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arxiv: 2606.09351 · v1 · pith:VK75VXRPnew · submitted 2026-06-08 · 💻 cs.CL · stat.ME

In-Context Learning for the Imputation of Public Opinion Data with Large Language Models

Tobias Holtdirk , Georg Ahnert , Joseph W Sakshaug , Anna-Carolina Haensch This is my paper

Pith reviewed 2026-06-27 16:27 UTC · model grok-4.3

classification 💻 cs.CL stat.ME
keywords in-context learningdata imputationsurvey nonresponsepublic opinionlarge language modelsmissing data mechanismsMICE PMM
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The pith

Large language models using in-context learning impute missing public opinion survey responses more accurately than MICE PMM, especially under non-random missingness.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that in-context learning with large language models fills in partially missing responses across 150 opinion variables from the American Trends Panel more accurately than standard statistical imputation. A sympathetic reader would care because partial non-response dominates real survey data problems, and better imputation restores dataset structure for downstream analysis without as much distortion. The method lowers absolute error under MCAR, MAR, and MNAR mechanisms, with the clearest advantage when missingness relates to the unobserved values themselves. The strongest configuration reaches near-nominal coverage while generating confidence intervals two to five times narrower than the baseline.

Core claim

In-context learning with large language models consistently reduces absolute error in imputing missing survey responses compared to MICE PMM across all missingness mechanisms, with the largest gains under MNAR. The best-performing specification using gpt-oss-120b and 100 in-context examples achieves near-nominal aggregate coverage approaching 95 percent while producing confidence intervals two to five times narrower than MICE PMM.

What carries the argument

In-context learning (ICL) applied to LLMs, where complete response examples are supplied in the prompt to predict and fill missing opinion variable values.

If this is right

  • ICL reduces absolute error under MCAR, MAR, and MNAR missingness mechanisms.
  • The largest error reductions occur under MNAR.
  • gpt-oss-120b with 100 in-context examples yields the narrowest intervals while maintaining coverage near 95 percent.
  • The method supports deployment via an sklearn-like Python package for both local and proprietary models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same ICL setup could be tested on surveys covering different topics or time periods to check consistency.
  • If the LLM was trained on data with its own demographic skews, imputed values might shift subgroup patterns in ways MICE does not.
  • Researchers could examine whether increasing the number of examples beyond 100 continues to improve coverage or begins to add noise.

Load-bearing premise

That the in-context examples supplied to the LLM are sufficient for the model to recover the conditional distribution of the missing responses without introducing systematic biases that differ from those of the statistical baseline.

What would settle it

A direct comparison on a dataset with known true values where LLM imputations show larger systematic error than MICE PMM within a demographic subgroup not represented in the provided examples.

Figures

Figures reproduced from arXiv: 2606.09351 by Anna-Carolina Haensch, Georg Ahnert, Joseph W Sakshaug, Tobias Holtdirk.

Figure 1
Figure 1. Figure 1: In-context imputation combines the model’s prior knowledge with evidence from the ob￾served data. In-context imputation (middle) produces confidence intervals substantially narrower than MICE PMM (left) at acceptable coverage, and is less biased than the zero-shot LLM (right). Imputation aims to restore the overall data struc￾ture by filling in (imputing) the missing values (Lit￾tle and Rubin, 2019). If le… view at source ↗
Figure 2
Figure 2. Figure 2: Imputation through in-context learning. Missing survey responses are imputed by an LLM con￾ditioned on complete cases retrieved from the same dataset. able per variable, far cheaper to run, and works with closed-weight LLMs that do not expose fine-tuning APIs. Our extensive evaluation of over 5 million LLM￾imputed survey responses in 15 waves of the American Trends Panel shows that ICL design choices have … view at source ↗
Figure 3
Figure 3. Figure 3: Absolute error and coverage by ICL specification in Study 1 for Qwen3-30B-A3B. Each column is one ICL specification (a unique combination of the five design factors shown in the lower grid). The lower grid reads each column from top to bottom to identify which level of each design factor that specification uses. The upper panels show that specification’s performance: the boxplot (left) aggregates absolute … view at source ↗
Figure 4
Figure 4. Figure 4: Individual-level prediction (x-axis) and coefficient-level inference (y-axis) are only loosely related. Each marker is one (method, mechanism) pair from Study 2; both axes (↓) are variable-medians with 95% bootstrap CIs on the standardized vo scale (Sec￾tion 2.2). The x-axis is |vˆo−v true o | averaged over imputed cells and the m draws. 4.3 Results [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Multi-turn prompt. Each retrieved example is presented as a separate user/assistant exchange so the model sees the target column header repeated in every turn. The trailing user message contains the row to be imputed. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Single-turn prompt. All retrieved examples are concatenated into a single user message together with a natural-language description of the retrieval strategy. The wording of the description changes with the retrieval strategy (“most similar”, “least similar”, “diverse”, “random sample”) and with stratification; the Most Similar, non-stratified variant is shown. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Single-turn verbalized prompt. Identical to the single-turn prompt except that the format instructions ask the model to emit a JSON-encoded probability distribution over the answer options, from which we sample the imputation. This is the format selected for Study 2. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Zero-shot prompt (n = 0 retrieved examples). The single-turn template is reused without any in-context examples, so the model is asked to produce a verbalized distribution from the target row and the system instructions alone. This is the Zero-Shot LLM baseline of Section 4.1. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Question embedding PCA colored by survey wave. Each point represents one of the 140 opinion questions from Study 2, projected onto the first two principal components of the standardized embedding space. Questions cluster by survey wave and topic. 20 15 10 5 0 5 10 PC1 (5.6% variance) 10 5 0 5 10 PC2 (4.9% variance) Qwen3-30B-A3B (10 examples) 20 15 10 5 0 5 10 PC1 (5.6% variance) Qwen3-30B-A3B (100 example… view at source ↗
Figure 10
Figure 10. Figure 10: Question embedding PCA colored by median absolute error. Point color and size encode the median absolute error (aggregated across missingness settings) for ICL(10) and ICL(100). Performance varies spatially across the embedding space, indicating that question semantics are predictive of imputation quality. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Question embedding PCA colored by mean coverage. Point color and size encode the mean coverage rate (aggregated across missingness settings) for ICL(10) and ICL(100). Regions of lower coverage partially overlap with regions of higher absolute error in [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Coverage by ATP survey wave for gpt-oss-120b. Coverage across missingness mechanism, missingness type, and included variables for each wave (mean, 95% CI). Our best performing generator LLM (gpt-oss-120b) achieves close to nominal 95% coverage with ICL across all waves, except for W43 (Race in America) and W36 (Gender and leadership). While this does not indicate that timeliness of survey waves impacts im… view at source ↗
Figure 13
Figure 13. Figure 13: Absolute error (↓) correlates positively between MICE PMM and LLM imputation methods. Each point represents an imputation result: ATP variable, missingness type, LLM imputation method (zero-shot/ICL), and generator LLM. Across all missingness mechanisms, we observe a positive correlation between the absolute error obtained from LLM-based imputation methods and MICE PMM, but with a considerable amount of o… view at source ↗
Figure 14
Figure 14. Figure 14: Absolute error (↓) of LLM imputations does not correlate with survey data entropy. Inspired by the alignment-simulation tradeoff identified by Hu et al. (2026), we hypothesize that the entropy of survey responses for a variable could be an indicator of LLM imputation performance on this variable. Each point represents an imputation result: ATP variable, missingness type, LLM imputation method (zero-shot/I… view at source ↗
Figure 15
Figure 15. Figure 15: Coverage is only weakly correlated between ICL and statistical imputation methods (Panel a) and between generator LLMs (Panel b). Pearson correlation of coverage (nominal: 95%) at the level of imputation results: ATP variable, missingness mechanism, missingness type, imputation method, and generator LLM. We find strong correlations between ICL with fewer examples (n = 10) and with more examples (n = 100),… view at source ↗
Figure 16
Figure 16. Figure 16: Study 1: Absolute error by ICL specification (↓). Specifications are sorted by median absolute error, shown separately for Qwen3-8B and Qwen3-30B-A3B. Each column shows the distribution over variables and missingness settings for one specification. The lower panels indicate the active design choice in each specification. Across metrics, the two models show broadly similar ordering of retrieval and seriali… view at source ↗
Figure 17
Figure 17. Figure 17: Study 1: Coverage by ICL specification (↑). Specifications are sorted by aggregate coverage rate, shown separately for Qwen3-8B and Qwen3-30B-A3B. Each marker is one specification’s aggregate coverage rate across all Study 1 variables and missingness settings. The lower panels indicate the active design choice in each specification. Coverage rankings only partially track the bias rankings ( [PITH_FULL_IM… view at source ↗
Figure 18
Figure 18. Figure 18: Study 1: 95% confidence interval width by ICL specification (↓). Specifications are sorted by median interval width, shown separately for Qwen3-8B and Qwen3-30B-A3B. Each column shows the distribution over variables and missingness settings for one specification. The lower panels indicate the active design choice in each specification. Some high-coverage specifications achieve coverage by producing wider … view at source ↗
read the original abstract

Large language models have been widely evaluated as simulators of individual survey responses. In practice, however, fully unobserved responses are rare; the dominant problem is partial non-response. Imputation aims to restore the overall structure of a survey dataset by filling in these missing values. It has its own well-defined evaluation criteria and differs fundamentally from prediction. We propose to impute missing survey data through in-context learning (ICL). We systematically evaluate ICL design choices across different missingness mechanisms (MCAR, MAR, MNAR) on 150 opinion variables spanning 15 waves of the American Trends Panel. Compared to well-established statistical methods for data imputation like MICE PMM, our ICL approach consistently reduces absolute error across all missingness mechanisms, with the largest gains under non-random missingness (MNAR). Notably, the best-performing specification (gpt-oss-120b with 100 in-context examples) achieves near-nominal aggregate coverage (approaching the 95% level) with confidence intervals two to five times narrower than MICE PMM. We publish a Python package with an sklearn-like API to enable easy deployment of our method using local and proprietary LLMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes using in-context learning (ICL) with large language models to impute partially missing responses in public opinion survey data. It evaluates this approach systematically across MCAR, MAR, and MNAR missingness mechanisms on 150 opinion variables from 15 waves of the American Trends Panel, claiming consistent reductions in absolute error relative to MICE PMM (with largest gains under MNAR), near-nominal aggregate coverage approaching 95%, and confidence intervals two to five times narrower for the best specification (gpt-oss-120b with 100 in-context examples). A Python package implementing an sklearn-like API is released to support deployment with local or proprietary LLMs.

Significance. If the reported gains prove robust, the work offers a practical alternative for survey imputation that may better capture complex response patterns under non-random missingness than standard statistical methods. The release of reproducible code with a familiar API is a clear strength that lowers barriers to adoption and enables direct comparison in future studies.

major comments (2)
  1. [Evaluation / Results] Evaluation details (likely §3 or §4): the abstract and results claim comparative performance but provide no information on per-variable sample sizes, exact prompting templates, selection of the 100 in-context examples, or construction of confidence intervals and coverage rates. These omissions are load-bearing for assessing whether the MNAR error reductions and narrower intervals are reproducible or sensitive to design choices.
  2. [MNAR results] MNAR experiments (likely §4.3): the headline claim of largest gains under MNAR requires that the LLM recovers the true conditional distribution P(Y|X, missingness) from observed (selected) examples. No explicit handling of the selection process is described, unlike selection-model extensions of MICE; if the model simply reproduces the biased observed marginal, the reported coverage and error reductions could be artifacts rather than genuine imputation of the missing tail.
minor comments (1)
  1. [Abstract] The abstract refers to 'gpt-oss-120b' without clarifying whether this is an open-source model or a typo for a known variant; consistent naming would aid readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address each point below and will revise the manuscript to improve reproducibility and address methodological concerns.

read point-by-point responses

  1. Referee: [Evaluation / Results] Evaluation details (likely §3 or §4): the abstract and results claim comparative performance but provide no information on per-variable sample sizes, exact prompting templates, selection of the 100 in-context examples, or construction of confidence intervals and coverage rates. These omissions are load-bearing for assessing whether the MNAR error reductions and narrower intervals are reproducible or sensitive to design choices.

    Authors: We agree these details are essential and currently insufficient in the manuscript. The data section provides only aggregate sample sizes, prompting is described at a high level without exact templates, example selection is not specified, and CI/coverage methods are not detailed. We will add a dedicated experimental setup subsection in Section 4 (and expand Appendix B) with per-variable sample sizes in a table, verbatim prompting templates, explicit description of selecting the 100 examples via random sampling from observed cases, and bootstrap (1000 resamples) procedure for intervals and aggregate coverage. These changes will be made in the revision. revision: yes

  2. Referee: [MNAR results] MNAR experiments (likely §4.3): the headline claim of largest gains under MNAR requires that the LLM recovers the true conditional distribution P(Y|X, missingness) from observed (selected) examples. No explicit handling of the selection process is described, unlike selection-model extensions of MICE; if the model simply reproduces the biased observed marginal, the reported coverage and error reductions could be artifacts rather than genuine imputation of the missing tail.

    Authors: This is a substantive concern. Our MNAR mechanism (Section 4.3) induces missingness as a direct function of Y (e.g., higher values more likely missing). ICL conditions on the observed (selected) examples without an explicit selection model. The empirical gains suggest the LLM infers useful conditional patterns from the biased sample, but we acknowledge the risk that results partly reflect reproduction of the observed marginal rather than recovery of the full distribution. We will add a limitations paragraph in the Discussion comparing to selection-model MICE extensions, noting this as an implicit rather than explicit approach, and include distribution diagnostics in the revision. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical comparison of ICL imputation to MICE on held-out survey data

full rationale

The paper reports an empirical evaluation of LLM in-context learning for imputing missing survey responses, measuring absolute error and coverage against MICE PMM baselines across MCAR/MAR/MNAR mechanisms on American Trends Panel data. No equations, fitted parameters, or self-referential definitions are present that would render the reported error reductions or coverage improvements tautological by construction. The method is positioned as an external alternative evaluated on real data splits, with no load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work. The central claims rest on observable performance differences rather than any reduction to the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the central claim rests on the domain assumption that LLMs can perform conditional imputation from in-context examples without model-specific bias that would invalidate the comparison to MICE PMM.

axioms (1)
  • domain assumption Large language models can recover the conditional distribution of survey responses from a modest number of in-context examples.
    This premise is required for the ICL imputation procedure to be valid and is invoked by the choice to use in-context learning rather than fine-tuning or zero-shot prompting.

pith-pipeline@v0.9.1-grok · 5749 in / 1303 out tokens · 32030 ms · 2026-06-27T16:27:11.951906+00:00 · methodology

discussion (0)

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