constraint

[Francis abayateye]

Hi All,

I am running a restricted regression but the constraint wouldn't work and I can't tell what I am missing between the lines
Below is what i have done so far

y = b0 + b1X1 + b2X2 + b3X3

constraint 1 b1+b2+b3 = 1

reg y X1 X2 X3, c(1)

How ever, it never worked. Something seems to be wrong with the constraint or I cannot have a constraint as such?

Thanks
Francis

[Clyde Schechter]

-regress- does not support constraints. You need -cnsreg- for that.

That said, showing model equations isn't really helpful. You need to show the actual code involved. For it is possible that there are other errors in the way you formulate the constraint, etc., so that even -cnsreg- might not work with it. For example b1 + b2 + b3 = 1 is neither syntactically correct nor meaningful to the -constraint- command. So you need to show exactly how you did it.

Another, often simpler approach, to constrained regressions is to use -test, coef- to impose the constraint. For example:

sysuse auto, clear
regress price mpg headroom trunk length
test trunk - length = 60, coef

Also saying something "never worked" isn't very helpful either--that could mean almost anything. Instead, show the output you got from Stata and, unless it's obvious, say how it differs from what you were expecting.

More generally, please read the entire Forum FAQ for excellent advice on how to post in ways that maximize your chances of getting timely, helpful responses.

[Richard Williams]

I agree with everything Clyde said. Taking his test suggestion a bit further, is this the sort of thing you want?

. webuse nhanes2f, clear

. reg health female black diabetes

      Source |       SS           df       MS      Number of obs   =    10,335
-------------+----------------------------------   F(3, 10331)     =    206.18
       Model |  849.323219         3   283.10774   Prob > F        =    0.0000
    Residual |  14185.6982    10,331  1.37311956   R-squared       =    0.0565
-------------+----------------------------------   Adj R-squared   =    0.0562
       Total |  15035.0214    10,334   1.4549082   Root MSE        =    1.1718

------------------------------------------------------------------------------
      health |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |  -.0658891   .0230867    -2.85   0.004    -.1111435   -.0206346
       black |  -.4661333   .0376353   -12.39   0.000    -.5399059   -.3923607
    diabetes |  -1.112933   .0538453   -20.67   0.000     -1.21848   -1.007385
       _cons |   3.551145   .0172967   205.31   0.000     3.517241     3.58505
------------------------------------------------------------------------------

. test female + black + diabetes = 1, coef

 ( 1)  female + black + diabetes = 1

       F(  1, 10331) = 1524.30
            Prob > F =    0.0000


Constrained coefficients

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |   .2240844   .0218594    10.25   0.000     .1812408    .2669281
       black |   .2880849   .0322991     8.92   0.000     .2247797      .35139
    diabetes |   .4878307   .0349035    13.98   0.000     .4194211    .5562403
       _cons |   3.242364   .0153826   210.78   0.000     3.212214    3.272513
------------------------------------------------------------------------------

Your original idea would work too but, as Clyde says, the constraint syntax is wrong and you need to cnsreg:

. constraint 1 female + black + diabetes = 1

. cnsreg health female black diabetes, c(1)

Constrained linear regression                   Number of obs     =     10,335
                                                Root MSE          =     1.2552

 ( 1)  female + black + diabetes = 1
------------------------------------------------------------------------------
      health |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      female |   .2240844   .0234154     9.57   0.000     .1781856    .2699832
       black |   .2880849   .0345983     8.33   0.000     .2202655    .3559043
    diabetes |   .4878307   .0373881    13.05   0.000     .4145429    .5611186
       _cons |   3.242364   .0164776   196.77   0.000     3.210065    3.274663
------------------------------------------------------------------------------

I think the differences in SEs has to do with whether you impose constraints before estimation or after.

[Francis abayateye]

Thanks so much everybody, I will cross check my syntax and post appropriately if my corrections don't work

[Richard Williams]

For good measure you can set this up as a lrtest of nested models:

webuse nhanes2f, clear
reg health female weight height
est store unconstrained
constraint 1 female + weight + height = 1
cnsreg health female weight height, c(1)
est store constrained
lrtest unconstrained constrained, force

Or,

webuse nhanes2f, clear
glm health female weight height
est store unconstrained
constraint 1 female + weight + height = 1
glm health female weight height, constraint(1)
est store constrained
lrtest unconstrained constrained

EDIT: I changed the variables in my different examples but hopefully you get the idea.

[Francis abayateye]

I'm really grateful Richard. I have really learnt a lot from all the helps so far.