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From |
Meng Zhao <mrzm_www@yahoo.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Interpretation of categorical independent variable |

Date |
Fri, 10 Sep 2010 02:36:34 -0700 (PDT) |

Very clear! Thanks. --- On Fri, 9/10/10, Maarten buis <maartenbuis@yahoo.co.uk> wrote: > From: Maarten buis <maartenbuis@yahoo.co.uk> > Subject: Re: st: Interpretation of categorical independent variable > To: statalist@hsphsun2.harvard.edu > Date: Friday, September 10, 2010, 9:23 AM > --- On Fri, 10/9/10, Meng Zhao > wrote: > > I use a three-category ID to predict a binomial > dependent > > variable. I included dummy variables for the first > two > > categories in the model. The result is: > > > > Odds Ratio > > p > > Category 1: 116.45 > > 0.000 > > Category 2: 17.76 > > 0.000 > > > > Is the following interpretion correct? > > > > 1.compared to category 3, being category 1 increases > the > > Odds Ratio by 116.45 for DV to happen (whatever it > > represents). > > > > 2.compared to category 3, being category 2 increases > the > > Odds Ratio by 17.76. > > > > 3.So category 1 has a stronger effect on DV than > category > > 2, and category 2 is stronger than category 3 > > Not quite, an odds ratio is a ratio of odds, while the way > you > formulated the results suggests that it is a difference. > So > the odds a the expected number of successes for every > failure, > and the odds ratio is the ratio by which this odds > changes. > > When interpreting the odds ratios, I find it helpful to > have > the baseline odds. Unfortunately, Stata supresses this by > default, but there is a trick you can use to get it > displayed, > which I learned from (Newson 2003). > > Consider the example below: > > *--------------- begin example ------------------ > sysuse auto, clear > recode rep78 1/2=3 > > gen byte baseline = 1 > > sum price if !missing(foreign, rep78), meanonly > gen c_price = price - r(mean) > > logit foreign i.rep78 c_price baseline, noconst or > *--------------- end example ---------------------- > (For more on examples I sent to the Statalist see: > http://www.maartenbuis.nl/example_faq ) > > The coefficient reported for baseline is the odds of > being foreign when one belongs to category 3 of rep78 > and one has an average price (I created c_price to be > 0 when the price is average). So for this type of car > we expect to find 0.08 foreign car for every domestic > car. This odds of being a foreing car changes by a > factor 12 (i.e. (12 - 1)*100% = 1100%) when the car > belongs to category 4, and by a factor 56 (i.e. 5500%) > when the car belongs to category 5. > > To get more feeling for what that means I often find it > useful to look at the odds directly. To get these > you can leave the baseline category in your model and > leave the constant (in our case the "variable" > baseline) out. In this case the coefficients of your > categories are now the odds of being a foreign car > within each category for an average priced car. > > So for category 3 we already knew that that was > 0.08 foreign cars for every domestic car. > > For category 4 cars the odds is 1 foreign car for every > domestic car (which is fortunately 12 times larger than > the odds for category 3 cars, so we are getting exactly > the same results as in our previous model). > > For category 5 cars we expect to find 4.5 foreign cars > for every domestic car (which is 56 times larger than > the odds for category 3 cars). > > *-------------- begin example ----------------- > logit foreign ibn.rep78 c_price, noconst or > di exp(_b[4.rep78])/exp(_b[3bn.rep78]) > di exp(_b[5.rep78])/exp(_b[3bn.rep78]) > *---------------- end example ------------------ > (For more on examples I sent to the Statalist see: > http://www.maartenbuis.nl/example_faq ) > > Hope this helps, > Maarten > > Roger Newson (2003) "Stata tip 1: The eform() option of > regress". The Stata Journal, 3(4): 445. > <http://www.stata-journal.com/article.html?article=st0054> > > -------------------------- > Maarten L. Buis > Institut fuer Soziologie > Universitaet Tuebingen > Wilhelmstrasse 36 > 72074 Tuebingen > Germany > > http://www.maartenbuis.nl > -------------------------- > > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: Interpretation of categorical independent variable***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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