Cool, thanks for sharing! Not directly for teaching. I wanted to show a psychology colleague sample selection bias as a source of endogeneity (context: convenience sample of psych students) and then was interested to cover other sources of endogeneity as well (such as measurement error)

But I get the feeling that I am overthinking and it's weekend time now 😅

X_true = X_obs - X_error, stacking that into the Y equation gives: Y=beta_true*X_obs + (u-beta_true*X_error) where the last term is the residual here, which somehow would imply a correlation between the measurement error and the residual in the DAG

yeah, using path tracing rules/cov alg it would be

b_obs = Cov(X_o,Y) / V(X_o) = b_true*V(X_t) / V(X_t) +V(x_error)

so if V(x_error)=0 everything is fine. I somehow suspect, that the DAG is not the right one but I am lacking arguments here..
If you rearrange the equation for X_obs you get

maybe interesting for causal inference experts @dingdingpeng.the100.ci @p-hunermund.com

probably i am missing something very basic in the DAG line of thought?

I mean it's the DAG of the data generating process:

library(tidyverse)
N <- 5000
df <- tibble(
X_true = rnorm(N),
X_error = rnorm(N),
X_obs = X_true + X_error,
Y_error = rnorm(N),
Y = 3*X_true + Y_error
)

summary(lm(Y ~ X_obs, data = df))

Do you mind sharing a reference or two on that issue? I’ve often heard similar points raised about multivariate analyses, but I’ve never actually encountered literature dealing with it. Would love to read more!

Without disentangling social from genetic transmission, parent–offspring associations may reflect changes in either social closure or heritability. Analyses that distinguish the two suggest that large parts of the association is due to genetic not social transmission.

I often wonder what the take-home message from these total estimates of intergenerational transmission is. Increase in parent-offspring association may be due to increasing heritability or more social closure - two very different mechanisms.