Lucy D'Agostino McGowan

I also don't think you want random error here: ```r plogis(beta0 + beta1 * x1 + beta2 * x2 + beta3 * x3 + rnorm(n, sd = .1)) ``` because...

Ah maybe I’m wrong! Is plogis deterministic? This seems to say yes! Edit: oh yeah of course it is 🫣 my poor little brain hahaha. I still think we don’t...

``` library(tidyverse) n

I thought we had this linked somewhere but couldn't find it in the issues. @malcolmbarrett this is a nice paper for generalized propensity scores with different targets: https://arxiv.org/pdf/1808.05339.pdf

Code to do weighted correlation by hand if helpful: ```r causal_collider_wts |> summarise( exposure_w = sum(swts * exposure) / sum(swts), covariate_w = sum(swts * covariate) / sum(swts), numerator = sum(swts...

Also this: https://dash.harvard.edu/bitstream/handle/1/25207409/90937280.pdf?sequence=2&isAllowed=y

Ding, Peng, and Luke W. Miratrix. 2015. “To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias.” Journal of Causal Inference 3 (1) (January 1). doi:10.1515/jci-2013-0021.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3166439/

> [Wooldridge (2009)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3166439/#R35) and [Pearl (2010)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3166439/#R12) have shown that when bias due to unmeasured confounding is present, control for an instrument can amplify the existing confounding bias.