Data Imputation

United Nations Statistics Division (UNSD)

16 March 2011Santiago, Chile

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Imputation

• Imputation resolves the problems of missing, invalid or incomplete responses identified during editing

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Imputation Options

• Interactive/Manual• Subjective imputation• Donor based imputation• Regression (model) based imputation

• Imputations can be done manually or automatically

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Interactive/Manual Treatment• Manual review of the record• Obvious and easily corrected records can be

interactively treated at the data capture stage– Ex: in a table formatted input, responses may be accidentally

shifted by a row

• Often a subject matter expert reviews the hard copy/original questionnaire– Errors can be found in questionnaire that are otherwise

undiscoverable – Manual imputation procedures, e.g. with historic data

• Re-contact respondent to correct data

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Imputation Cells

• Usually, data is split into imputation cells similar to strata– Example criteria include industry type, geography,

employment size, etc.

• Imputation cells are intended to be relatively homogeneous

• This ensure that imputations are done within similar respondents

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Subjective Imputation• Generally rule or logic based• Can be used when there is only one (reasonably)

possible response to the question– Ex: balance edit – single missing variable in a balance edit– Ex: rule based – if respondent reports zero months worked, then

income can be imputed to be zero

• Can be used when missing/erroneous values can be determined unambiguously from edits– Ex: rule based – if the ratio of anticipated value (e.g. historic

value) to current value is greater than 300, assume a thousands error. Value = 135,000Previous value = 130

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Donor Imputation

• Donor based – replacement by non-erroneous donors– Hot deck – replace with values from the current

survey– Cold deck – replace with values from other

source (e.g. previous surveys)

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Donor Imputation – Substitution• Historic value

– Simple historic value is a cold deck imputation• Historic value with trend

– Trend can be based on growth in another variable within the record, variables in other records, etc.

• This is a very common imputation technique

Suggestions• Useful method when variables or growth rates are stable over

time• Less useful method when changes in variables are of primary

interest– Ex: monthly employment in monthly employment surveys

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Donor Imputation – Mean/Modal

• Missing value is replaced by the mean/modal of respondents for a variable (within a subset or imputation cell of similar respondents)– E.g. if wages is missing for one respondent, the average

wage within the imputation cell can be used

Suggestions• Useful method when variance is small within an

imputation cell

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Donor Imputation – Nearest Neighbor

• For each missing value, find a donor value from a record that is closest to the missing value record based on the distance between a set of variables– E.g. Employees, Additions, Dismissals– Record to be imputed (t):

• E = 100, A = ?, D = ?– Donor record (s):

1.E = 80, A = 10, D = 5 : Distance = 202.E = 90, A = 12, D = 4 : Distance = 10

– Imputed record:• E = 100, A = 12, D = 4

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Donor Imputation – Nearest Neighbor(2)

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Donor Imputation - Ratio

• Missing values are replaced with a ratio of donor record values– E.g.: T = P + C– Record to be imputed:

• T = 400, P = ?, C = ?– Donor record

• T = 100, P = 25, C = 75– Imputed record

• T = 400, P = 100, C = 300

• The donor can be:– Chosen using a distance function– The mean value within the imputation cell

Donor Imputation – Ratio (2)

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Regression (model-based) Imputation

• Regression/model– An imputation model predicts a missing or erroneous

value using a function of some auxiliary variables– Auxiliary variables can be from the current survey or

other sources. E.g. sampling frame (size class, branch of economic activity), historical information (previous period value)

– Regression coefficients can be determined from historic survey data

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Model-based Imputation (2)

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Imputation Process: Fellegi-Holt• An isolated imputation may not satisfy all editing rules• Key principle: the data of a record should be made to

satisfy all edits by changing the fewest possible number of fields.

• Solves edit rules simultaneously through linear programming

• Advantages– Preserves as much original data as possible– Leads to consistent data satisfying all edits

• Disadvantages– All edits specified for a certain record are considered fatal– Powerful edits are required– Not easy to implement

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How/Why to choose one method over the other?

• Depends on specificities of the survey and the available time, cost, expertise, etc.– Ex: a short term survey estimating changes in employment

in the manufacturing sector, using historic data for employment would bias the estimate downwards

• When designing imputation processes, simulations using a variety of imputation techniques should be experimented with

• Fine tuning of imputation process to survey particulars is necessary