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# st: How to Compare the Coefficients of Specific Variable where Each Group is Estimated Separately

 From Yuval Arbel To statalist Subject st: How to Compare the Coefficients of Specific Variable where Each Group is Estimated Separately Date Tue, 18 Dec 2012 22:16:33 -0800

```Dear Statalisters,

I am running a -stcox- model on two groups, where my particular
interest is to compare the coefficients of the variable red_runmax1

The difference between the two coefficients is -0.0246686 and I would
like to show that this difference is significant

Below I'm attaching the full output

I tried to run the hausman test, and it worked fine.The problem is
that I need -suest- instead, and -suest- does not work with -stcox-

I also tried: "test
[eq1:_b[red_runmax1_down]]==[eq3:_b[red_runmax1_down]]" but I got an
error message.

Finally I tried to run the test on a model with interactions with the
dummy. The problem is that I don't get the estimated -0.0246686
difference of coefficients.

Any ideas will be highly appreciated.

P.S. If i don't have a choice I suppose I can construct the calculated
statistic manually. The question is whether stata has a shortcut

Here is the full output starting from the relevant part::

. stcox group2 runmax1_zero runmax1_down red_runmax1_down runmax1_zero2 runmax1
> _down2 red_runmax1_down2 if (group==0 | (group==1
> & group2==1)) & ref~=.,nohr

failure _d:  fail == 1
analysis time _t:  time_index
id:  appt

Iteration 0:   log likelihood = -52961.884
Iteration 1:   log likelihood = -50674.015
Iteration 2:   log likelihood =  -50439.54
Iteration 3:   log likelihood = -50404.933
Iteration 4:   log likelihood = -50402.516
Iteration 5:   log likelihood = -50402.474
Iteration 6:   log likelihood = -50402.474
Iteration 7:   log likelihood = -50402.474
Refining estimates:
Iteration 0:   log likelihood = -50402.474

Cox regression -- Breslow method for ties

No. of subjects =         6738                     Number of obs   =    308083
No. of failures =         6738
Time at risk    =       308491
LR chi2(7)      =   5118.82
Log likelihood  =   -50402.474                     Prob > chi2     =    0.0000

-------------------------------------------------------------------------------
> ----
_t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Inter
> val]
------------------+------------------------------------------------------------
> ----
group2 |  -1.754371   .3654717    -4.80   0.000    -2.470682    -1.0
> 3806
runmax1_zero |   .0274737   .0006838    40.18   0.000     .0261334     .02
> 8814
runmax1_down |    .029343   .0010589    27.71   0.000     .0272677    .031
> 4184
red_runmax1_down |  -.0630043   .0029347   -21.47   0.000    -.0687562   -.057
> 2524
runmax1_zero2 |    .011897   .0042914     2.77   0.006      .003486     .02
> 0308
runmax1_down2 |   .0105009   .0049942     2.10   0.035     .0007125    .020
> 2892
red_runmax1_down2 |   .0027031   .0165674     0.16   0.870    -.0297684    .035
> 1746
-------------------------------------------------------------------------------
> ----

. //outreg2 using "D:\kingston\public_housing\loss_aversion4.xls", replace tsta
> t asterisk(tstat) addstat(subjects, e(N_sub), fail
> ures, e(N_fail), Chi Square Statistics, e(chi2),log likelihood, e(ll) )
. nlcom _b[red_runmax1_down]+_b[red_runmax1_down2]

_nl_1:  _b[red_runmax1_down]+_b[red_runmax1_down2]

------------------------------------------------------------------------------
_t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_nl_1 |  -.0603012   .0163346    -3.69   0.000    -.0923165    -.028286
------------------------------------------------------------------------------

. //gen
. stcox runmax1_zero runmax1_down red_runmax1_down if (group==0 | (group==1 & g
> roup2==1)) & ref~=.,nohr

failure _d:  fail == 1
analysis time _t:  time_index
id:  appt

Iteration 0:   log likelihood = -52961.884
Iteration 1:   log likelihood = -50735.416
Iteration 2:   log likelihood = -50517.039
Iteration 3:   log likelihood = -50486.867
Iteration 4:   log likelihood = -50485.033
Iteration 5:   log likelihood = -50485.023
Refining estimates:
Iteration 0:   log likelihood = -50485.023

Cox regression -- Breslow method for ties

No. of subjects =         6738                     Number of obs   =    308083
No. of failures =         6738
Time at risk    =       308491
LR chi2(3)      =   4953.72
Log likelihood  =   -50485.023                     Prob > chi2     =    0.0000

-------------------------------------------------------------------------------
> ---
_t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interv
> al]
-----------------+-------------------------------------------------------------
> ---
runmax1_zero |   .0278138   .0006674    41.67   0.000     .0265057    .0291
> 219
runmax1_down |   .0293033   .0010319    28.40   0.000     .0272808    .0313
> 257
red_runmax1_down |  -.0626103    .002899   -21.60   0.000    -.0682921   -.0569
> 284
-------------------------------------------------------------------------------
> ---

. outreg2 using "D:\kingston\public_housing\loss_aversion4.xls", replace tstat
> asterisk(tstat) addstat(subjects, e(N_sub), failur
> es, e(N_fail), Chi Square Statistics, e(chi2),log likelihood, e(ll) )
D:\kingston\public_housing\loss_aversion4.xls
dir : seeout

. estimates store eq1

.
. stcox runmax1_zero runmax1_down red_runmax1_down if group==1 & ref~=.,nohr

failure _d:  fail == 1
analysis time _t:  time_index
id:  appt

Iteration 0:   log likelihood = -1485.5571
Iteration 1:   log likelihood = -1371.0364
Iteration 2:   log likelihood = -1369.2168
Iteration 3:   log likelihood = -1369.1651
Iteration 4:   log likelihood =  -1369.165
Refining estimates:
Iteration 0:   log likelihood =  -1369.165

Cox regression -- Breslow method for ties

No. of subjects =          310                     Number of obs   =     23971
No. of failures =          310
Time at risk    =        23995
LR chi2(3)      =    232.78
Log likelihood  =    -1369.165                     Prob > chi2     =    0.0000

-------------------------------------------------------------------------------
> ---
_t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interv
> al]
-----------------+-------------------------------------------------------------
> ---
runmax1_zero |   .0309905   .0031046     9.98   0.000     .0249056    .0370
> 755
runmax1_down |   .0225985   .0041437     5.45   0.000     .0144771    .0307
> 199
red_runmax1_down |  -.0412099   .0112469    -3.66   0.000    -.0632535   -.0191
> 663
-------------------------------------------------------------------------------
> ---

. estimates store eq2

. outreg2 using "D:\kingston\public_housing\loss_aversion4.xls", tstat asterisk
> (tstat) addstat(subjects, e(N_sub), failures, e(N_
> fail), Chi Square Statistics, e(chi2),log likelihood, e(ll) )
D:\kingston\public_housing\loss_aversion4.xls
dir : seeout

.
. stcox runmax1_zero runmax1_down red_runmax1_down if ((group==1 & group2==1))
> & ref~=.,nohr

failure _d:  fail == 1
analysis time _t:  time_index
id:  appt

Iteration 0:   log likelihood = -846.98151
Iteration 1:   log likelihood = -787.50564
Iteration 2:   log likelihood = -786.90072
Iteration 3:   log likelihood = -786.88341
Iteration 4:   log likelihood = -786.88338
Refining estimates:
Iteration 0:   log likelihood = -786.88338

Cox regression -- Breslow method for ties

No. of subjects =          195                     Number of obs   =     17214
No. of failures =          195
Time at risk    =        17226
LR chi2(3)      =    120.20
Log likelihood  =   -786.88338                     Prob > chi2     =    0.0000

-------------------------------------------------------------------------------
> ---
_t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interv
> al]
-----------------+-------------------------------------------------------------
> ---
runmax1_zero |   .0358589   .0054647     6.56   0.000     .0251483    .0465
> 696
runmax1_down |   .0249492   .0062168     4.01   0.000     .0127646    .0371
> 338
red_runmax1_down |  -.0379417   .0158971    -2.39   0.017    -.0690994    -.006
> 784
-------------------------------------------------------------------------------
> ---

. estimates store eq3

. outreg2 using "D:\kingston\public_housing\loss_aversion4.xls", tstat asterisk
> (tstat) addstat(subjects, e(N_sub), failures, e(N_
> fail), Chi Square Statistics, e(chi2),log likelihood, e(ll) )
D:\kingston\public_housing\loss_aversion4.xls
dir : seeout

. //testnl _b[eq1:red_runmax1_down]==_b[eq2:red_runmax1_down]
. //testnl [eq1]red_runmax1_down==[eq3]red_runmax1_down
. //gen
. //test [eq1:_b[red_runmax1_down]]==[eq3:_b[red_runmax1_down]]
. hausman eq1 eq2

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|      eq1          eq2         Difference          S.E.
-------------+----------------------------------------------------------------
runmax1_zero |    .0278138     .0309905       -.0031767               .
runmax1_down |    .0293033     .0225985        .0067048               .
red_runmax~n |   -.0626103    -.0412099       -.0214004               .
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from stcox
B = inconsistent under Ha, efficient under Ho; obtained from stcox

Test:  Ho:  difference in coefficients not systematic

chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=   -13.52    chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

. hausman eq1 eq3

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|      eq1          eq3         Difference          S.E.
-------------+----------------------------------------------------------------
runmax1_zero |    .0278138     .0358589       -.0080451               .
runmax1_down |    .0293033     .0249492        .0043541               .
red_runmax~n |   -.0626103    -.0379417       -.0246686               .
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from stcox
B = inconsistent under Ha, efficient under Ho; obtained from stcox

Test:  Ho:  difference in coefficients not systematic

chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=   -16.10    chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

.
. test [eq1:_b[red_runmax1_down]]==[eq3:_b[red_runmax1_down]]
eq1:_b invalid name
r(198);

end of do-file

--
Dr. Yuval Arbel