Thank you for the replies. I see your point about the difference in
regression coefficients for x1 unadjusted and adjusted by x2. The
problem arises when calculating the variance of the difference in
coefficients, for example, when one wants to calculate a confidence
interval for the "proportion mediated" defined as the difference above
divided by the unadjusted effect of x1 (see Freedman and Schatzman,
Stats in Medicine, 1992). It turns out the variance of the proportion
is large and produces CI often outside of [0,1].
This motivated me to seek another measure of mediation, which arises
from the path model approach, namely the indirect effect = product of
the paths from x1->x2 and x2->x3, which was my motivation for using
gllamm to fit a discrete outcome SEM. If I use this approach, there is
also a problem finding the standard errors for the indirect effect
because the variance of the residuals in logistic regression model is
fixed at pi^2/3, which means the scale of the outcome depends on the
other variables in the model, which means I can't combine variances from
two separate logistic regression models to get the variance of the
indirect effect (see MacKinnon and Dwyer, Evaluation Review, 1993).
Anyway, I'm just about to say "screw the standard errors" and just
report the mediation proportion. Bill H.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Maarten Buis
Sent: Tuesday, October 11, 2005 3:12 AM
To: [email protected]
Subject: RE: st: can gllamm fit this?
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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