Timeline for Omitting a variable in IV estimation
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 10, 2018 at 23:00 | vote | accept | Badalyan | ||
| Apr 10, 2018 at 21:49 | comment | added | Carlos Cinelli | Hi, @Badalyan in the first graph conditioning on $X$ opens the collider path $Z \leftrightarrow X \leftrightarrow Y$ and induces an association between $Z$ and $Y$ not "via" $D$. Colliding paths are opened when conditioned upon, this other answer might help as well: stats.stackexchange.com/questions/330943/… | |
| Apr 10, 2018 at 15:30 | comment | added | Badalyan | Thanks! Would you be able to expand a little on why Z is not a valid instrument anymore if we control for non-causal X (1st model you explain)? Trying to get some intuition | |
| Apr 7, 2018 at 18:18 | history | edited | Carlos Cinelli | CC BY-SA 3.0 |
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| Apr 7, 2018 at 18:14 | comment | added | Carlos Cinelli | @Badalyan I complemented the answer, and included the derivation of the bias as well in the case where you should include $X$. | |
| Apr 7, 2018 at 18:13 | comment | added | Carlos Cinelli | @Badalyan yes, $X \rightarrow Y$ means X causes Y and $X \leftrightarrow Y$ means the disturbances of $X$ and $Y$ are dependent (for instance, correlated). | |
| Apr 7, 2018 at 18:12 | history | edited | Carlos Cinelli | CC BY-SA 3.0 |
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| Apr 7, 2018 at 7:26 | comment | added | Badalyan | thanks a lot for the illustrative answer! Just to clarify from your DAG, what are the meanings of dashed and solid lines: correlation and causality? | |
| Apr 6, 2018 at 21:58 | history | edited | Carlos Cinelli | CC BY-SA 3.0 |
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| Apr 6, 2018 at 21:19 | history | answered | Carlos Cinelli | CC BY-SA 3.0 |