How to Combine the Results after the Multiply Imputation

How to Combine the Results after the Multiple Imputation

The overall estimate of Q is simply the average of the M estimates from M multiple imputed datasets.

The overall variance of is

Where the average variance of M within-imputed datasets () is and the variance between-imputed dataset is

The overall degree of freedom (df) is

Where the df of imputed datasets is and the df of observed data is


If the df of the complete data (df_completed) are large [Notes: for complex sampling design, df_complete = # of PSU - # of Strata], the overall degree of freedom is

Then, the confidence intervals can be

The estimated percent rate of missing information for Q is

Notes: Usually M = 5 or 10 is enough, but the M is better to be great than the percent rate of missing information. 

Can 'margins' be used after 'mi estimate'?

Can 'margins' be used after 'mi estimate'?

The -margins- command may not be used in the usual way after -mi estimate-. You'll need to write a short "wrapper command" that can be run with the -mi estimate- prefix. My colleagues outlined the method on Statalist: Average marginal effects for a multiply imputed complex survey. You'll want to change the 11 in the -version 11- statement to 12. One of our FAQs will also be helpful: How can I combine results other than coefficients in e(b) with multiply imputed data? - by A Statistician, Stata


Here is my modified program based on codes of UCLA Stata Portal

use http://www.ats.ucla.edu/stat/data/hsbmar, clear
/* set MI dataset */
mi set mlong
mi register imputed female math read science socst
mi svyset [pw=write], strata(ses)
mi impute chain (logit) female (regress) math read science socst ///
       =ses write awards, add(10) rseed(123456)
/* program */
capture program drop mimargins
program mimargins, eclass properties(mi)
  version 12
  svy: logit honors i.female##i.prog read math science socst
  margins female#prog, post
end
/* run the program */ 
mi estimate, cmdok: mimargins 1
matlist r(table)'*100, tw(20) format(%8.2f)
mi estimate (_b[1.female#2.prog]/_b[1.female#1bn.prog]): mimargins 1

Notes: The 'cmdok' option forces 'mi estimate' to estimate the current Stata unsupported model. The 'cmdok' is not necessary because of already including the 'properties(mi)' in the program.

mi estimate: svy: logit honors i.female##i.prog read math science socst
mi test 1.female#2.prog 1.female#3.prog

mi estimate (diff:1.female#2.prog-1.female#3.prog), saving(miest, replace): svy: logit honors i.female##i.prog read math science socst
mi testtransform diff

mi estimate (rdiff:1.female#2.prog/1.female#3.prog - 1) using miest
mi testtr rdiff


Useful Resources:

• MIMRGNS: Stata module to run margins after mi estimate
• UCLA: How can I get margins and marginsplot with multiple imputed data?
• Klein (2016): Marginal Effects in Multiply Imputed Datasets
  

Multiple Imputation (MI)

Multiple Imputation (MI)

• Hippel (2019): How many imputations do you need?
• SAS (2016): Survey Data Imputation with RPOC SURVEYIMPUTE
• A very good classic reference by Donald B. Rubin (1996). Multiple Imputation After 18+ Years
• Formula for Combining Results across the Multipe Imputed Datasets.
• Sterne (2009). Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls
• Kenward (2007). Multiple imputation: current perspectives or full text here
• Graham (2007). How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory
• Books: 
• Applied Missing Data Analysis, see Google book as well.
• Applied Survey Data Analysis is one of my favorite books of complex sampling data analysis with a whole chapter about multiple imputation (Chapter 11). The way of teaching is very intuitive to an epidemiologist without much high level math background.
• Paul Allison: Multiple Imputation for Missing Data: A Cautionary Tale
• Multiple Imputation Online is not updated for a while, but this website is still have some useful linkages. It mentioned a few software for MI analyses; it doesn't include Stata, which is an my current first choice.
• SSCC: Multiple Imputation in Stata
• UCLA: Multiple Imputation in Stata
• Stata: How can I combine results other than coefficients in e(b) with multiply imputed data?
• Stata: Multiple imputation in Stata (2010) by Bill Rising. Multiple imputation using Stata’s mi command by Yulia Marchenko
• UCLA: How can I get margins and marginsplot with multiply imputated data?
• UCLA: How can I get margins for a multiply imputed survey logit model?
• Blog: Can 'margins' be used after 'mi estimate' for complex samplied data with 'svy' in Stata?
• Multiple Imputation FAQ by Joe Schafer
• SAS: Multiple Imputation for Missing Data