Imputation

Imputation

1. Patterns of Missingness

   • MAR
     • missing does not depend on missing value
     • depends on other characteristics
     • doesn't matter too much
     • people live alone, just have been missed by interviewer
   • NMAR
     • Hard to predict
     • working people- harder to get to, are out a lot
     • No info else where about what value should be
     • NO GENERAL SOLUTION
     • certain characteristics less likely to respond
     • lead to bias

2. Non-response

   • levels
     • Unit
     • item
     • Occur at:
       • Household
       • Individual
       • item
   • Deal
     • Do nothing
       • Inconsistent estimates between analysts
       • Different assumptions
       • treat as missing data based on incomplete information
     • Adjust weights
       • at different levels
       • post-stratification
       • reduce or increase bias
       • difficult to ensure consistency for ad-hoc tests
     • Imputation
       • create internally consistent records
       • most feasible for NR
       • preferable
       • preserves relationship between variables
       • reduce NR data
       • increase complexity of variance

3. How to choose

   • unknown rules
   • data is homogeneous
   • levels of erroneous/ missing data
   • kind of missingness
   • auxiliary variables
   • kind of analysis
   • timing or constraints
   • Run imputation study
     • create clean complete dataset
     • model NR patterns
     • make 'holes' to simulate missingness
     • find best method
     • run multiple times
     • measure

4. Methods

   • Stochastic and Deterministic
     • Stochastic
       • Better Statistically, different results each time
       • data taken from random respondant
       • better for distribution
       • less for M M M
       • examples
         • from randomly selected case
         • random regression
         • random donor
     • Deterministic
       • same imputation every time
       • suitable when estimating certain types of aggregates
       • may not preserve shape of distribution
       • not suitable for estimating distribution parameters
       • underestimates variance if standard methods are used
       • examples
         • Deductive
           • based on logical relationships between variables
           • completed anytime
           • derived from edit rules
           • Example: LFS- 'child' < 16
         • mean, median or mode
           • Get more peaks
             • more with same value
           • estimation goes down
           • equivalent to applying same weight to everyone
           • reasonable totals
           • no distributions
           • last resort
         • apply ratio
         • donor methods
   • Ratio / Logistic
     • regression
       • y approx linear to x
       • impute missing y with:
     • ratio of means
     • means of ratio
     • trimming and weighting
       • R is sensitive to outliers
       • more robust R
       • trimming:removes top and bottom
       • Weighting: combines two growths,
         • R=wRt+(1-w)Rt-1
         • w = 0.8
   • Donor Imputation
     • Hot deck
       • common way to find donor
       • deck of completed
       • choice at ranodm
       • sequential
         • order responses
         • donor is most recent
         • PROBLEMS
           • too few
           • limited control
           • too many classes
           • multiple use of donor
       • Hierarchical
         • sorted by class
         • match as many variables as possible
         • preferable but less efficient
     • Nearest neighbour
       • set of donors with similar characteristics
       • calculate distance
       • choose at random from k smallest (k=5)
       • each variable given a weight
     • uses values from fully returned records
     • needs large pools of donors
     • each donor only once
     • preserves population distribution
     • usually stochastic

5. Concept of Classes

   • WHEN MAR
   • can use dependence:
     • partition samples into classes
     • finds similar respondent to impute
   • classes:
     • equivalent to weighting
     • parameters of interest: domains, means or totals
     • social surveys use regression
   • CHAID
     • classification rule to split data, non overlapping
     • predefined rules
     • repeatedly splitting data into more subsets
     • Continuous until criteria is met