Hi Eliot & Xavier.
I think that Xavier's suggestion is not a particularly good idea in this
case because random error will tend to depress phylogenetic signal. In
other words - random data error does not introduce random error in
phylogenetic signal, rather it biases phylogenetic signal towards 0.
A better approach is to incorporate error in the estimation of species
means directly - following Ives et al. (2007). This is implemented in
phylosig of the phytools package.
Your formula for the standard error of a proportion is indeed the
formula for the correct standard error given your data; however, it
raises the question of whether the assumed model (BM) is suitable for
your data (or perhaps this is what you are trying to find out). For
small samples (n<30), some people have recommended an "n+4" correction -
in which 2 successes and 2 failures are added during calculation of the
SE. If you are using an arcsine transformation, as is common for
proportion data, you need to be aware that your standard errors are on
the original scale! (I don't know the formula for standard errors on the
transformed scale.)
- Liam
Liam J. Revell, Assistant Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://blog.phytools.org
On 7/4/2013 3:36 AM, Xavier Prudent wrote:
Dear Eliot,
One way to cope with the uncertainty on the inputs in an analysis is vary
these inputs by some amount (like +- 1 standard deviation) and rerun your
analysis. The spread of the result tells you then how robust your analysis
is.
Pay attention that the inputs may be varied in an independent way if they
ARE independent, if they highly correlated you may prefer to vary them
simultaneously.
Hope that helps,
Regards,
Xavier
2013/7/4 Eliot Miller <eliotmil...@umsl.edu>
Hello all,
I have been trying to get something to work in a number of different
packages and with a number of different approaches today that I couldn't
get to run in a believable way. Before I spend another day on this, I was
wondering what people think about the idea in general.
I have a dataset of disease prevalence across ~100 species. There are ~2000
individuals total across the dataset, with >4 individuals per species.
Prevalence per individual is coded as 0 or 1. I am interested in the
phylogenetic signal of disease prevalence across the species. One approach
that works is to simply calculate prevalence as the species-specific mean,
i.e. if 3 individuals of 6 for a species had the disease, the prevalence
would be 3/6 = 0.5. Then one can use these values with e.g. phylosig() (I
arcsin sqrt transformed these proportions here). Like the few other
published tests of phylogenetic signal in disease prevalence, there is
little signal here. I could leave it at that, because in general there are
very low detections in this dataset and it's probably not ideally suited to
address this question anyhow.
That aside however, because not all individuals of a given species always
have the disease, I wanted to incorporate "measurement error". So, based on
the calculation for SE for binary data from the site:
http://www.researchgate.net/post/Can_standard_deviation_and_standard_error_be_calculated_for_a_binary_variable
,
I also calculated a species-specific SEs as the
sqrt(mean(prevalence)*((1-
mean(prevalence))/individuals)).
What do people think about this? It's hardly measurement error in the sense
we normally mean it. On the other hand, I think it would be neat if there
were some way to account for variation among individuals in prevalence, and
the influence this has on phylogenetic signal.
Cheers,
Eliot
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