On Mon, 22 May 2000 11:49:44 -0700, "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) )
>
> 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. < ...>
(Herman has made a try; now I will.)
By definition, "variance" has to do with squared deviations around a
mean of what you are predicting.
You might do a transformation and have it point-to approximately the
same "mean" -- but it has to change the elements that you are totaling
together as "deviations". I think that it is in Mosteller and Tukey,
where you can read about the Box-Cox transformations, and how to use
them so that they *tend to* keep the same apparent total as
sum-of-squares; but it explicitly has to happen, that the components
are changing which make up that total.
The effectiveness of a transformation has to do with how much it
squeezes together one set of numbers, and (relative to that) how much
it spreads apart some others. Changing the weights, and changing the
relative variances: that is what transformations are for.
> Plus, I've run the multiple
> regression without the transform and seen only about a 5% difference
> (not much).
- damned if I know what that sentence means. You mean, like,
accounting for 99% of the variance, instead of 94%? -- that means "5%"
by two different criteria.
> 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).
Well, "biasing" is a thoroughly confusing term. And the requirement
of normality for tests is somewhat over-rated. When you test it two
or three different ways, do you always get the same result? -- if that
works out, then you can point that out, and select the analysis that
you want for which-ever-comparisons.
Are you concerned with tests, or with models where you can compare
"variance"? Personally, if I see counts, I often assume that the
linearity is going to be measured with the square root of the counts.
Also, the variability, or the interesting "variance."
But if you are trying to compare "variance in the dependent variable"
when that variable is measured in Counts, then you HAVE to measure it
in Counts.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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