# st: Multiple dummies - what does the constant measure?

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## st: Multiple dummies - what does the constant measure?

 Suppose you have two sets of categorical dummies: A1 A2 A3 A4 B1 B2 B3 B4 When you regress Y on them you must drop one category from each dummy to avoid the dummy variable trap, i.e., Y = a + A1 + A2 + A3 + B1 + B2 + B3 + e.   So Stata's regression output looks like this: A1     0.826 A2     0.224 A3     0.187 B1     0.376 B2     0.997 B3     0.736 _cons  0.556 Question:  What does the coefficient for the constant represent?  Is it the intercept of A4 plus the intercept for B4?  If so, how does one ascertain the intercepts for A4 and B4 separately? Does one pick different dummies to omit and run the regression again? Thx. Jimmy Verner Graduate Student University of Texas at Dallas Jimmy L. Verner, Jr. Verner & Brumley, P.C. 3131 TurtleCreek Blvd. Penthouse Suite Dallas, Texas  75219 214.526.5234 214.526.0957.fax [hidden email] www.vernerbrumley.com Board Certified, Family Law and Civil Trial Law, Texas Board of Legal Specialization Also admitted in New Mexico * *   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/
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## st: RE: Multiple dummies - what does the constant measure?

 It is the mean in the A4*B4 category. Remember, you have categories only, so speaking of this as an "intercept" is a little awkward. It is, in the sense that it is the value when A1=0 and A2=0 and A3=0 and B1=0 and B2=0 and B3=0, but that is just the mean when A4=1 and B4=1. Summarize Y when A4==1 and B4==1 and you'll see this is true:   summ Y if A4 & B4 So, what do you mean when you say you want the intercept for B4? This: ?   summ Y if B4 (the average ignoring A) Should be the same as the _cons from a regression ignoring A:   regress Y B1 B2 B3 Likewise for A4 (ignoring B)   summ Y if A4 Or _cons from:   regress Y A1 A2 A3 -----Original Message----- From: [hidden email] [mailto:[hidden email]] On Behalf Of Jimmy Verner Sent: Monday, December 01, 2008 5:21 PM To: [hidden email] Subject: st: Multiple dummies - what does the constant measure? Suppose you have two sets of categorical dummies: A1 A2 A3 A4 B1 B2 B3 B4 When you regress Y on them you must drop one category from each dummy to avoid the dummy variable trap, i.e., Y = a + A1 + A2 + A3 + B1 + B2 + B3 + e. So Stata's regression output looks like this: A1     0.826 A2     0.224 A3     0.187 B1     0.376 B2     0.997 B3     0.736 _cons  0.556 Question:  What does the coefficient for the constant represent?  Is it the intercept of A4 plus the intercept for B4?  If so, how does one ascertain the intercepts for A4 and B4 separately? Does one pick different dummies to omit and run the regression again? Thx. Jimmy Verner Graduate Student University of Texas at Dallas Jimmy L. Verner, Jr. Verner & Brumley, P.C. 3131 TurtleCreek Blvd. Penthouse Suite Dallas, Texas  75219 214.526.5234 214.526.0957.fax [hidden email] www.vernerbrumley.com Board Certified, Family Law and Civil Trial Law, Texas Board of Legal Specialization Also admitted in New Mexico * *   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/CONFIDENTIALITY  NOTE:  This e-mail message, including any attachment(s), contains information that may be confidential, protected by the attorney-client or other legal privileges, and/or proprietary non-public information. If you are not an intended recipient of this message or an authorized assistant to an intended recipient, please notify the sender by replying to this message and then delete it from your system. Use, dissemination, distribution, or reproduction of this message and/or any of its attachments (if any) by unintended recipients is not authorized and may be unlawful. * *   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/
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## Re: st: RE: Multiple dummies - what does the constant measure?

 Thx. for the feedback.  Actually, the model would have some interval   variables, too - I just oversimplified it. What I'm really trying to do is fixed effects regression with more   than one categorical variable.  I'm thinking it's not possible unless   I interact the categorical variables, in which case my database would   require 84 separate regressions (Category A (4) x Category B (21))   slopes. Jimmy Verner Graduate Student University of Texas at Dallas On Dec 1, 2008, at 4:49 PM, Steichen, Thomas J. wrote: > It is the mean in the A4*B4 category. Remember, you have categories   > only, so speaking of this as an "intercept" is a little awkward. It   > is, in the sense that it is the value when A1=0 and A2=0 and A3=0   > and B1=0 and B2=0 and B3=0, but that is just the mean when A4=1 and   > B4=1. > > Summarize Y when A4==1 and B4==1 and you'll see this is true: > >  summ Y if A4 & B4 > > So, what do you mean when you say you want the intercept for B4? > This: ? > >  summ Y if B4 (the average ignoring A) > > Should be the same as the _cons from a regression ignoring A: >  regress Y B1 B2 B3 > > Likewise for A4 (ignoring B) >  summ Y if A4 > Or _cons from: >  regress Y A1 A2 A3 > > -----Original Message----- > From: [hidden email] [mailto:[hidden email] > ] On Behalf Of Jimmy Verner > Sent: Monday, December 01, 2008 5:21 PM > To: [hidden email] > Subject: st: Multiple dummies - what does the constant measure? > > Suppose you have two sets of categorical dummies: > > A1 A2 A3 A4 > > B1 B2 B3 B4 > > When you regress Y on them you must drop one category from each   > dummy to avoid the dummy variable trap, i.e., Y = a + A1 + A2 + A3 +   > B1 + B2 + B3 + e. > > So Stata's regression output looks like this: > > A1     0.826 > A2     0.224 > A3     0.187 > B1     0.376 > B2     0.997 > B3     0.736 > _cons  0.556 > > Question:  What does the coefficient for the constant represent?  Is   > it the intercept of A4 plus the intercept for B4?  If so, how does   > one ascertain the intercepts for A4 and B4 separately? Does one pick   > different dummies to omit and run the regression again? > > Thx. > > Jimmy Verner > Graduate Student > University of Texas at Dallas > > Jimmy L. Verner, Jr. > Verner & Brumley, P.C. > 3131 TurtleCreek Blvd. > Penthouse Suite > Dallas, Texas  75219 > 214.526.5234 > 214.526.0957.fax > [hidden email] > www.vernerbrumley.com > > Board Certified, Family Law and Civil Trial Law, > Texas Board of Legal Specialization > Also admitted in New Mexico > * > *   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/> > CONFIDENTIALITY  NOTE:  This e-mail message, including any   > attachment(s), contains information that may be confidential,   > protected by the attorney-client or other legal privileges, and/or   > proprietary non-public information. If you are not an intended   > recipient of this message or an authorized assistant to an intended   > recipient, please notify the sender by replying to this message and   > then delete it from your system. Use, dissemination, distribution,   > or reproduction of this message and/or any of its attachments (if   > any) by unintended recipients is not authorized and may be unlawful. > > * > *   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/