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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: z-score as a dependent variable in a linear regression |

Date |
Thu, 15 Nov 2007 07:26:37 +0000 (GMT) |

--- Dan Weitzenfeld <dan.weitzenfeld@emsense.com> wrote: > I've reviewed the assumptions of OLS, etc., and I can't find a > glaring objection to using a z-score as a dependent variable in a > linear regression. However, it feels strange, especially because the > units of a z-score are not uniform, in that the difference in > probability between a z-scores 0 and .5 is not the same as the > difference in probability beween z-scores .5 and 1. In other words, > I feel that by using the z-score, I am not giving adequate weight to > observations with very high and very low z-scores. This sounds to me like a very common misunderstanding. Turning a variable into a z-scores does not make that variable normally distributed. It is a linear transformations of your variable, nothing more. So each value retains the same relative weight as in your original variable. You are only changing the way you interpret the result but your are not changing any of the underlying information. The way to realize that is to see that you can get those standardized estimates using a normal regression on your unstandardized variables without estimating a new model, as you can see in the example below: *-------------------- begin example -------------------- sysuse auto, clear reg pri mpg sum pri local standardized = _b[mpg]/r(sd) sum mpg local standardized = `standardized'*r(sd) di `standardized' reg pri mpg, beta sum pri gen double z_pri = (pri-r(mean))/r(sd) sum mpg gen double z_mpg = (mpg-r(mean))/r(sd) reg z_pri z_mpg *---------------------- end example ----------------------- (For more on how to use examples I sent to the Statalist, see http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html ) -- Maarten ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- ___________________________________________________________ Yahoo! Answers - Got a question? Someone out there knows the answer. Try it now. http://uk.answers.yahoo.com/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: z-score as a dependent variable in a linear regression***From:*"Dan Weitzenfeld" <dan.weitzenfeld@emsense.com>

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