--- In [email protected], "Erik Melander" <erik.melander@p...>
wrote:
>
> 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.
Well, yes, that is true. I am not quite sure though how this would affect
the estimation procedure. Most likely, it will in a similar way it does
for the linear regession, i.e., biasing the estimates. You'll get them
biased at any rate if you simply include your lagged PTS as is due to
measurement error (the one that makes it discrete from the unobserved
continuous index).
> My dependent variable is the so-called Political Terror Scale [...]
> 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?
Well here rho is the ratio of the panel term variance to the total
variance of the residual (if you have u_i for the i-th panel, and e_it for
i,t-th observation, then rho = var(u)/(var(u)+var(e)) ). It seems to be in
a reasonable range of about a quarter of the total variance. You don't
have a direct estimate of the autocorrelation -- it is buried somewhere in
the coefficient of your dummies corresponding to the categories of lagged
PTS -- see my discussion below.
Another potential problem I see in those results is that the cuts /
thresholds give a very broad range of 5.4. It means that the underlying
index should have at least that much of a range, or better a broader
range. I would suspect that most of your data fall somewhere in the
beginning of the scale, in the first two categories or so, and the highest
categories of 4 and 5 are only observed in a handful of observations in
the tail of the normal distribution, so those are not estimated very
accurately. If that is the case, you might want to pool the upper
categories into something like 4 and above.
You can compare this range with the range of the coefficients of the
categories of the lagged variable, which is about 2.5. So the order of
magnitude of your autocorrelation coefficient is about 0.5 (the range of
5+ on the normal scale is mapped into the range of 2.5) -- of course this
is a very rough estimate, as those cuts are not quite comparable to the
dummy variable estimates (which are rather means of the subgroups of the
normal distribution divided by those cuts), and may suffer from the
correlation of the explanatory variable and the residual. All coefficients
are strongly significant, so the autocorrelation is quite strong.
What exactly are you interested in in your model? What is the question
that you need to answer with it? The estimated model will have some
statistical problems from various sides, so you may need to think more
about it before submitting it for a publication, but I personally would
utilize those results to at least assess where I stand, especially as long
as I don't see any better way to go with this model.
> 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
--- Stas Kolenikov
-- Ph.D. student in Statistics at UNC-Chapel Hill
- http://www.komkon.org/~tacik/ -- [email protected]
* This e-mail and all attachments to it are not intended to provide any
* reasonable point of view and was transmitted to you in error. It
* should be immediately deleted by all recipients unless they really
* enjoy communicating with the author :). Other restrictions apply.
*
* 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/
