Re: Ratio as a response variable

On Thu, 09 Aug 2007 11:47:32 EDT, jonesor <owen.jones@xxxxxxxxxxxxxx>
wrote:

Hi,

Can someone please outline what the problems are with using a ratio as a response variable in a regression model.

I know there are problems with using a ratio who's denominator is also an explanatory variable but what are the issues if the denominator is NOT among the explanatory variables?


A lot of ratios are used as responses, with no problem at all,
when the denominators are large positive numbers within a
small range (for example, Body-Mass Index, for adults). Or
when the subsequent ratios are consistent because the
numerators and denominators are highly correlated ("fuel
economy" measured in mpg or whatever). In fact, using
certain ratios is almost mandatory for 'standardizing' some
outcomes to a per-mile or per-person (or whatever) basis.

The problems arise when the values of the denominator
have a large multiplicative range, independent of the
numerator.

These problems fall under "scaling". The regression can
inherit all the bad properties -- Heterogeneity of variance
across the range, non-linearity of associations (probably),
non-normality of residuals.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.