In article <[EMAIL PROTECTED]>, G. Anthony Reina <[EMAIL PROTECTED]> wrote:
>We use multiple linear regression to perform our analyses. Because we
>work with binned data (discharge frequency of a neuron) which follow a
>non-normal (Poisson) distribution, we typically use the square root
>transform on the dependent variable (discharge rate of the neuron).
>(Actually, the transformation is sqrt(spike rate + 3/8) )
Is there enough independence that the counts should be Poisson?
If so, the square root transformation does stabilize the
variance, but it introduces a bias. In addition, any
non-linear transformation destroys the linearity of the
model.
The most important criterion for a regression or similar
procedure is the form of the model; for a linear regression,
with any number of independent variables, the linearity is
most important. You COULD run a non-linear regression,
using the square root of a linear combination of independent
variables, or you could use a Poisson model and maximum
likelihood, or others.
>I've been trying to show that some independent variables account for
>more of the variance explained in the dependent variable. However, some
>researchers in my field argue that the square root transform could
>artificially bias my results so that some independent variable account
>for more of the variance than they really should. I don't see how this
>could be from a theoretical level. Plus, I've run the multiple
>regression without the transform and seen only about a 5% difference
>(not much).
It certainly can. If one variable is more important at the low
end, and another at the high end, this will happen.
>Does anybody know if these criticisms have any theoretical merit? I
>can't see how this can be so. I thought that the square-root transform
>was a pretty sound way of reducing your chance of biasing the analysis
>if the data is non-normal (which most parametric tests require).
Your tests are only approximate, anyhow. The most important
thing is the form of the model; use your theoretical knowledge
to decide which ones to use. It usually does not matter how
good the tests are if the model is not accurate, and whatever
null hypothesis you test is going to be false, anyhow.
It is up to you to decide the meaning of the form of the model,
without regard to statistical testing.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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