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Re: st: rcal, measurement error model question


From   "Stas Kolenikov" <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: rcal, measurement error model question
Date   Fri, 12 Dec 2008 10:31:46 -0600

Richard,

As with most measurement error models, the first question is whether
the postulated relation holds between the variables measured with
error, or between the "ideal" unobservable variables. You might want
to clarify that.

There might be identification issues, too: if you treat this as an
econometric simultaneous equations model, it is identified as a
triangular/recursive system if everything is perfectly observable. I
am not sure how those identification rules work with measurement error
models.

Models with latent variables (and nothing observed without error) can
be fit using -gllamm- (see another paper in that Stata Journal special
issue on measurement error models,
http://www.stata-journal.com/sjpdf.html?articlenum=st0052). A direct
application might not be terribly helpful since -gllamm- will try to
model the error variance(s) marginally, and you already know them.
This can probably be circumvented by specifying fixed loadings equal
to sqrt(v1) and sqrt(v2), and the fixed variance of the error terms
equal to 1. Still -gllamm- would overlay an assumption of the (model)
normality for u1 and u2, which you may or may not like.

Given your position, I would suspect you have access to the raw survey
data. May be you can try and fit the model using those directly?

Otherwise, your (small area estimation?) problem might just be an
exercise in matrix algebra if none of the pre-canned routines are
directly applicable. And you would need to bring the covariances
between u1 and u2 (model covariance) as well as the (design-based?)
covariances between e1 and e2 if those are estimable/applicable. So
unless I am imagining things (and I well might), things are more
complicated than what you said.

If your model is a direct translation of something from Sarndal's
yellow book, just give the reference, we'll see if we can figure it
out from there :)).

On 12/11/08, Richard Valliant <rvalliant@survey.umd.edu> wrote:
> I'm a new user who is trying to fit a simple measurement error model to
>  a set of estimates from two independent surveys.  The surveys are
>  measuring the same things.  My data look like
>
>  (e1, v1) = set of 30 estimates and their variances from survey 1
>  (e2, v2) = set of 30 estimates and their variances from survey 2
>
>  The model I want to fit is basic:
>  e1 = a + b*e2 + u1
>  e2 = E2 + u2     (u1 and u2 are the model errors, E2 is E(e2)  )
>
>  I've tried:
>   mkmat v2
>   mat D = diag(v2)
>   rcal (e1) (w: e2), suuinit(D)
>
>  This gives "invalid syntax". If I put some arbitrary variable x in the
>  model (which I don't want), this works:
>     rcal (e1=x) (w: e2), suuinit(D)
>
>  But rcal apparently does not allow aweights to account for v1 =
>  var(e1).
>  Is there a way to use rcal or some other procedure to fit the model
>  above, accounting for the fact that I have (1) estimates of variance for
>  both e1 and e2 and (2) no covariates measured without error to put in
>  the model?

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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