Re: st: Random thresholds in ordered logit/probit in -gllamm-

[Kristian Karlson <kristian.karlson@gmail.com>]

Stas, I hope it is okay with one more remark on the random thresholds in 
ordered probit/logit. I came across the following paper by sociologists 
Breen and Luijkx,
http://smr.sagepub.com/content/early/2010/04/15/0049124110366240. They 
estimate a model with heterogeneous thresholds. They present a latent 
class ordered logit model with heterogeneous thresholds and locations 
(see, e.g., page 18). They model the threshold-heterogeneity by letting 
the scale vary across latent classes. They use LEM 
(http://smr.sagepub.com/content/suppl/2010/11/11/0049124110366240.DC1/DS_10.1177_0049124110366240.pdf). 
Do you think it would be possible to estimate that model with -gllamm-? 
As I see it, -gllamm- doesn't allow the scale to be random (but only a 
function of observed covariates, just as with the -thresh/ethresh- 
options, as you mentioned).
Best, Kristian


Den 27-11-2010 23:57, Stas Kolenikov skrev:
> I guess you would do that with -thresh()- or -ethresh()- option, but
> -gllamm- only allows to use observed variables rather than random
> effects. There are good reasons for that: the thresholds are collinear
> with the constant (and when you estimate a model with the thresholds,
> you cannot estimate the constant term; so if you try to get random
> thresholds, you'd have to forego the random intercepts, as well). I
> would imagine that without additional strong identification
> conditions, the model would just fall apart if you had random
> thresholds in the model.
>
> I think the paper you mentioned describes essentially a -gllamm,
> thresh()- model with a single random effect which essentially shifts
> all thresholds together for a given individual (although you would
> need to have repeated measurements for an individual to identify it).
> The author may have re-written it in Mata to speed it up, but I don't
> see anything in the abstract that goes beyond -gllamm-, frankly.
>
> On Sat, Nov 27, 2010 at 3:17 AM, Kristian Karlson
> <kristian.karlson@gmail.com>  wrote:
> > Hi,
> >
> > I want to estimate an ordered probit/logit model with random thresholds.
> > That is, the thresholds should vary across individuals. I have tried using
> > -gllamm-, but I fail to see how I must specify -gllamm- in order for the
> > thresholds to be random. I am specifically interested in this heterogeneity.
> > Can anyone help me on that?
> >
> > In passing, I note that I came across a paper dealing with these issues,
> > http://econpapers.repec.org/paper/bocisug08/02.htm, but I can't identify
> > which command the paper refers to.
> >
> > Best wishes,
> > Kristian
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