st: RE: Tobit with gllamm

["Nick Cox" <n.j.cox@durham.ac.uk>]

This is in part not my usual territory, but it seems to me that you are
conflating two quite distinct issues, censoring of responses and bounded
responses. -tobit- is for censored responses and the essence of the
problem is that at least some responses were, we believe, really greater
and/or less than was recorded. 

Although you describe your variable as "censored", what is most obvious
from your description is that it is a bounded variable, which in
principle cannot be greater or less than the bounds specified. This is
in a sense the opposite situation from censoring. As you say, you can
rescale so that limits lie between 0 and 1, but the problem with -tobit-
necessarily remains exactly the same. But rescaling to [0,1] does make
other things easier. 

You might benefit from Kit Baum's mini-review 

SJ-8-2  st0147  . . . . . . . . . . . . . . Stata tip 63: Modeling
proportions
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.
F. Baum
        Q2/08   SJ 8(2):299--303                                 (no
commands)
        tip on how to model a response variable that appears
        as a proportion or fraction

I don't think the use of -gllamm- affects this central question. 

Nick 
n.j.cox@durham.ac.uk 

Walter McManus

I am using gllamm to estimate a model with a censored dependent variable
and two random effects: an intercept and a price-slope.
The data are from a survey of consumers about plug-in hybrid electric
vehicles (PHEV), and the dependent variable is the stated probability of
purchasing a PHEV in several price scenarios.

I read the suggestions in statalist:

> Re: st: xttobit
> From Sophia Rabe-Hesketh <sophiarh@berkeley.edu> To
statalist@hsphsun2.harvard.edu
> Subject Re: st: xttobit Date Sun, 29 Feb 2004 21:26:24 -0800
> Matt,
> I suggest first running xttobit and using the estimates as starting
values for gllamm. For the example command you gave in your email, the
data manipulation and gllamm command would be:
> xttobit zteq `vars', ll(0) ul(100) i(sys_id)
> * create a new dependent variable equal to 1 if right-censored * and 0
if left-censored:
> gen y=cond(zteq>=100,1,cond(zteq<=0,0,zteq)) if zteq<.
> * create offset variable equal to -100 if right-censored at * 100, 0
otherwise:
> gen off = cond(zteq>=100,-100,0)
> * create var=2 for censored observations, 1 otherwise:
> gen var=cond(zteq>=100|zteq<=0,2,1)
> * get starting values from xttobit (last two elements, /sigma_u * and
/sigma_e need to be switched and need logarithm of /sigma_e:
> matrix a=e(b) local n=colsof(a) matrix a[1,`n']=a[1,`n'-1] matrix
a[1,`n'-1]=ln(a[1,`n'])
> gllamm y `vars', offset(off) i(sys_id) fam(gauss binom) link(ident
sprobit) /* */ lv(var) fv(var) from(a) copy adapt
> The default number of quadrature points gllamm uses is 8 (which may be
more accurate than 12 with ordinary quadrature). You may have to
increase this using nip(20), etc. (perhaps do a kind of quadcheck
manually).
> Please let me know if you have any problems.

My dependent variable was originally measured on a scale from 0 to 100,
so I followed your suggestions with an offset of -100. However, some of
the results were puzzling--the predicted mu values for the censored
observations were between 0 and 1 and the mu values for the uncensored
observations included values > 100 and < 0. Thinking that the offset
might be the source of the puzzlement, I rescaled the dependent variable
to be on a 0 to 1 scale. This model requires no offset. The puzzle
remains--I still get values above 1 and below 0.


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