using xtdpdml to perform SEM on panel data

[Jennifer Nutakor]

I have a panel of 46 countries and 4 time periods. My main outcome variable is the number of investments into a country, and I have around 10-12 (depending on the model) predictor variables that are all time-variant. I would like to run a structural equation model to understand causal pathways among variables. I ran a typical GSEM pooling all observations (I have copied the command and output at the bottom of this message), but that GSEM doesn't account for the panel data structure (each country is in the dataset 4 times with varying values on the country-level variables).

I am trying to use xtdpdml in Stata 14.2 to account for the panel structure. When I use the xtdpdml command the model hasn't converged (so far) but there aren't errors. To do this, I use the following command:

xtdpdml numInvstm ysIMFFinMktDepth ysIMFFinMktAccess ysIMFinMktEfficient ysGrowthGDP yspcGDP ysGDP ysCosttoEnforceCtrctDBI ysPropRights ysCorruptGCI ysShareLawsuitsDBI ysJudicialStrong ysCrime , fiml semf(xtdpdml, r)

However, this command does not specify the various paths I would like to constrain in the model, which is the main reason I'd like to use SEM.


I tried simply copying the GSEM sytax into the xtdpdml command, but I get an error message, "invalid name" r(198)

xtset hostCountryNum yearSpanNum 
       panel variable:  hostCountryNum (unbalanced)
        time variable:  yearSpanNum, 1 to 4
                delta:  1 unit


xtdpdml (ysIMFFinMktDepth -> numInvstm, ) (ysIMFFinMktDepth -> ysGrowthGDP, ) ( zYSIMFFinMktAccess -> numInvstm, ) (yspcGDP -> numInvstm, ) (ysIMFinMktEfficient -> numInvstm, ) (ysGDP -> numInvstm, ) (ysGrowthGDP -> numInvstm, ) (ysControlCorruptionWGI -> numInvstm, ) (ysControlCorruptionWGI -> ysIMFFinMktDepth, ) (ysControlCorruptionWGI -> yspcGDP, ) (ysControlCorruptionWGI -> ysGettingCreditDBI, ) (ysControlCorruptionWGI -> ysCosttoEnforceCtrctDBI, ) (ysControlCorruptionWGI -> ysPropRights , ) (ysGettingCreditDBI -> numInvstm, ) (ysGettingCreditDBI -> ysIMFFinMktAccess , ) (ysCosttoEnforceCtrctDBI -> numInvstm, ) (ysShareLawsuitsDBI -> numInvstm, ) (ysJudicialStrong -> ysIMFinMktEfficient, ) (ysJudicialStrong -> ysCosttoEnforceCtrctDBI, ) (ysJudicialStrong -> ysPropRights , ) ( ysPropRights -> numInvstm, ) ( ysPropRights -> yspcGDP, ) ( ysPropRights -> ysGettingCreditDBI, ) ( ysPropRights -> ysCosttoEnforceCtrctDBI, )

Is there a way to specify paths using the xtdpdml and if so, what is the syntax?

If there is not, then can you recommend a different way of accounting for panel structure using a GSEM?


-------------------------------------------------------------------------------------------------

My command/results from a GSEM using pooled data are as follows:

gsem (ysIMFFinMktDepth -> numInvstm, ) (ysIMFFinMktDepth -> ysGrowthGDP, ) ( zYSIMFFinMktAccess -> numInvstm, ) (yspcGDP -> numInvstm, ) (ysIMFinMktEfficient -> numInvstm, ) (ysGDP -> numInvstm, ) (ysGrowthGDP -> numInvstm, ) (ysControlCorruptionWGI -> numInvstm, ) (ysControlCorruptionWGI -> ysIMFFinMktDepth, ) (ysControlCorruptionWGI -> yspcGDP, ) (ysControlCorruptionWGI -> ysGettingCreditDBI, ) (ysControlCorruptionWGI -> ysCosttoEnforceCtrctDBI, ) (ysControlCorruptionWGI -> ysPropRights , ) (ysGettingCreditDBI -> numInvstm, ) (ysGettingCreditDBI -> ysIMFFinMktAccess , ) (ysCosttoEnforceCtrctDBI -> numInvstm, ) (ysShareLawsuitsDBI -> numInvstm, ) (ysJudicialStrong -> ysIMFinMktEfficient, ) (ysJudicialStrong -> ysCosttoEnforceCtrctDBI, ) (ysJudicialStrong -> ysPropRights , ) ( ysPropRights -> numInvstm, ) ( ysPropRights -> yspcGDP, ) ( ysPropRights -> ysGettingCreditDBI, ) ( ysPropRights -> ysCosttoEnforceCtrctDBI, ), difficult iterate(5000)  nocapslatent

Generalized structural equation model    Number of    obs    =    184

Response       : numInvstm    Number of    obs    =    174
Family         : Gaussian
Link           : identity

Response       : ysGrowthGDP    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Response       : ysIMFFinMktDepth    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Response       : yspcGDP    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Response       : ysGettingCreditDBI    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Response       : ysCosttoEnforceCtr~I    Number of    obs    =    177
Family         : Gaussian
Link           : identity

Response       : ysPropRights    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Response       : ysIMFFinMktAccess    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Response       : ysIMFinMktEfficient    Number of    obs    =    184
Family         : Gaussian
Link           : identity

Log likelihood = -4432.3728 
Coef.
Std. Err.
z
P>z
[95% Conf.
Interval]










numInvstm <-







ysGrowthGDP
  -544.5438
390.142
-1.40
0.163
-1309.208
220.1204

ysIMFFinMktDepth
    158.0025
239.8043
0.66
0.510
-312.0052
628.0103

yspcGDP
   -.0241747
.0108955
-2.22
0.027
-.0455294
-.00282

ysGettingCreditDBI
-.8636417
2.021269
-0.43
0.669
-4.825256
3.097973

ysCosttoEnforceCtrctDBI
  -3.686959
2.724383
-1.35
0.176
-9.026652
1.652733

ysPropRights   -
56.15982
69.96886
-0.80
0.422
-193.2963
80.97663

ysIMFinMktEfficient
  -375.6699
139.4893
-2.69
0.007
-649.0639
-102.276

zYSIMFFinMktAccess
   -30.47716
41.72698
-0.73
0.465
-112.2605
51.30622

ysGDP
 .5888149
.0322119
18.28
0.000
.5256806
.6519491

ysControlCorruptionWGI
  184.8379
110.4447
1.67
0.094
-31.62974
401.3055

ysShareLawsuitsDBI
2.970568
1.747723
1.70
0.089
-.4549067
6.396043

_cons
  527.9779
376.123
1.40
0.160
-209.2097
1265.165









ysGrowthGDP <-







ysIMFFinMktDepth
-.0057494
.0336923
-0.17
0.865
-.071785
.0602862

_cons    .0885477
.0103453
8.56
0.000
.0682712
.1088242










ysIMFFinMktDepth <-







ysControlCorruptionWGI
 .0881752
.0313986
2.81
0.005
.0266351
.1497153

_cons    .2719619
.0196398
13.85
0.000
.2334686
.3104552










yspcGDP <-







ysPropRights
 -1034.483
458.2239
-2.26
0.024
-1932.585
-136.3808

ysControlCorruptionWGI
3464.177
715.1258
4.84
0.000
2062.557
4865.798

_cons
   10573.29
1966.944
5.38
0.000
6718.15
14428.43









ysGettingCreditDBI <-







ysPropRights
 -1.524463
2.689148
-0.57
0.571
-6.795096
3.746171

ysControlCorruptionWGI
 10.75614
4.084933
2.63
0.008
2.74982
18.76246

_cons
 67.12487
11.52756
5.82
0.000
44.53127
89.71848









ysCosttoEnforceCtr~I <-







ysPropRights
-1.847554
2.509315
-0.74
0.462
-6.76572
3.070613

ysControlCorruptionWGI
  7.643785
2.767113
2.76
0.006
2.220343
13.06723

ysJudicialStrong
  1.10415
2.05058
0.54
0.590
-2.914914
5.123214

_cons
  73.69556
7.321003
10.07
0.000
59.34665
88.04446









ysPropRights <-







ysControlCorruptionWGI
  .35701
.0761227
4.69
0.000
.2078123
.5062077

ysJudicialStrong
  .5886083
.0408296
14.42
0.000
.5085837
.6686328

_cons
  1.874249
.1676438
11.18
0.000
1.545673
2.202825









ysIMFFinMktAccess <-







ysGettingCreditDBI
 -0002657
.0009793
-0.27
0.786
-.0021851
.0016536

_cons
   .2421832
.0583001
4.15
0.000
.127917
.3564493









ysIMFinMktEfficient <-







ysJudicialStrong
.0744381
.0249939
2.98
0.003
.025451
.1234253

_cons   -.0128845
.0903314
-0.14
0.887
-.1899308
.1641617










var(e.numInvstm)
 170360.2
.


.
.

var(e.ysGrowthGDP)
 .0082315
.0008582


.0067102
.0100977

var(e.ysIMFFinMktDepth)
.0377896
.0039398


.0308055
.0463571

var(e.yspcGDP)   1.11e+07
.


.
.


var(e.ysGettingCredit~I)
  345.8314
.


.
.

var(e.ysCosttoEnforce~I)
153.3717
.


.
.

var(e.ysPropRights)
  .1387054
.0144616


.1130696
.1701536

var(e.ysIMFFinMktAccess)
  .0571513
.0059584


.0465889
.0701084

var(e.ysIMFinMktEffic~t)
 .0832336
.0086777


.0678508
.102104


 Warning: convergence notachieved

(Although this particular model didn't achieve convergence, I've played around with it in the past and it has converged...)

[Richard Williams]

If you haven't already, take a look at

https://www3.nd.edu/~rwilliam/dynamic/SJPaper.pdf

It includes convergence tips. The entire support page is

https://www3.nd.edu/~rwilliam/dynamic/index.html

With only 46 countries you may be pushing it with 12 independent variables. Consider simplifying the model and building back up. (That is my generic advice for almost any convergence problem. You may be able to identify a variable that is causing you grief, and then figure out what to do about it. Don't try to estimate the entire monster model all at once. For example, a time-varying variable that actually varies very little across time may cause xtdpdml problems,)

xtdpdml can generate the Stata code. You can then possibly hand tweak to do things xtdpdml can't do easily. It can also generate code for Mplus and R's lavaan, which may or may not be able to handle the problem better.

[Jennifer Nutakor]

Given that the 46 countries is a small N for the complexity of the model, I'm hoping to take advantage of the data panel structure (about 200 observations across the 4 time periods). I'm wondering-- would it be valid (helpful) to run the SEM with groups=time periods and with structural coefficients constrained to be the same across all groups? (Rather than using the panel data structure?)

[Richard Williams]

It would be simpler to use the group structure. I don't know if it would be better since the groups aren't independent and you are ignoring all the cross-time correlations. But you could try it.

[Jennifer Nutakor]

Thanks for your help! One more question. Since the final outcome variable is a count of the number of investments into a country (within a given time period, it ranges from zero investments into some countries to about 9000 into others, and is right skewed; all other variables are continuous), I have been trying to run models as GSEM. However, when I run as SEM, they converge very quickly. Also, SEM has some features GSEM doesn't have such as constraining coefficients across groups. How inaccurate is it to use SEM rather than GSEM in this context. I'm thinking I can at least use SEM for intermediate models to see what variables may be causing grief, for instance, and to get starting values for GSEM) but I'm wondering how far off the SEM results are from what I would get in GSEM.

Thanks again for all of your help with this!

[Richard Williams]

If you need to use a count model that further complicates things. Sometimes linear models work fine with count variables.As μ increases, the Poisson distribution approximates a normal distribution. So SEM might be ok.

You are trying to do pretty complicated things here. You may just have to settle for what works, while acknowledging the limitations, e.g. either the stat theory isn't clear or the software and hardware aren't up to the task.

You might try doable approximations first and then let you computer estimate the final model while you are away for a month on winter break!