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From |
"Howells, William" <Howells_W@bmc.wustl.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: can gllamm fit this? |

Date |
Wed, 12 Oct 2005 09:54:03 -0500 |

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: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis Sent: Tuesday, October 11, 2005 3:12 AM To: statalist@hsphsun2.harvard.edu 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: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Svend Juul Sent: maandag 10 oktober 2005 23:23 To: statalist@hsphsun2.harvard.edu 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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ <br/>The materials in this message are private and may contain Protected Healthcare Information. If you are not the intended recipient, be advised that any unauthorized use, disclosure, copying or the taking of any action in reliance on the contents of this information is strictly prohibited. If you have received this email in error, please immediately notify the sender via telephone or return mail. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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