SEM and convergence problem ADF method

[iman gharraie]

Hello all,
I have a convergence issue. I have a SEM model which is working in SAS without any problems but when I run it in STATA it gives me the convergence error but the values that it shows after the error are the same as my estimates in SAS. I am using ADF method my sample size is 1601. the covariance that I added helped with the overall goodness of fit in my SAS model. Can somebody point out my mistake please? thank you.

Iteration 15999: discrepancy = .18240435 (not concave)
Iteration 16000: discrepancy = .18240435 (not concave)
convergence not achieved
Structural equation model Number of obs = 1,601
Estimation method = adf
Discrepancy = .18240435

( 1) [TOT_VHCL0]KES = 1
( 2) [ACCISEV]CRASH = 1
( 3) [SKTRESNM2]SPEED = 1

----------------------------------------------------------------------------------------------------
	|	Coef.	Std. Err.	z	P>|z|	[95% Conf.	Interval]
-------------------	-------------+	-----------	----------	--------	--------	------------	----------
Structural	|
KES	|
SPEED |		0.200147	0.153684	1.3	0.193	-0.10107	0.501363
-----------------	-------------+	---------	----------	--------	-------	------------	----------
CRASH	|
KES |		2.68267	0.872474	3.07	0.002	0.972653	4.392687
SPEED |		1.114295	0.645734	1.73	0.084	-0.15132	2.37991
-------------------	---------------+	-------------	----------	--------	--------	------------	----------
Measurement	|
SKTRESNM2	|
SPEED |		1	(constraine	d)
_cons |		1.202464	0.02869	41.91	0	1.146232	1.258696
-----------------	--------------+	------------	----------	--------	--------	------------	----------
ALCINVOLV	|
SPEED |		0.172996	0.113374	1.53	0.127	-0.04921	0.395205
_cons |		0.023203	0.004265	5.44	0	0.014844	0.031561
-----------------	--------------+	----------	----------	--------	--------	------------	----------
TRWAYCHR	|
SPEED |		0.113768	0.074707	1.52	0.128	-0.03266	0.260192
_cons |		1.031542	0.004318	238.88	0	1.023078	1.040006
-----------------	--------------+	------------	----------	--------	--------	------------	----------
GENDR	|
SPEED |		0.180859	0.210502	0.86	0.39	-0.23172	0.593434
_cons |		1.496121	0.012075	123.91	0	1.472455	1.519786
-----------------	--------------+	------------	----------	--------	--------	------------	----------
DAYOFWEEK	|
SPEED |		0.340221	0.212306	1.6	0.109	-0.07589	0.756333
_cons |		1.290697	0.010847	118.99	0	1.269436	1.311957
-----------------	--------------+	------------	----------	--------	--------	------------	----------
LIGHTCND1	|
SPEED |		0.115429	0.073965	1.56	0.119	-0.02954	0.260396
_cons |		1.01729	0.003661	277.84	0	1.010114	1.024466
-----------------	--------------+	-----------	----------	--------	--------	------------	----------
TIME3	|
SPEED |		-0.47336	0.23695	-2	0.046	-0.93777	-0.00895
_cons |		1.245035	0.010443	119.23	0	1.224568	1.265502
-----------------	--------------+	------------	----------	--------	--------	------------	----------
RDSURFCD	|
SPEED |		-0.11368	0.119389	-0.95	0.341	-0.34768	0.12032
_cons |		1.095947	0.007148	153.33	0	1.081937	1.109956
-----------------	--------------+	------------	----------	--------	--------	------------	----------
AGE_ATFAULT2	|
SPEED |		-0.70507	0.649262	-1.09	0.277	-1.9776	0.567458
_cons |		2.835712	0.036264	78.2	0	2.764636	2.906788
-----------------	--------------+	----------	----------	--------	--------	------------	----------
TOT_VHCL0	|
KES |		1 (	constraine	d)
_cons |		2.098298	0.010979	191.13	0	2.076781	2.119816
-----------------	--------------+	------------	----------	--------	--------	------------	----------
VHTYP2	|
KES |		-0.1698	0.278581	-0.61	0.542	-0.71581	0.376208
_cons |		1.351595	0.011799	114.56	0	1.32847	1.37472
-----------------	-------------+	------------	----------	--------	--------	------------	----------
VHMOVE_ATFAULT	|
KES |		-0.41692	0.233256	-1.79	0.074	-0.87409	0.040257
_cons |		1.088591	0.007033	154.78	0	1.074806	1.102376
-----------------	--------------+	------------	----------	--------	--------	------------	----------
PNTIMP_ATFAULT	|
KES |		-1.51186	0.867359	-1.74	0.081	-3.21185	0.188131
_cons |		1.510912	0.012086	125.02	0	1.487225	1.5346
-----------------	--------------+	------------	----------	--------	--------	------------	----------
VHYEAR2	|
KES |		-1.20199	0.690825	-1.74	0.082	-2.55598	0.152006
_cons |		2.303332	0.022631	101.78	0	2.258976	2.347688
-----------------	--------------+	------------	----------	--------	--------	------------	----------
ACCISEV	|
CRASH |		1 (	constraine	d)
_cons |		2.060651	0.024043	85.71	0	2.013527	2.107775
-----------------	------------+	------------	----------	--------	--------	------------	----------
TOT_VH_DMG1	|
CRASH |		0.63975	0.049732	12.86	0	0.542277	0.737223
_cons |		2.357337	0.02804	84.07	0	2.30238	2.412294
-----------------	------------+	------------	----------	--------	--------	------------	----------
TOT_INJR1	|
CRASH |		1.200589	0.074196	16.18	0	1.055168	1.346009
_cons |		1.141933	0.028033	40.74	0	1.08699	1.196877
-----------------------------------+----------------------------------------------------------------
var(e.SKTRESNM2)|	1.357836	0.036123	1.28885	1.430515
var(e.ALCINVOLV)|	0.009742	.	.	.
var(e.TRWAYCHR)|	0.068629	.	.	.
var(e.GENDR)|	0.184055	.	.	.
var(e.DAYOFWEEK)|	0.137293	.	.	.
var(e.LIGHTCND1)|	0.02579	.	.	.
var(e.TIME3)|	0.18399	.	.	.
var(e.RDSURFCD)|	0.07841	.	.	.
var(e.AGE_ATFAULT2)|	2.31953	0.047229	2.228785	2.41397
var(e.TOT_VHCL0)|	0.085461	0.011939	0.06499	0.112379
var(e.VHTYP2)|	0.237998	0.005898	0.226715	0.249843
var(e.VHMOVE_ATFAULT)|	6710832	.	.	.
var(e.PNTIMP_ATFAULT)|	4012065	.	.	.
var(e.VHYEAR2)|	0.847778	0.024015	0.801993	0.896177
var(e.ACCISEV)|	0.321992	0.035152	0.259967	0.398815
var(e.TOT_VH_DMG1)|	1.068064	0.038958	0.994374	1.147215
var(e.TOT_INJR1)|	0.369509	0.055423	0.275393	0.495789
var(e.KES)|	0.009936	0.006632	0.002686	0.036757
var(e.CRASH)|	0.462889	0.084022	0.324317	0.660668
var(SPEED)|	0.033458	0.025775	0.007392	0.151443
-----------------------------------+----------------------------------------------------------------
cov(e.PNTIMP_ATFAULT,e.TOT_VH_DMG1)| -.0430937 .0125956 -3.42 0.001 -.0677806 -.0184067
----------------------------------------------------------------------------------------------------
Note: The Discr. test of model vs. saturated is not reported because the
fitted model is not full rank.
convergence not achieved
r(430);
.
.

[Weiwen Ng]

Imran, I'm not sure how much you know about maximum likelihood theory, and I'm not an expert myself. However, because this is a complex model, the likelihood function is probably not as well-behaved as others. Normally, Stata (and all other software) iteratively maximize the likelihood function by finding a better direction to step towards. Here, what I believe is happening is that the maximizer reached a point where the likelihood function is not concave, which means that the software isn't confident that it's at a global maximum, but it also can't find a better direction to step. (I'm an applied statistician, so I am not well-versed in the math, and this sort of thing is hard to explain in plain language.)

Now, different software apply different convergence criteria. In all software, the change in log-likelihood (i.e. first derivative) from one iteration to the last has to be below a certain tolerance, e.g. 1 * 10^-7 (I think this is Stata's default). Stata applies a secondary criterion to the second derivative of the log-likelihood, but I am not sure if other software use a looser criterion or if they apply this criterion at all. Anyway, I believe this is what's giving rise to the error messages you see. SAS, apparently, declared convergence at this log-likelihood. (Actually, I see that your output doesn't report a log-likelihood and instead reports a discrepancy, so while I think the concepts I outlined have a parallel under asymptotic distribution free estimation, I'm not exactly sure if there's a log likelihood.)

Unfortunately, in this case, I'm not sure what to do. Remember that this is a pretty complex model. I would not be surprised if estimation for this sort of model is a topic of ongoing research. One thing you can do is to inspect parameters with missing standard errors. Sometimes, this can reveal issues with the parameter (even if it can be unclear what to do). If the variance of something is nearly zero (e.g. less than 1 * 10^-10 or so), I think that can cause estimation to choke. If the variance is that small, you may be justified in removing that coefficient. I don't see that issue here.

Two of the error variances, for vhmove and pntimp, look very large in absolute terms. Relative to the other variables in your model, is the scale of those variables very large? For example, do you mainly have binary variables, or continuous variables with a range of 0 to 100, but two continuous variables have ranges of 0 to 10,000? I think this can sometimes cause estimation problems. You might want to rescale the variables if this is so - you could simply express them in thousands, or take logs, or whatever.