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RE: st: RE: why is F statistic still missing even though there is no singleton dummy problem?
Thanks, Mark and Maarten! Your answers are really helpful!
Best regards,
Jian Zhang
> Jian Zhang,
>
> In fact, it is a singleton dummy problem. The key variables are var5
> and var6. You can drop var3 and
>
> reg var1 var5 var6, nocons robust
>
> gives you the same problem.
>
> The way this arises is as follows. var5 and var6 are collinear, with
> the exception of observation 5:
> Maarten
> +-------------+
> | var5 var6 |
> |-------------|
> 1. | 0 0 |
> 2. | 0 0 |
> 3. | -4 4 |
> 4. | 0 0 |
> 5. | 14 -7 |
> |-------------|
> 6. | 0 0 |
> 7. | 0 0 |
> 8. | 0 0 |
> 9. | -123 123 |
> 10. | 0 0 |
> |-------------|
> 11. | 0 0 |
> 12. | 0 0 |
> 13. | 0 0 |
> +-------------+
>
> After your regression (or the regression dropping var3), the residual
> for observation 5 is essentially zero:
>
> . reg var1 var5 var6, nocons robust
>
> <snip>
>
> . predict double e, resid
>
> . list e in 5
>
> +-----------+
> | e |
> |-----------|
> 5. | 1.927e-13 |
> +-----------+
>
> Recall that the robust var-cov matrix comes from the inverse of X'e*e'X,
> where e is the residual and X is the matrix of regressors. Thus each of
> the observations of var5 and var6 is getting weighted by the residual
> for that observation. But after weighting by e, var5 and var6 collinear
> because the residual for observation 5 is zero, and observation 5 was
> the only thing that stopped them from being collinear. The result is a
> var-cov matrix that is not full rank.
>
> To see that this is the same thing as the singleton dummy problem,
> create a new variable var567 which is a linear transformation of var5
> and var6:
>
> . gen var567=(var5+var6)/7
>
> . list var5 var6 var567
>
> +----------------------+
> | var5 var6 var567 |
> |----------------------|
> 1. | 0 0 0 |
> 2. | 0 0 0 |
> 3. | -4 4 0 |
> 4. | 0 0 0 |
> 5. | 14 -7 1 |
> |----------------------|
> 6. | 0 0 0 |
> 7. | 0 0 0 |
> 8. | 0 0 0 |
> 9. | -123 123 0 |
> 10. | 0 0 0 |
> |----------------------|
> 11. | 0 0 0 |
> 12. | 0 0 0 |
> 13. | 0 0 0 |
> +----------------------+
>
> This new variable is a singleton dummy. But since it's a linear
> transformation of var5 and var6, you can replace either var5 or var6 and
> you get the same regression, e.g.,
>
> . qui regress var1 var5 var6, nocons robust
>
> . di _b[var6]
> .84687073
>
> . di e(mss)
> 91.557676
>
> . qui regress var1 var5 var56, nocons robust
>
> . di _b[var56]
> .84687073
>
> . di e(mss)
> 91.557676
>
> --Mark
>
>
> Prof. Mark E. Schaffer
> Director
> Centre for Economic Reform and Transformation
> Department of Economics
> School of Management & Languages
> Heriot-Watt University
> Edinburgh EH14 4AS UK
> 44-131-451-3494 direct
> 44-131-451-3296 fax
> http://www.sml.hw.ac.uk/cert
>
>
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf Of Jian Zhang
> > Sent: Friday, August 18, 2006 12:51 AM
> > To: [email protected]
> > Subject: st: why is F statistic still missing even though
> > there is no singleton dummy problem?
> >
> > Dear Statalisters,
> >
> > I am running a ols regression on a small data set. The
> > reported F statistic is still mssing although the data set
> > doesn' have so-called singleton dummies. Is there anyone
> > knowing what is going on? Here are the data set and the
> > regression results. Many thanks!
> >
> >
> > . list var1 var3 var5 var6
> >
> > +---------------------------+
> > var1 var3 var5 var6
> > ---------------------------
> > 1. 1 789 0 0
> > 2. 3 45 0 0
> > 3. 5 2358 -4 4
> > 4. 4 65 0 0
> > 5. 5 12 14 -7
> > ---------------------------
> > 6. 453 12 0 0
> > 7. 6 4 0 0
> > 8. 45 2 0 0
> > 9. 8 3 -123 123
> > 10. 897 5 0 0
> > ---------------------------
> > 11. 43 87 0 0
> > 12. 43 56 0 0
> > 13. 4 25 0 0
> > +---------------------------+
> >
> >
> > reg var1 var3 var5 var6, robust nocons
> >
> > Linear regression Number of obs = 13
> > F( 2, 10) = .
> > Prob > F = .
> > R-squared = 0.0002
> > Root MSE = 318.67
> >
> >
> > Robust
> > var1 Coef. Std. Err. t P>t [95%
> > Conf. Interval]
> >
> > var3 .0046225 .0031 1.49 0.167 -.0022847
.0115297
> > var5 .7696625 .0060938 126.30 0.000
> > .7560848 .7832403
> > var6 .8329636 .007418 112.29 0.000
> > .8164353 .8494919
> >
> >
> >
> >
> >
> >
> >
> > Best regards,
> > Jian Zhang
> > *
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> >
> >
>
> *
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>
*
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