The angular transformation
arcsin(square root of p)
is used more commonly than just the arcsine transformation
as far as I can tell.
The angular looks arbitrary if not bizarre, but emerges
out of a variance-stabilizing argument for the binomial,
as I recall.
For most purposes, you are probably better off with
logit. It is true that logit 0 and logit 1 are not
defined, but that doesn't trouble model-fitting software,
and in any case if you have data spikes at 0 or 1,
you probably need a more complicated model accounting
for bimodality or trimodality. The major argument
I think is that if and as you want to complicate a model
by adding more predictors, interactions, etc. you can
stay quite happily with the same Stata commands, whereas
an angular transformation would need more thought ad hoc.
The logit is a stronger transformation. Some graphical
experiments with
set obs 101
range p 0 1
gen angular = asin(sqrt(p))
gen logit = logit(p)
scatter angular logit
scatter angular logit p
etc. will give you some feel for what is going on. Only
in the far tails will logit behave in a qualitatively
different manner from angular.
Transformation isn't inescapable here. An alternative
is model the response as a beta distribution.
Nick
[email protected]
sstww
> To use proportion (percentage) data as a dependent
> variable in a regression, you would need to transform
> the data before doing regression for two purposes: to
> confine the projected value within 0-1 and to make the
> data distribution closer to normal. I have read a
> description on stata Q&A about using logistic
> transformation for proportion (percentage) data
> (y=ln(x/(1-x)) and it seems working fine. However,
> recently, I read about another highly recommendated
> transformation method for percentage data, arcsine
> transformation: (y=sine(x)^-1). Can anyone tell me
> about the pros and cons of these two methods for
> transforming proportion (percentage) data, and which
> one should be used for what situation?
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