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# Re: st: can gllamm fit this?

 From "Svend Juul" To Subject Re: st: can gllamm fit this? Date Mon, 10 Oct 2005 23:22:31 +0200

```Bill wrote:

I have three binary variables, say x1, x2, and x3.  I want to fit two
logistic regression models simultaneously, x2=b12*x1 and
x3=b13*x1+b23*x2.  I want to fit them simultaneously in order to
calculate the indirect effect proportion = (indirect effect)/(total
effect) = (b12*b23)/(b12*b23 + b13).  Because the data are not
continuous, I cannot use pathreg.  I believe this model falls in the
category of latent variable (SEM) using manifest variables, which I've
read gllamm can fit.  Any advice or guidance is appreciated,
specifically how to specify the B matrix, or if I even need a B matrix.
The documentation is pretty tough to work through.
-----------------------------------

This isn't an answer, but a speculation from an epidemiologist who
is used to think: "What is the question (or hypothesis)?"

Bill's two equations can be put graphically:
x1 --------------->
|                      x3
------> x2 ------>

It looks like what we epidemiologists call the confounding triangle
(the untriangular look is only due to a practical shortcoming of
text mode). However, x2 should not be considered a confounder since
it may be in the causal pathway from x1 to x3. The corresponding
questions are:
1. What is the overall (crude) effect of x1 on x3?
2. How much is explained by x2 being a consequence of x1 and a cause of x3?

Example:
Does smoking (x1) affect birthweight (x3)?
Does smoking (x1) affect duration of pregnancy (x2)?
Does duration of pregnancy (x2) affect birthweight (x3)?

The crude x1-x3 association might reflect the x1 -> x2 -> x3
effects only, but there might also be a direct x1 -> x3 effect.

The primary tool is -cc- (see [ST] cc). It gives the crude (x1 -> x3)
odds ratio estimate and the adjusted x1 -> x3 estimate, i.e. the odds
ratio estimate remaining when the x1 -> x2 -> x3 effect has been
accounted for. (Actually, it seems that smoking increases the risk of
preterm birth, but that it has an effect on birthweight beyond that).

With -cc- you would:
. cc x3 x1
. xx x3 x1 , by(x2)

With -logistic- you would:
. logistic x3 x1
. logistic x3 x1 x2

I don't know if this is useful to you. But I have the feeling that
we are trying to invent the same wheel in various disciplines.

Svend

________________________________________________________

Svend Juul
Institut for Folkesundhed, Afdeling for Epidemiologi
(Institute of Public Health, Department of Epidemiology)
Vennelyst Boulevard 6
DK-8000 Aarhus C,  Denmark
Phone, work:  +45 8942 6090
Phone, home:  +45 8693 7796
Fax:          +45 8613 1580
E-mail:       sj@soci.au.dk
_________________________________________________________

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