Multiple%20Imputation

1
Multiple Imputation

• Stata (ice)
• How and when to use it.

2
How ice() works

• Each variable with missing data is the subject of
  a regression.
• Typically all other variables are used as
  predictors
• Estimate ß, s via the regression
• Draw s from its posterior distribution
  (non-informative prior)
• Draw ß from its posterior distribution
  (non-informative prior)
• Find predicted values YXß, then either
• Keep Y for the missing values (default option)
• Predictive Mean Matching
• Move on to the next variable, using the
  newly-predicted values
• Cycle through the variables a number of times (10
  is default)

3
Assumptions

• Missing at Random
• No getting around this one. MCAR is fine, of
  course.
• Distinct Parameters
• Does the missing data mechanism govern what
  data-generating parameters you can see? Ex
  limits of detection.
• Adequate Sample Size
• Hard to quantify. Regression on continuous
  variables doesnt take much, but other methods
  certainly can
• Convergence to a Posterior Distribution
• Standard MI (such as Proc MI) is known to
  converge to a posterior distribution with enough
  iterations. Ice() does not have this guarantee.
  This is typically ignored when ice() is used.

4
Predictive Mean Matching

• We have Ymis for the variable with missing
  information
• Previously
• Find the yobs that is closest to ymis, fill in
  the missing observations value with the true
  value of the yobs
• Was the default behavior for previous versions of
  ice()
• Could be a problem not enough variability.
• Currently
• Find a set of yobs that are close to ymis, choose
  one randomly, fill in the missing observations
  value with the true value of the yobs
• Invoked by using the match argument

5
Other Regression Methods

• Multinomial Logistic Regression
• For categorical variables, ordered or unordered
• Finds a probability for each category value, then
  imputes a value using those probabilities.
• My advice try to avoid using it, as Ive found
  its results to be incorrect (biased)
• Ordinal Logistic Regression
• For ordered categorical variables
• My advice it seems to work well, but it needs a
  large (ngt1000) sample size to work

6
Useful Material How to run ice()

• Getting the program
• Help -gt Search -gt Search all ice imputation
• Click on st_0067_2 (www.stata-journal.com)
• Click click here to install
• This gets you ice and micombine, as well as a few
  other commands

7

• Running ice
• Have the dataset open
• insheet using "C\path\example.csv", clear
• Four variables with missing information
• npnitm binary variable
• npceradm, npneurm continuous variables
• npbrkm 3-category ordered variable
• Four variables with complete data
• We need to make dummy variables for categorical
  variables
• recode npbrkm (40) (51) (60) (..),
  generate(brk5)
• recode npbrkm (40) (50) (61) (..),
  generate(brk6)

8

• Running ice, continued (1)
• Call ice()
• ice educ mmselast npdage npgender npnitm npceradm
  npbrkm brk5 brk6 npneurm using "C\path\outfile",
  m(5) passive(brk5npbrkm5 \ brk6npbrkm6)
  substitute(npbrkmbrk5 brk6) cmd(npbrkmmlogit,
  npnitmlogit)
• Heres what the code pieces do
• educ npneurm Variables to be used for
  imputation
• using "C\path\outfile the result outfile.dta
• m(5) 5 imputed datasets
• passive(brk5npbrkm5 \ brk6npbrkm6)
• Stata will not impute for brk5 and brk6 they
  will be updated from the new values in npbrkm

9

• Running ice, continued (2)
• Heres what the code pieces do
• substitute(npbrkmbrk5 brk6)
• npbrkm wont be used to impute other variables
  brk5 and brk6 will be used in its place
• cmd(npbrkmmlogit, npnitmlogit)
• npbrkm will have multiple logistic regression
• npnitm will have logistic regression
• all other variables with missing data use default
  methods
• continuous OLS
• n2 categories Logistic Regression
• ngt2 categories Multinomial Logistic Regression

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Results

• A dataset, outfile.dta
• use C\path\outfile.dta, clear
• New variables
• _i row number per dataset (not generally used)
• _j imputed dataset number (same as _Imputation_
  from Proc MI)
• Analyzing the results using micombine, an example
• xi micombine regress mmselast npgender npnitm
  npceradm i.npbrkm
• xi expand interactions. Used to break npbrkm
  into dummy variables for the analysis
• micombine automatically does the MI analysis,
  using _j to distinguish between the imputed
  datasets
• See its help file for a list of supported
  regression commands
• For some methods, SASs MIANALYZE may be needed

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The end.

• Questions?