Using FIML in R with Multilevel Data (Part 3) A recurring question that I get asked is how to use full information maximum likelihood (FIML) when performing a multiple regression analysis BUT this time, accounting for nesting or clustered data structure. For this example, I use the the leadership dataset in the mitml package (Grund et al., 2021). We’ll also use lavaan (Roseel, 2012) to estimate the two-level model. The chapter of Grund et al.

ROUGH NOTES: [let me know if you spot any errors– there might be a couple!] Often, in randomized control trial where individuals are randomly assigned to treatment and control conditions, covariates are included to improve precision by reducing error and improving statistical power. However, when binary outcomes are used (e.g., patient recovers or not), there are several additional concerns that have gone unnoticed by many applied researchers.
Take a simulated example where our true model data generating process is (to keep things simple, the intercept is zero and the parameters are both set to 1):

Using FIML in R (Part 2) A recurring question that I get asked is how to handle missing data when researchers are interested in performing a multiple regression analysis. There are so many excellent articles, books, and websites that discuss the theory and rationale behind what can be done. Often, what is recommended is to either use full information likelihood (FIML) or multiple imputation (MI). Many excellent articles explain in detail how these work.

Earlier this year, I wrote an article on using instrumental variables (IV) to analyze data from randomized experiments with imperfect compliance (read the manuscript for full details; link updated; it’s open access). In the article, I described the steps of IV estimation and the logic behind it.
The sample code using two stage least squares regression (the correct analysis) is shown below (see article for specifics):
library(ivpack) dat <- read.csv('http://faculty.missouri.edu/huangf/data/pubdata/pare/ivexample.csv') head(dat) ## assign takeup y ## 1 0 0 0 ## 2 0 0 0 ## 3 0 0 0 ## 4 0 0 0 ## 5 0 0 0 ## 6 0 0 0 tail(dat) ## assign takeup y ## 195 1 1 9 ## 196 1 1 10 ## 197 1 1 10 ## 198 1 1 12 ## 199 1 1 11 ## 200 1 1 9 summary(dat) ## assign takeup y ## Min.

Illustrates why OVB is an issue This issue plagues a lot of the analysis using secondary or observational data
Data are already existing We may have unobserved characteristics that were not collected To illustrate how OVB may affect regression results, we examine some simulated data.
Create some correlated data library(stargazer) #to create simpler regression output library(gendata) #to simulate data #1 create two correlated variables X1 and X2 (r = .

Instrumental variables, ITT, and TOT Based on:
Angrist, J. D. (2006). Instrumental variables methods in experimental criminological research: what, why and how. Journal of Experimental Criminology, 2, 23-44. https://doi.org/10.1007/s11292-005-5126-x
Evaluation of the Minneapolis Domestic Violence Experiment (MDVE): Evaluated the police response to domestic violence reports. Experiment conducted in 1981-82 by Lawrence Sherman and Richard Berk. Police may be reluctant to get involved for various reasons (e.g., might be viewed as a private matter, may not want to get involved).

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