Herman Rubin wrote:
> 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.
>
Yes, there's enough independence that the counts are Poisson-like. Most people use
a random Poisson distribution when generating computer models for spike rates
(i.e. firing rates for neurons). However, some researchers note that the mean of
the distribution goes with the standard deviation and not with the variance (which
is why I'm caution and use the term Poisson-"like"). In any case, the data is
always binned which, from what I've been taught, is a good reason for using a
square root transform. Finally, I've compared the distribution with that of a
normal distribution-- the two are definitely different so the assumptions of
parametric tests will be violated without some sort of transformation (or, the use
of a non-parametric test).
>
> >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.
>
Could you provide any reference to this? We've used standardized regression
coefficients to determine the "importance" of the independent variable in the
regression. If I'm interpreting this correctly, then you're saying that if
variable A is more important at low spike rates and variable B is more important
at high spike rates, then there will be some bias. Can you specify what that bias
would be? I can certainly defend the analysis by showing that the data with and
without the square root transform results in the same conclusions, but I'd really
like to have a little more solid footing in the statistical theory of any biases I
may be introducing.
Thanks.
-Tony
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