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From |
Ana Gabriela Guerrero Serdan <ag_guerreroserdan@yahoo.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Fri, 16 Nov 2007 10:08:36 -0800 (PST) |

Hm.... Sorry to jump into this but I dont see whay Dan cannot use z-scores as a dependent variable, even if z-scores are standarized. Wouldnt it depend on which are the independent variables used? Gaby --- Austin Nichols <austinnichols@gmail.com> wrote: > Maarten et al.-- > The issue is that Dan is standardizing using > individual variation, I > think, so these models are not equivalent to > standardized > coefficients, and the interpretation is a bit > odd--something like, > what is the effect of X on y relative to past > variability in y at the > individual level, rather than what is the effect of > a one-unit change > in X on y measured in SD units of y? This example > measuring the > "return to experience" may clarify: > > webuse psidextract, clear > g w=lw if t<4 > egen sdw=sd(w), by(id) > egen mw=mean(w), by(id) > g iswage=(lw-mw)/sdw if t>3 > la var isw "Indiv stdized ln wage" > keep if if t>3 > * Transformed data > reg iswage exp > xtreg isw exp, fe > * Transformed coefs give dy/dx in SD units > su lw if e(sample) > loc sd=r(sd) > reg lw exp > di _b[exp]/`sd' > xtreg lw exp, fe > di _b[exp]/`sd' > * Alternative: downweight high Var cases > reg lw exp [aw=sdw] > xtreg lw exp [aw=sdw], fe > > All of the above have different interpretations. > Does another year of > experience on the job increase wages by a constant > percent, in > absolute terms or relative to individuals' past > wages, or does it > increase wages by some constant shift in the > individual's own > distribution of past wages? Or do we just get less > information about > the avg percent increase in wages due to another > year of experience on > the job from the experiences of individuals who have > higher > variability in their past earnings histories? > > On 11/15/07, Maarten buis <maartenbuis@yahoo.co.uk> > wrote: > > --- 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) > * > * 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/ > Gaby Guerrero Serdan Deparment of Economics Royal Holloway, University of London TW20 OEX Egham, Surrey England, UK http://www.rhul.ac.uk/economics/About-Us/postgrads.html http://www.flickr.com/photos/49939890@N00/ Tel: +44 7912657259 ____________________________________________________________________________________ Get easy, one-click access to your favorites. Make Yahoo! your homepage. http://www.yahoo.com/r/hs * * 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/

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