Dear Stas,
Thanks for your reply. I must admit that this really is a little bit beyond
my statistical skills. I am just a peace and conflict researcher with a few
short courses in quantitative methods under my belt. But I intend to learn
more when I get an opportunity.
What made me question random effects ordered probit was when I saw that
Greene (Econometric Analysis, 2003, p 307) warns that if a lagged dependent
variable is included it will be correlated with the disturbance.
My dependent variable is the so-called Political Terror Scale, ranging from
1 to 5 and intended to capture the level of personal integrity rights abuse
(political imprisonment, torture, murder and disappearances) in a country.
It is judgmentally coded based on the annual reports by Amnesty
International and the US State Department:
[1] Countries [are] under a secure rule of law, people are not imprisoned
for their views, and torture is rare or exceptional. . . . Political murders
are extremely rare.
[2] There is a limited amount of imprisonment for nonviolent activity.
However, few persons are affected, torture and beating are exceptional. . .
. Political murder is rare.
[3] There is extensive political imprisonment, or a recent history of such
imprisonment. Execution or other political murders and brutality may be
common. Unlimited detention, with or without trial, for political views is
accepted.
[4] The practices of [level 3] are expanded to larger numbers. Murders,
disappearances are a common part of life. . . . In spite of its generality,
on this level terror affects primarily those who interest themselves in
politics or ideas.
[5] The terrors of [level 4] have been expanded to the whole population. . .
. The leaders if these societies place no limits on the means or
thoroughness with which they pursue personal or ideological goals.
I guess that it is reasonable to view this measure as representing an
underlying index that has been chopped into ordered categories.
I have data for most countries of the world during the years 1976-96.
Following your suggestion I created a dummy variable equal to 1 for each of
the categories 2-5 of the lagged dependent variable and included these four
dummies along with my other independent variables, and then I used reoprob.
But the log of the likelihood iterations (included below) looks funny to me:
what does it mean in this context that rho >=1?
Fitting constant-only model:
Iteration 0: log likelihood = -1913.2714
Iteration 1: log likelihood = -1624.8395
rho >= 1, set to rho = 0.99
Iteration 2: log likelihood = -1618.5555 (not concave)
Iteration 3: log likelihood = -1612.0323 (not concave)
Iteration 4: log likelihood = -1610.2913
Iteration 5: log likelihood = -1609.5952
Iteration 6: log likelihood = -1609.5949
Iteration 7: log likelihood = -1609.5949
Fitting full model:
Iteration 0: log likelihood = -1416.2615 (not concave)
Iteration 1: log likelihood = -1378.9136 (not concave)
Iteration 2: log likelihood = -1362.3694
Iteration 3: log likelihood = -1352.2499
Iteration 4: log likelihood = -1351.2405
Iteration 5: log likelihood = -1351.2266
Iteration 6: log likelihood = -1351.2266
Random Effects Ordered Probit Number of obs =
1615
LR chi2(12) =
516.74
Log likelihood = -1351.2266 Prob > chi2 =
0.0000
----------------------------------------------------------------------------
--
PolTS | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
eq1 |
y t-1 =2 | 1.190776 .1362784 8.74 0.000 .923675
1.457877
y t-1 =3 | 1.984349 .1622633 12.23 0.000 1.666319
2.30238
y t-1 =4 | 2.873937 .190133 15.12 0.000 2.501283
3.246591
y t-1 =5 | 3.719126 .2362928 15.74 0.000 3.256001
4.182252
X1 | -.0177493 .0063743 -2.78 0.005 -.0302427 -.0052559
X2 | -.0329977 .0071047 -4.64 0.000 -.0469225 -.0190728
X3 | 1.229424 .6062995 2.03 0.043 .0410985 2.417749
X4 | -.1695904 .0519423 -3.26 0.001 -.2713954 -.0677854
X5 | .194112 .0497613 3.90 0.000 .0965816 .2916424
X6 | .9392769 .1504445 6.24 0.000 .6444111 1.234143
X7 | .6116019 .1881763 3.25 0.001 .2427832 .9804206
-------------+--------------------------------------------------------------
--
_cut1 |
_cons | 1.075184 .850905 1.26 0.206 -.5925591
2.742927
-------------+--------------------------------------------------------------
--
_cut2 |
_cons | 3.07571 .856076 3.59 0.000 1.397832
4.753588
-------------+--------------------------------------------------------------
--
_cut3 |
_cons | 4.857695 .864742 5.62 0.000 3.162832
6.552558
-------------+--------------------------------------------------------------
--
_cut4 |
_cons | 6.432284 .8734574 7.36 0.000 4.720339
8.144229
-------------+--------------------------------------------------------------
--
rho |
_cons | .2358363 .0489779 4.82 0.000 .1398414
.3318312
----------------------------------------------------------------------------
--
Again, thanks for your help.
Erik Melander
-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Stas Kolenikov
Sent: Saturday, January 24, 2004 7:14 PM
To: [email protected]
Subject: Re: st: ordinal dynamic panel data
> I want to analyze an ordinal dependent variable using cross sectional
> time series data, and I want to include the lagged dependent variable on
> the right hand side.
>
> Is there a command that can do this?
>
> First I thought that perhaps -reoprob- could work, but now I am inclined
> to believe that this random effects command is unsuitable for a lagged
> dependent variable.
First, about estimation of the ordered logit / probit in the panel
context. This indeed can be done with -reoprob-, but a more appropriate
way would probably be -gllamm- as it has been reworked somewhat by Stata
Corp. to run somewhat faster. Quadrature integration is not much fun,
computationally. So yes, ordinal panel random effect estimation is
possible in Stata. I doubt that fixed effect estimation is possible...
well let's put it this way -- I don't see an immediate way to go around
it. The fixed effect logit (= McFadden's conditional logit) just happens
to work nicely be conditioning on the fixed effects, and I don't think
such conditioning is possible for the ordinal context. I know that
economists tend not to like RE as those give biased estimates, but I
personally don't see that much fault with biased estimates (Stein's
admissibility of a multivariate mean and all that stuff, you know :)),
especially when there is no better solution available.
Now, the second question is, what exactly is the model you want to
estimate? How do you want to see your lagged variable incorporated?
Usually people tend to think of the ordinal models as if there is an
underlying index that is chopped into ordered categories. (You can also
view this as a measurement error that makes this index discrete, together
with some nonlinear transformation of scale.) So the question is, if you
want to incorporate this index as your lagged variable (and that is going
to be a very messy computation), or you want to include the observed
ordinal variable from the previous period (and then it is subject to the
measurement error that leads to biased estimates), or finally you can just
create category indicators, a dummy variable equal to 1 for each
particular category of your lagged dependent varaible (that's probably the
most reasonable way to go; you might need to think of testing whether the
coefficients of those dummy variables follow a monotone pattern, and that
is far from trivial). Of course you would also need to make all sorts of
exogeneity assumptions for all of that to be trustworthy. Was this
the issue that turned you away from the random effect model?
--- Stas Kolenikov
-- Ph.D. student in Statistics at UNC-Chapel Hill
- http://www.komkon.org/~tacik/ -- [email protected]
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