Why HIGHER? If not, A² also be part of the Y model, implying A² → Y, which violates the exclusion restriction. This shows why the DAG representation suggested in https://t.co/A3919fIxfB is useful. A² = A × A can be described in DAGs, offering intuition for analysis mechanics.
Clear from the DAG, A² acts as an instrumental variable (conditional on A), enabling the identification of the M → Y effect even with U. This is what https://t.co/svoi5djzxH: mediation analysis can be valid (even with U) if the M model has a higher order of A than the Y model.
Why does centering X1 only (not X2) change the coef on X2 while leaving the coefs on X1 and the (centered) interaction term unchanged? For those who enjoy DAGs, here is a slightly modified visual explanation we provided (https://t.co/M1w86PSsqd)
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
DAGs can be used to understand the mechanics of linear interaction analysis. Easy to see the zero correlation between the first-order and interaction terms after centering (though this is not the reason for centering). See more here: https://t.co/zfRnw50PRL
I saw earlier posts on DiD, so I thought some of you might be interested in my recent work in causal inference!
Our paper illustrates how DiD can be used, albeit positivity violation: https://t.co/AWYPHOzabC
Go check it out if interested!
#DiD#causalInference#lordsParadox
Typo correction. <Can two variables have the same values but different impacts? Revisiting Card & Krueger (1994) and Lord’s (1967) paradox> A new perspective & a new answer on Lord’s paradox
These definitions may help to resolve some confusion b/t #DIF (association) and item bias (causation) in the psych measurement literature. Interpretation of spurious differential item functioning: https://t.co/Tj31XARCUk
@KristopherJPre1 thanks for helping me out. Just wanted to understand the new concept from the paper. Seems like there is something more behind it, I didn't realize at first glance. Thanks!
Preacher’s (2006) e.g. to explain “fitting propensity”: A model’s property to fit data better than other. With randomly generated data, he showed that B fits the data better than A.
Do we really need the concept, though? Look at the v-str in A, implying zero-cor b/w V1 & V2.
VanderWeele’s critique of psychological research practices based on factor analysis. https://t.co/NaAE1pAoge It seems to be related to the debate on bifactor models.
@JohannesTextor Hmm.. true. Then maybe fitting propensity might capture something different.. or I think the two constraints may result in different consequences for the fit indexes.
@JohannesTextor Thanks, good point. I think the global fit index he used just compared the covariance matrices. Not considered conditional (in)dependences.
@oscar_olvera100 Thanks for the comment. I read them as a general critique of factor analysis practices, not just about unidimensionality. The point I enjoyed was the causal meanings of factor analysis results. Also, well demonstrated here: https://t.co/1PyS9dvKQV by @mijkenijk
"Race, COVID Mortality, and Simpson's Paradox." Dana Mackenzie, my co-author in #Bookofwhy, has discovered another case of Simpson's Paradox in COVID data, and has posted an interesting analysis of its implications here:
https://t.co/3MfnyC17x5