Multi-level model (xtmelogit) vs. adjusting for PSU and strata (svy: logit)?

What is the appropriate way to specify models that incorporate two levels of clustering (if that is the right term)? I initially used xtmelogit (level 1=child, level 2=sibling groups, level 3=counties). These are experimental data; the intervention was implemented separately in 9 counties and served children (many in sibling groups). A colleague recommended that, since I don’t care about estimating county-level impacts, xtmelogit might be overkill and I could run models simply adjusting for strata (county) and PSU (sibling group) which I then did using svy: logit. (If I understand correctly, this suggestion is also made by the authors of GLLAMM.) However, results using the two approaches differ, which makes me think either that I’m doing something wrong, or that one approach is better than the other. Can anyone advise? Thank you in advance!

Below I've provided some sample output and definitions of my key variables.

EXPER: 1=treatment, 0=control (Independent variable of interest)
MOMCLOSE: 1= good outcome, 0=bad outcome
Siteid=county identifier (level 3 id, with dummy indicators called site# )
randcid = case id/sibling group id (level 2 id)
fpcvar =(fpc, calculated per county, number of respondents divided by number of youth in the original sample)


. svyset randcid, strata (siteid) fpc(fpcvar)

pweight: <none>
VCE: linearized
Single unit: missing
Strata 1: siteid
SU 1: randcid
FPC 1: fpcvar

MODEL 1

.
. foreach var in momclose {
2. svy: logit `var' exper, or
3. }
(running logit on estimation sample)

Survey: Logistic regression

Number of strata = 9 Number of obs = 303
Number of PSUs = 263 Population size = 303
Design df = 254
F( 1, 254) = 0.21
Prob > F = 0.6451

------------------------------------------------------------------------------
| Linearized
momclose | Odds Ratio Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | 1.053215 .1184012 0.46 0.645 .8440495 1.314214
_cons | .6947368 .0540147 -4.68 0.000 .5961066 .8096862
------------------------------------------------------------------------------

MODEL 2
.
. foreach var in momclose {
2. svy: logit `var' exper site268 site269 site271 site272 site273 site274 sit
> e275 site276, or
3. }
(running logit on estimation sample)

Survey: Logistic regression

Number of strata = 9 Number of obs = 303
Number of PSUs = 263 Population size = 303
Design df = 254
F( 9, 246) = 6.36
Prob > F = 0.0000

------------------------------------------------------------------------------
| Linearized
momclose | Odds Ratio Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | 1.135454 .1281456 1.13 0.261 .9091681 1.41806
site268 | 1.169825 .282946 0.65 0.517 .7265324 1.883593
site269 | .5536779 .1434254 -2.28 0.023 .3324338 .9221662
site271 | .8257458 .1561435 -1.01 0.312 .5690086 1.198323
site272 | 1.252144 .280899 1.00 0.317 .8049818 1.947701
site273 | 1.53346 .2869998 2.28 0.023 1.060719 2.216892
site274 | .5546835 .1121758 -2.91 0.004 .3724597 .8260591
site275 | 3.282409 .9750136 4.00 0.000 1.828688 5.891772
site276 | .7522824 .1431926 -1.50 0.136 .5171112 1.094405
_cons | .6761679 .0953349 -2.78 0.006 .5122318 .8925705
------------------------------------------------------------------------------

. svyset, clear

.
MODEL 3

. xtmelogit momclose exper || siteid: || randcid: , or

Refining starting values:

Iteration 0: log likelihood = -206.31694 (not concave)
Iteration 1: log likelihood = -203.61326
Iteration 2: log likelihood = -202.51347

Performing gradient-based optimization:

Iteration 0: log likelihood = -202.51347
Iteration 1: log likelihood = -202.47848
Iteration 2: log likelihood = -202.4783
Iteration 3: log likelihood = -202.4783

Mixed-effects logistic regression Number of obs = 303

--------------------------------------------------------------------------
| No. of Observations per Group Integration
Group Variable | Groups Minimum Average Maximum Points
----------------+---------------------------------------------------------
siteid | 9 20 33.7 57 7
randcid | 263 1 1.2 4 7
--------------------------------------------------------------------------

Wald chi2(1) = 0.11
Log likelihood = -202.4783 Prob > chi2 = 0.7348

------------------------------------------------------------------------------
momclose | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | 1.144452 .455809 0.34 0.735 .5243044 2.49811
_cons | .5649229 .1772804 -1.82 0.069 .3054012 1.044979
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
siteid: Identity |
sd(_cons) | .2495608 .4194843 .0092555 6.729036
-----------------------------+------------------------------------------------
randcid: Identity |
sd(_cons) | 1.9571 .7909925 .8863118 4.321548
------------------------------------------------------------------------------
LR test vs. logistic regression: chi2(2) = 6.42 Prob > chi2 = 0.0404

Note: LR test is conservative and provided only for reference.

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