--Wiji Arulampalam <[email protected]> wrote:
> I have just run a random effects probit using the same data on Limdep
> as well as stata7 and get very different results. I should be most
> grateful if someone could tell me whether I am doing something wrong
> please. Limdep gives a reasonable rho but stata does not!
After exchanging emails with Wiji privately, I think the problem can be solved
by choosing appropriate starting values for -xtprobit-.
The Limdep results Wiji sent to me:
--> probit;lhs=sue; rhs=one,lague;pds=ni;hpt=12;maxit=200 $
[...]
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant -2.658526026 .25480532 -10.434 .0000
LAGUE .9639215666 .24003142 4.016 .0001 .29448362E-01
Rho .5395074303 .10243535 5.267 .0000
In Stata, we can use the estimated coefficients from -probit- and make a guess
for the value of "rho" as the starting values:
. probit sue lague
. mat b = e(b)
. local rho = .7
. local lnsig2u = ln(`rho'/(1-`rho'))
. mat b = b, `lnsig2u'
. xtprobit sue lague, i(ind1) quad(12) from(b, copy)
Iteration 0: log likelihood = -396.6959
Iteration 1: log likelihood = -322.90498
Iteration 2: log likelihood = -321.81662
Iteration 3: log likelihood = -321.48201
Iteration 4: log likelihood = -321.47527
Iteration 5: log likelihood = -321.47523
Iteration 6: log likelihood = -321.47523
Random-effects probit Number of obs = 2411
Group variable (i) : ind1 Number of groups = 500
Random effects u_i ~ Gaussian Obs per group: min = 1
avg = 4.8
max = 7
Wald chi2(1) = 13.70
Log likelihood = -321.47523 Prob > chi2 = 0.0002
------------------------------------------------------------------------------
sue | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lague | .9639215 .2603925 3.70 0.000 .4535616 1.474281
_cons | -2.658526 .3061776 -8.68 0.000 -3.258623 -2.058429
-------------+----------------------------------------------------------------
/lnsig2u | .15836 .5165766 -.8541115 1.170831
-------------+----------------------------------------------------------------
sigma_u | 1.082399 .279571 .6524272 1.795737
rho | .5395075 .1283378 .2985711 .7632953
------------------------------------------------------------------------------
-xtprobit- goes to the same maximum as Limdep (having the same log-likelihood
and the estimated coefficients) with 12 quadrature points. However, when we
change the number of quadrature points from 12 to 20, some of the estimated
standard errors become missing again.
. xtprobit sue lague, i(ind1) quad(20) from(b, copy)
Iteration 0: log likelihood = -398.78414
Iteration 1: log likelihood = -353.83521
Iteration 2: log likelihood = -332.0604
Iteration 3: log likelihood = -327.03289
Iteration 4: log likelihood = -326.89695
Iteration 5: log likelihood = -326.89692
Random-effects probit Number of obs = 2411
Group variable (i) : ind1 Number of groups = 500
Random effects u_i ~ Gaussian Obs per group: min = 1
avg = 4.8
max = 7
Wald chi2(1) = 113.50
Log likelihood = -326.89692 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
sue | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lague | 1.768019 .1659566 10.65 0.000 1.44275 2.093288
_cons | -1.999568 .0575664 -34.73 0.000 -2.112397 -1.88674
-------------+----------------------------------------------------------------
/lnsig2u | -2.786059 . . .
-------------+----------------------------------------------------------------
sigma_u | .2483219 . . .
rho | .0580822 . . .
------------------------------------------------------------------------------
we use -quadchk- to check the stability of the quadrature technique after the
previous -xtprobit- with 12 quadrature points.
. quadchk, noout
Refitting model quad() = 8
Refitting model quad() = 16
Quadrature check
Fitted Comparison Comparison
quadrature quadrature quadrature
12 points 8 points 16 points
-----------------------------------------------------
Log -321.47523 -321.59583 -321.54191
likelihood -.12059364 -.0666759 Difference
.00037513 .00020741 Relative difference
-----------------------------------------------------
sue: .96392153 .97959511 .9789156
lague .01567358 .01499407 Difference
.01626022 .01555528 Relative difference
-----------------------------------------------------
sue: -2.6585261 -2.6060869 -2.6226448
_cons .05243927 .03588129 Difference
-.01972494 -.01349669 Relative difference
-----------------------------------------------------
lnsig2u: .15835995 .04112992 .09345529
_cons -.11723003 -.06490467 Difference
-.74027574 -.4098553 Relative difference
-----------------------------------------------------
The output shows that changing the number of quadrature points significantly
affects the results, especially for the estimated ln(sigma_u^2). When the
results change with the number of quadrature points, it indicates that it is
not possible to reliably approximate the integral. So the results should be
treated as if they came from an unconverged estimation process.
If we try with different numbers of quadrature points, the results will vary.
The Limdep results Wiji sent also show:
--> probit;lhs=sue; rhs=one,lague;pds=ni;hpt=12;maxit=200 $
[...]
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant -2.658526026 .25480532 -10.434 .0000
LAGUE .9639215666 .24003142 4.016 .0001 .29448362E-01
Rho .5395074303 .10243535 5.267 .0000
--> probit;lhs=sue; rhs=one,lague;pds=ni;hpt=20;maxit=200 $
[...]
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant -2.624126188 .24731920 -10.610 .0000
LAGUE .9784651287 .24861435 3.936 .0001 .29448362E-01
Rho .5237007959 .10460116 5.007 .0000
When "hpt" (number of Hermite quadrature points) is changed from 12 to 20, the
estimated "rho" varies about 3%.
Weihua Guan <[email protected]>
Stata Corp.
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