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Re: st: simulation for generalized ordered logit models


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: simulation for generalized ordered logit models
Date   Thu, 19 May 2011 14:50:14 +0200

On Wed, May 18, 2011 at 9:11 PM, Jun Xu <mystata@hotmail.com> wrote:

> I am trying to study performance of some extensions of the order logit models (e.g., generalized ordered logit models and partial proportionality models.  However, it appears the data generating process is a bit tricky.  My problem is that I don't know (or I don't know if I did it right) how to turn latent y's into an observed ordered response variable.  In addition, because of that, I think the gologit2 estimates seem to be off quite a bit.

One problem I see is in the way you create the error term: you should
use the same error term for both equations. Anyhow, below is an
example that seems to work well. For summarizing the simulation
results I use Ian White's -simsum- command, as discussed in (White
2010). You can install it by typing in Stata. -findit simsum- and
follow the instruction. In this example -gologit2- seems do very well
with respect to both bias and coverage.

*--------------------- begin example -----------------------------
set seed 1234
program drop _all
program define sim
	drop _all
	set obs 500
	gen x1 = rnormal()
	gen x2 = rnormal()

	gen u = runiform()

	gen ystar2 =  1 + x1 - .5*x2 + ln(u/(1-u))
	gen ystar3 = -1 + x1 -  1*x2 + ln(u/(1-u))

	gen y = cond(ystar2 < 0, 1, ///
			cond(ystar3 < 0, 2, 3))

	gologit2 y x1 x2, pl(x1)
end
simulate _b _se, reps(5000) : sim
simsum _eq1_b_x1  , true(1  ) se(_eq3_se_x1)   ///
       mcse bias cover
simsum _eq1_b_x2  , true(-.5) se(_eq3_se_x2)   ///
       mcse bias cover
simsum _eq1_b_cons, true(1  ) se(_eq3_se_cons) ///
       mcse bias cover
simsum _eq2_b_x1  , true(1  ) se(_eq4_se_x1)   ///
       mcse bias cover
simsum _eq2_b_x2  , true(-1 ) se(_eq4_se_x2)   ///
       mcse bias cover
simsum _eq2_b_cons, true(-1 ) se(_eq4_se_cons) ///
       mcse bias cover
*------------------------ end example ------------------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Ian R. White (2010) "simsum: Analyses of simulation studies including
Monte Carlo error" The Stata Journal, 10(3):369-385.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------

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