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st: RE: Multilevel modeling


From   Timothy Mak <tshmak@hku.hk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Multilevel modeling
Date   Mon, 2 Dec 2013 14:33:18 +0800

The purpose of propensity-score weighting is to estimate what are called "Average causal effects", that is, these are effects defined as in: 

\sum_i CE_i / N

where CE is the causal effect of subject i, and are assumed to be different for different individuals. 

Note that there are no "random effects" in the definition. 

In "random effects"/multilevel model, we are (strictly speaking) assuming that given the random effects, the individual effects are all the same. This is very different from the assumptions in the average causal effects model. 

If subjects are recruited in clusters, or if the independence assumption is being violated for whatever reason, then in the average causal effects model, we should account for the lack of independence across observations using Generalized Estimating Equations - These allow you to specify a correlation matrix which represent the correlation in effect estimates between individuals. This framework also naturally accounts for over/under-sampling in subpopulation. 

On another note, although PS-weighting can give consistent estimates of the average causal effects (provided your propensity scores are estimated consistently), the estimates are generally not efficient, and in certain cases, can lead to really big error. Thus, matching/stratification based on PS are generally preferred approaches. 

HTH, 
Tim

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Christina Wei
Sent: 30 November 2013 04:03
To: statalist@hsphsun2.harvard.edu
Subject: st: Multilevel modeling

Hi everyone!  Happy Holidays :)
I have a question about multilevel modeling.  I'm new to this type of
analysis, and am planning on doing the analysis in Stata 12.

The question is:  Is it possible to do a "propensity-score weighted"
multilevel modeling?  I searched the literature and have found none.

I plan to derive my propensity scores from a logistic regression model
regressing baseline group membership on the baseline values of some
selected covariates.  I have a panel/longitudinal data with 5 follow
up visits, but I plan to just use baseline data to derive a "baseline
cross-sectional" propensity score.  I plan to use the propensity
scores to weight-adjust my final multi-level model.  Theoretically,
the probability of being assigned to a specific treatment group is
only "valid" at baseline (e.g. prior to initiation of treatment).

I greatly appreciate any help I could get on this.

~Christina
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