Is hot deck the same as filling in the mean?

No. It generally borrows actual donor values.

Can a donor be reused?

Yes, depending on the procedure; reuse should be monitored.

Does the method solve nonresponse automatically?

No. Its success depends on donor comparability, missingness assumptions, and appropriate uncertainty estimation.

AI Glossary / Statistics and probability / Intermediate

Hot deck imputation

Definition

Hot deck imputation fills a missing value using an observed value from a suitable donor record in the same current dataset or survey collection. Donors are selected to resemble the recipient on relevant observed characteristics. The method supplies plausible values while retaining an explicit distinction between reported information and imputed information; it does not recover a person's or business's unknown true response.

What it means

Rather than replacing every missing answer with one overall average, the method borrows an answer from a comparable responding case. A missing support-duration value might receive the duration of another case with the same issue type and service channel.
The word hot refers to donors drawn from the collection being processed. Cold deck approaches use previously collected or external information. Neither label alone tells you whether the assumptions are credible or the uncertainty has been handled properly.

How it works

Identify genuine missing values and distinguish them from valid zeros, not-applicable items, and logically determined values. A question skipped correctly should not automatically receive a donor's response.
Define eligible donors and matching variables that help explain both the missing variable and response patterns. Matching can use adjustment cells, nearest neighbors, or a specified sequential procedure. Random selection among eligible donors is common, but some hot deck procedures select donors deterministically.
For a random cell-based method, divide records into comparable groups and draw a responding donor for each recipient within its group. Record the donor identifier, selection rule, imputed variable, and any fallback used when no eligible donor exists.
More matching characteristics can improve comparability but also create sparse or empty cells. Establish a defensible rule for relaxing matches or using another method. Quietly borrowing from an unrelated group can conceal a serious assumption change.
A conventional justification is that, after conditioning on the matching information, respondents adequately represent recipients for the missing variable. Missingness related to the unobserved value even within those groups can still bias results. Plausible-looking completed data do not verify this assumption.
Borrowing several related values together can help maintain their joint coherence, provided donors are compatible with the recipient's observed information. Separate variable-by-variable borrowing can create inconsistent combinations. Check logical restrictions and relationships after imputation.
Do not treat copied values as new independent measurements. Repeated donor use and missing-data uncertainty affect standard errors. Appropriate replication, fractional imputation, or a properly designed multiple-imputation procedure may be needed for inference. Simply repeating random draws is not sufficient to establish that a multiple-imputation method is statistically proper.
For machine-learning evaluation, define the donor procedure within each training split and keep validation outcomes out of donor selection. Document how the procedure will operate when new cases arrive. Otherwise, preprocessing can leak information or rely on donors unavailable in actual use.

Three practical examples

A business survey borrows a missing item response from a similar responding business in the current survey.
An AI training-data team fills missing customer-service durations from eligible cases sharing observed service characteristics, while preserving imputation flags.
A data-quality team compares estimates under alternative donor rules to see whether sparse groups drive the conclusions.

Think of it this way

Think of replacing a missing recipe card with a card from a comparable kitchen in the same collection. The replacement is an actual recipe, which helps plausibility. It is still not evidence of what the original kitchen cooked, and a poor match can mislead.

Worked example

Suppose group A has observed values 2, 4, and 6 plus one missing value. Group B has observed values 10 and 14 plus one missing value. Independently choose one donor uniformly within each group.
One possible draw assigns 6 to the missing A record and 10 to the missing B record. The completed total is 2 + 4 + 6 + 6 + 10 + 14 + 10 = 52, and the mean is 52/7, approximately 7.4286.
The expected A imputation is 4; the expected B imputation is 12. Since the observed total is 36, the expected completed total is also 52. Other donor draws can give different totals.
Conditional on these fixed donor pools, the random donor values have variances 8/3 and 4. Independence gives completed-mean variance (8/3 + 4)/49 = 20/147, approximately 0.13605. This is only the variability caused by these random draws, not a full survey variance or all uncertainty about missing values.

Illustrative case study

In this fictional case, Beacon Service Analytics uses overall-mean replacement for missing case durations. The team switches to donors within issue-type and channel groups, then discovers one rare group has no responding donor. It flags those cases and investigates alternative rules instead of silently using common-case donors. Its report retains imputation indicators and shows how average duration changes across plausible donor choices before the figures support staffing decisions.

Common misconceptions and mistakes

An observed donor value is not the recipient's known true value. Preserving the range of observed values does not guarantee preservation of correlations or rare events. Hot deck does not always mean random selection, and nearest-neighbor imputation is one possible approach rather than the whole definition.
A completed table can still contain biased estimates. Treating all completed entries as observed can understate uncertainty. More matching variables are not always better when they leave no usable donors.

Business use

Hot deck imputation can support consistent survey outputs and practical analysis of incomplete operational records. Assess donor availability, reuse concentration, imputation rates, and sensitivity of key results. Retain original missingness information so analysts can distinguish reported facts from statistical replacements and evaluate whether important groups depend heavily on imputation.

Check your understanding

Why should group A not automatically borrow from group B in the example?

Answer: Their observed values differ systematically, so cross-group borrowing changes the implied assumptions.

Does the calculated variance include sampling uncertainty?

Answer: No. It conditions on the observed donor pools and describes only random donor selection.

Related terms

Missing data
Donor (imputation)
Imputation variance
cold deck imputation
missing at random
multiple imputation

Learn next

Learn missing-data mechanisms and donor matching first. Then study survey variance methods, joint consistency checks, and validation designs for preprocessing incomplete machine-learning data.

Sources

US Census Bureau, Data Editing and Imputation: https://www.census.gov/programs-surveys/sipp/methodology/data-editing-and-imputation.html US Census Bureau, Changes to Imputed Earnings: https://www.census.gov/programs-surveys/sipp/tech-documentation/user-notes/2018-usernotes/2018-chg-imputed-earnings.html OECD, Oslo Manual 2018, Methods for collecting data on business innovation: https://www.oecd.org/en/publications/oslo-manual-2018_9789264304604-en/full-report/component-16.html

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