toes        L                 11.40       1
> 2         on toes        L                 17.31       2
> 3         on toes        L                 21.87       3
> 4         on toes        M                37.81       1
> 5         on toes        M                21.84       2
> 6         on toes        M                25.96       3
> 7         on toes        S                 40.03       1
> 8         on toes        S                 68.72       2
> 9         on toes        S                 61.18       3
> 10                             L                26.03       1
>
> Nicholas
>  On Wed, 29 Sep 2010 11:46 -0700, "Dennis Murphy" <djmuser@gmail.com>
> wrote:
>
> Hi:
>
> On Wed, Sep 29, 2010 at 10:47 AM, Nicholas Lewin-Koh <nikko@hailmail.net>wrote:
>
> Hi Folks,
> I have an experiment with about 80 mice. Mice were randomized to
> treatment and control arms. The experiment consisted of 3 balance beams,
> Wide, Medium and Narrow. The mice were each given 3 trials on each
> balance beam (no not in random order). So the beam should get
> sequentially harder as it gets narrower. The responses were the latency,
> the time to cross the beam and the number of footslips as they crossed
> the beam. So I have beam nested in mouse and trial nested in beam. I
> tried the following model:
>
>
> The only way beam is nested within mouse is if different sets of beams
> were used for different mice. If all mice used the same set of beams, then
> mice and beams are crossed factors. Recall that factor B is nested within
> factor A if each level of B is associated with exactly one level of A.
> Conversely, A and B are (completely) crossed if each level of A occurs
> in combination with each level of B.
>
> As far as the trials go, each mouse gets three trials, so if trial were to
> be
> nested within anything, it would have to be the mouse. The key question
> is what is the experimental unit - the mouse or the beam?
>
> Now that I think about it, each trial uses a different beam, so beam and
> trial are confounded, no? If that's the case, the model gets much
> simpler...
>
> HTH,
> Dennis
>
>
>
> lmer(latency.s.~ Treatment + BeamSize +
> (1|ID./BeamSize/TrialNo),data=dat,na.action=na.omit)
> Error: length(f1) == length(f2) is not TRUE
> In addition: Warning messages:
> 1: In TrialNo:(BeamSize:ID.) :
>  numerical expression has 827 elements: only the first used
> 2: In TrialNo:(BeamSize:ID.) :
>  numerical expression has 827 elements: only the first use
>
> But I am not sure that this is the "right" way to specify this model.
> Ideally
> There are two questions. 1) Is the overall marginal latency lower in the
> treated animals, and 2) is the Beam size Slope
> for treated animals shallower than for untreated animals. I have looked
> at Park and Lee (2002) Statistics in Medicine 23:143-164, who give SAS
> code for a similar model. However, I am not very good at translating SAS
> to lme/lme4.
>
> Once I have this figured out, is it possible to jointly model foot slips
> and latency?
>
> Thanks for any input.
>
> Nicholas Lewin-Koh
> Senior Statistical Scientist
> Genentech
>
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>

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