Hello - I've tried using -xtrchh- to estimate the parameters of a simple
random slopes model using data that I randomly generated to fit the model.
Despite having 500 clusters and 5 obs/cluster, the results were not very
good. By contrast, MLWIN estimates were right on. Here's the model I used:
y = (mu + ai) + (be + bi)*xij + eij
mu, be are constants
(ai,bi)' ~ N(0,Sig) where SIG=(siga^2, r*siga*sigb \ r*siga*sigb, sigb^2)
eij~N(0,sig^2)
*/
and here's the .do file that generated the data. "zor" just generates a
standard N(0,1) variate.
NS = 500
n = 5
siga=1.0
sigb=0.20
r = -0.50
sig = 0.5
seed=7777
args NS n siga sigb r sig be seed
local c=`r'*`siga'*`sigb'
scalar sig2a=`siga'^2
scalar sig2b=`sigb'^2
scalar c=`c'
scalar sig2=`sig'^2
cap set seed `seed'
drop _all
set obs `NS'
gen jsub=_n
zor z1
zor z2
gen ai=`siga'*z1
gen bi=`c'*z1/`siga'+sqrt(`sigb'*`sigb'-(`c'/`siga')^2)*z2
expand `n'
sort jsub
zor z3
gen x=10*uniform()
gen y=ai+(`be'+bi)*x+`sig'*z3
exit
Results from xtrchh:
. xtrchh y x
Hildreth-Houck random-coefficients regression Number of obs =
2500
Group variable (i) : jsub Number of groups =
500
Obs per group: min =
5
avg =
5.0
max =
5
Wald chi2(1) =
8360.15
Prob > chi2 =
0.0000
----------------------------------------------------------------------------
--
y | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
x | .9969157 .0109031 91.43 0.000 .9755459
1.018285
_cons | .0548312 .0573487 0.96 0.339 -.0575703
.1672327
----------------------------------------------------------------------------
--
Test of parameter constancy: chi2(998) = 41582.65 Prob > chi2 =
0.0000
Note: The estimates of the fixed parameters are good (should be 1.0 and 0.0)
. matrix SIG=e(Sigma)
. matrix R=corr(SIG)
Here's
symmetric SIG[2,2]
x _cons
x .05110038
_cons -.15280976 1.3870031
The covariance matrix SIG with x-component first, should be (0.04, -0.1 \
-0.1, 1.00). For this many clusters (500), the estimate doesn't appear to be
very good. Especially poor on the estimate of siga^2.
On the other hand, here's the results from MLWIN:
->rand
LEV. PARAMETER (NCONV) ESTIMATE S. ERROR(U) PREV. ESTIM
CORR.
----------------------------------------------------------------------------
---
2 cons /cons ( 1) 1.006 0.08091 1.004
1
2 x /cons ( 1) -0.09593 0.01288 -0.09581
-0.476
2 x /x ( 1) 0.04036 0.003127 0.0404
1
----------------------------------------------------------------------------
---
1 cons /cons ( 1) 0.244 0.008859 0.2441
->fixe
Note the estimates of SIG are very good: (1.006 for 1.000. -0.09593 for
-0.10, 0.04036 for 0.04)
PARAMETER ESTIMATE S. ERROR(U) PREV. ESTIMATE
cons 0.04481 0.05079 0.04481
x 0.9986 0.009953 0.9986
The estimates of the fixed parmaeters are about as accurate as in xtrchh.
So my question is what's going on?
AL Feiveson
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
