Just gave a guest lecture on Bayesian Causal Inference at Williams College, with slides and R code at which is an introduction to our review paper
@fabri_mealli
@FanLiDuke
(I never taught any Bayesian Statistics at Berkeley.)
I just posted my notes for Stat 230 ``Linear Models'' to ArXiv: It covers the linear model and many extensions. I will teach it again in the spring and continue polishing the notes. Comments are welcome.
Z-bias is mysterious. I learned the intuition from Robins: ``If we adjust for the instrumental variable, the treatment variation is driven more by the unmeasured confounder, which could result in increased bias due to this confounder...'' in Section 1.
The inverse of this is also interesting: adjusting for covariates that only predict X (thereby reducing Var(X̃)) increases β, thereby producing bias (known as Z-bias -
@pengding00
notes:).
Think back to facile comments in seminars about "but have you controlled for <something>".
Done with python code to accompany all chapters of
@pengding00
's textbook. IV and matching are not well supported in python, so I might spin those out into a package eventually.
This is an interesting and useful trick. However, centering factors has some special restrictions on the estimated factorial effects when there are more than 3 factors (3 is the magic number there!). This motivates us to write this paper:
A fun fact about regression that many know but maybe is new to you:
If you have an interaction bw continuous X1 and binary X2, mean-centering X1 will make the coefficient on X2 be its marginal effect when X1 is at its mean level rather than 0 without changing the interaction
IPW with the estimated propensity score is another example. The first-stage estimation reduces the asymptotic variance, which surprises many people. A recent paper is Also, Newey&McFadden chapter 6 is about "two-step estimation"
Anyone have other examples of multi-step estimation problems where one needs to propagate uncertainty in first-step estimation into subsequent-stage coefficients?
Generated regressors would be a standard example (eg centering regressors as in qt)
Dennis observed the numerical equivalence of the Horizontal and Vertical Regression in panel data
@gitinmabellayo
based on the OLS interpolator. Now we are interested in the OLS interpolator itself:
Hi
#EconTwitter
! 📈
Interested in causal inference based on panel data?
Check out 👇this recent
#econometrics
paper (accepted in Econometrica) by Dennis Shen, Jasjeet Sekhon and
@UCBerkeley
statisticians
@pengding00
& Bin Yu.
They explore the merger of time series &
Happy to see my paper with
@pengding00
and Anqi Zhao
@DukeU
"Covariate adjustment in randomized experiments with missing outcomes and covariates" is out
This 8-pages paper gives a simple and clean solution to a prevalent practical problem.
The bias-corrected matching estimator has the same form as the doubly robust estimator; see proposition 15.2 of Zhexiao and Fang made the argument rigorous!
@zzzxlin
@johnleibniz
Done another semester teaching causal inference🙂. Updated my course slides, added survival data, labs, corrected more typos this time. Close to 800 pages now. Always more to update next year.
``control'' means many different things in statistics, e.g. treatment-control experiment; control for confounding; case-control study; negative control; controlled direct effect; control function. ``control'' can even mean covariates (good or bad controls).
@pengding00
@carolcaetanoUGA
May I ask what does “control” mean? I feel people usually just call it potential outcome. “Control” sounds like a mediation terminology.
@linstonwin
@Apoorva__Lal
@FelixThoemmes
@matt_blackwell
Also, the bootstrap is always a panacea to problems like this. But we need to center x in each bootstrap sample. If we center x before the bootstrap, we will get the EHW se again. I included this as a numerical exercise in Problem 9.2 of the book:
@AngYu_soci
In theory (and intuitively), if you include more terms in the logit pscore model, you can get better efficiency and potentially achieve the efficiency bound.
@Yiqiao_Zhong
@karlrohe
I think Gauss showed more: for OLS to be optimal, the noise must be Gaussian. The other way is easier to show and it is a current textbook result.
@Apoorva__Lal
Maybe you can try a simpler variance estimator in the first displayed formula on page 208 of It is equivalent to Otsu and Rai (2017)'s bootstrap variance estimator. But you do not need to bootstrap.
@Apoorva__Lal
@johnleibniz
@zzzxlin
This seems a hard question in practice. Maybe the best way is to display a sequence of estimates and se's with varying M.
@Apoorva__Lal
@RobDonnelly47
I drew the DAGs for M-bias and Z-bias using \xymatrix -:)
$$
\xymatrix{
U_1 \ar[dd]\ar[dr] &&U_2 \ar[dd]\ar[dl] \\
&X& \\
Z && Y
}
$$
and
$$
\xymatrix{
&&&U \ar[dl]_b \ar[dr]^c \\
X \ar[rr]^a &&Z\ar[rr]^\tau && Y
}
$$