I had the same idea as Svend, though coming from a different discipline. In my parlance I would say that the model you are trying to estimate is recursive, so there is no need to simultaneously estimate equation 1 and 2. Consequently you can just estimate two separate logistic regressions as Svend suggested, and there is no need to use GLLAMM.
Hope this helps,
Maarten
-----Original Message-----
From: [email protected] [mailto:[email protected]]On Behalf Of Svend Juul
Sent: maandag 10 oktober 2005 23:23
To: [email protected]
Subject: Re: st: can gllamm fit this?
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
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