Re: Beta distribution
- From: David Winsemius <doe_snot@xxxxxxxxxxx>
- Date: Wed, 31 Oct 2007 12:00:05 -0500
"doherjo1@xxxxxxxxx" <doherjo1@xxxxxxxxx> wrote in
news:1193840038.646278.316380@xxxxxxxxxxxxxxxxxxxxxxxxxxx:
How do I approach regression if my raw data exhibits the profile of a
beta or gamma distribution. For example, if I have sales data that is
bounded on the left tail at zero and has a heavy right tail. I
usually use a log-transformation, but is there an approach using OLSR
that incorporates these distribution vs. the normal?
If you are making decisions based on the "raw data" then you missed the key
point in class about the normality assumption applying only to the
residuals, ... rather than to the marginal distribution of the dependent
variable. You should do the analysis without any transformation (ordinary
least squares) and then examine the residuals. Only then would you have a
basis for choosing another analysis. The estimates will be much easier to
interpret if you avoid unnecessary transformations.
The estimates from the OLS method will still be unbiased, but there may be
errors in the inferential tests (confidence intervals or F tests) that need
to be assessed by other methods. Most of the analytic/inferential results
will be resistant to skewness (in the residuals), especially if they can
reasonably be expected to be only right-tailed. The usual statement is that
transformations (log or rank) may be needed to avoid inferential errors
brought on by heteroscedasticity. (Neither sort of transformation will help
if some regions of the predictor space have left skewed and other right
skewed dependent variables.)
--
David Winsemius
.
- References:
- Beta distribution
- From: doherjo1@xxxxxxxxx
- Beta distribution
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