Testing Ehrenberg-Bass regularities against four archived retail datasets
Revision notice — July 2026
This is version 0.2. The original version 0.1 (September 2025) is archived and remains available.
Re-auditing the original analysis code and logs against the published text showed that several statements in v0.1 exceeded what the code measured. Five claims are withdrawn:
- Top-decile Double Jeopardy deviation. No top-decile or middle-quantile split exists in the script. The reported r=0.627 was computed across all 27 retained labels.
- R²=0.472 as response to an additional contact. The regression contains no contact, campaign, or treatment variable. It measures adjacent-quarter frequency persistence only.
- CEP coverage rising from 38% to 52%. No before/after comparison exists in the archived output, and the associated
<5% Δaccuracystatement is removed with it.- Language-bias detection across 27 languages. The logged run retained one language and used ASINs as brand identifiers.
- Poor Dirichlet model fit. The evaluation path predicted the sample mean for every user, so R²≈-7×10⁻⁶ evaluates a constant-mean predictor, not the fitted NBD distribution.
Implementation defects were also found in the bootstrap, negative-control, and NBD evaluation paths. The remaining numerical outputs are retained as an audit trail. They are not presented as a validated replication of the Ehrenberg-Bass laws.
What v0.1 got right is retained: the weighted Duplication of Purchase statistic did not cross its pre-set gate, and the simplified unweighted statistic was not substituted to manufacture a pass.
DoP weighted MAD 0.015863 — FAIL (>0.015) · DJ Pearson r 0.627 — FAIL (<0.80) · Q4 lagged-frequency R² 0.472 — descriptive only · CEP pipeline — not validated
Author: Kyo Harada
Original analysis: September 2025
Revised public edition: July 2026
Subject: Marketing science replication audit
This report audits a September 2025 analysis pipeline built from the dunnhumby Complete Journey, Instacart, UCI Online Retail II, and Amazon Review Data (2018) datasets. The archived outputs contain one near-miss and several negative results. The dunnhumby Duplication of Purchase run recorded a weighted mean absolute deviation of 0.015863 against a pre-set 0.015 gate. The UCI Double Jeopardy run recorded Pearson r=0.627 against a 0.80 gate and failed its stationarity check. A buyer-frequency regression produced R²=0.472 in its highest purchase-volume quartile, but it contains no intervention variable and does not estimate a marketing effect.
Re-auditing the code narrows the claims further. The reported bootstrap intervals are percentile intervals rather than BCa intervals; the CEP parser does not match the configuration schema; and the NBD diagnostic evaluates constant-mean predictions rather than fitted NBD predictions. The numerical outputs remain useful as an audit trail. They do not yet constitute a successful replication of the Ehrenberg-Bass laws.
This document reports an exploratory replication attempt. It is not a client case study, causal evaluation, or peer-reviewed result.
The 2025 project should be read as a replication audit, not as a validated marketing playbook. Its strongest property is that the archived decision gates preserve unfavorable results. Its principal weakness is that several public claims exceeded what the code measured.
| Analysis | Archived result | Gate or check | Defensible conclusion |
|---|---|---|---|
| Duplication of Purchase, dunnhumby | weighted MAD 0.015863 | ≤0.015 | Near-miss; the run failed |
| Duplication of Purchase, Instacart | weighted MAD 0.021854 | ≤0.015 | Failed |
| Double Jeopardy, UCI | Pearson r=0.627 | ≥0.80 | Failed; stationarity also failed |
| Buyer-frequency persistence, UCI Q4 | R²=0.472 | no confirmatory gate | Descriptive association only |
| CEP lexical pipeline, Amazon | r=-0.280 | no valid language-bias test | Not interpretable because the parser and configuration schemas disagree |
| NBD diagnostic, UCI | R²≈-7×10⁻⁶ | no valid goodness-of-fit test | Not interpretable as NBD fit because predictions were set to the sample mean |
Three claims in the previous edition are withdrawn.
The negative results still matter. The weighted DoP calculation did not cross its gate, and the simplified unweighted calculation cannot be substituted to manufacture a pass. That reporting discipline should be retained when the analysis is rebuilt.
The current asset is not decision-ready or publication-ready. Publication requires corrected estimators, versioned analysis code, redistributable or checksum-verified inputs, and an independent rerun from a clean environment.
The project combined four datasets that differ in sampling frame, market definition, and unit of observation. Their outputs cannot be pooled as if they described one market or one period.
| Dataset | Role in the archive | Logged analysis sample |
|---|---|---|
| dunnhumby Complete Journey | Duplication of Purchase | 1,735 households, 46 retained labels |
| Instacart Online Grocery Shopping 2017 | Duplication of Purchase comparison | 1,617 users, 129 retained labels |
| UCI Online Retail II | Double Jeopardy, buyer-frequency persistence, NBD diagnostic | 1,264 users and 27 labels for DJ; 1,666 users for the quarterly analysis; 1,648 users for NBD |
| Amazon Review Data (2018) | lexical CEP prototype | 1,000,000 review rows processed; 58 ASINs in the retained output |
The intended question was whether cross-brand buyer duplication remains close to a common level in a repertoire market. The project summarized off-diagonal duplication values with a weighted mean absolute deviation and compared the result with an internal gate of 0.015.
The UCI run correlated each retained label's buyer penetration with its average transaction frequency among buyers. The internal gate required Pearson r≥0.80 and a lower confidence bound of at least 0.70.
Users were assigned to purchase-volume quartiles within each calendar quarter. Within each quartile, the script regressed one quarter's transaction count on the adjacent observed quarter's transaction count. This measures within-user frequency persistence under the script's grouping rule. It does not measure response to advertising, reminders, or incremental contact.
The intended construct was the prevalence of Category Entry Point language in product reviews. The implemented run searched a multilingual lexicon, aggregated hits by ASIN and detected language, and correlated average lexical coverage with review count. A configuration-schema mismatch prevents the output from measuring the intended CEP dimensions or multilingual coverage.
The project did not observe a 2025 Q3 client market, did not run a marketing intervention, did not estimate incremental sales, did not compare a 38% baseline with a 52% post-treatment value, and did not test Double Jeopardy separately in middle and top buyer quantiles.
The closest archived run used a 26-week dunnhumby beauty slice after retaining users at or above the 0.90 purchase-count quantile, requiring at least two labels per user, and requiring at least 20 buyers per label. The final matrix contained 1,735 users and 46 labels.
| Metric | Result | Gate | Decision |
|---|---|---|---|
| Weighted MAD | 0.015863 | ≤0.015 | FAIL |
| Gap to gate | +0.000863 | — | Near-miss |
| Unweighted MAD | 0.015143 | not the confirmatory metric | No decision |
| Logged interval | [0.014792, 0.016928] | — | Descriptive only |
| Median labels per user | 2.0 | ≥2.0 | Met |
| Negative-control MAD | 0.015629 | ≤0.05 | Met under the project rule |
The Instacart comparison was less favorable: weighted MAD=0.021854 on 1,617 users and 129 labels. Its unweighted MAD was 0.011934. The lower unweighted value cannot replace the pre-specified weighted statistic after the result is known.
The narrow conclusion is that no archived specification-labelled run crossed all gates. Calling 0.015863 a near-miss is accurate; calling it a pass is not.
The distance from the gate does not show that the Duplication of Purchase law is almost verified. Fourteen filter combinations were examined, and the reported run was selected as the closest result. The threshold is also an internal project rule, not a universal rejection boundary supplied by the underlying theory. A confirmatory replication must fix the category definition, observation window, inclusion rules, duplication estimator, and decision gate before examining the new data.
The current script copies one directional conditional duplication rate into both halves of a symmetric matrix. It also calculates weights after reducing the data to one user-label row, so the values called "purchase-count weights" are effectively retained buyer counts. The logged interval uses percentile resampling of matrix cells, not a bias-corrected and accelerated bootstrap of buyers. These defects prevent inferential use of the interval and require the point estimate to be treated as an archived pipeline output rather than a validated estimator.
The UCI run retained 27 labels and 1,264 users in a 26-week slice. Across those 27 labels, buyer penetration and average transaction frequency among buyers had Pearson r=0.6269 and Spearman r=0.5624.
| Metric | Result | Gate | Decision |
|---|---|---|---|
| Pearson correlation | 0.627 | ≥0.80 | FAIL |
| Spearman correlation | 0.562 | descriptive | — |
| Pearson p-value | 0.00047 | not a fit gate | — |
| Logged stationarity | false | required for stable interpretation | FAIL |
| Maximum logged drift | 0.375 | ≤0.10 under the script rule | FAIL |
The result does not support the project's strong Double Jeopardy criterion. It also does not establish a failure of the empirical law. The UCI source is a UK giftware retailer, while the "bodycare" slice and label field were produced by heuristic category and brand transformations. The analysis therefore mixes a theoretical question with uncertain construct validity.
The script contains no middle-quantile or top-decile Double Jeopardy split. The value r=0.627 is the correlation across all retained labels. Claims that the relationship held in the middle but weakened among the top 10% are unsupported by this run.
The logged interval [0.275, 0.462] does not contain the point estimate 0.627. Code inspection explains the mismatch: the bootstrap path computes penetration with a different denominator than the point-estimate path, and sampling users with replacement is reduced to set membership before recomputation. The interval is not used in this report.
The quarterly UCI analysis assigned users to purchase-volume quartiles within each quarter, then regressed transaction frequency in one observed quarter on the adjacent observed quarter within each quartile. The predictor was standardized before estimation.
| Purchase-volume quartile | Observations | Users | Standardized slope | R² |
|---|---|---|---|---|
| Q1 | 126 | 107 | -0.002 | 0.00001 |
| Q2 | 88 | 76 | 0.321 | 0.196 |
| Q3 | 77 | 67 | 0.765 | 0.204 |
| Q4 | 190 | 120 | 3.341 | 0.472 |
Q4 had the strongest within-sample association. The result says that adjacent-quarter transaction counts were more predictable among the highest purchase-volume observations under this grouping rule.
There is no marketing-contact variable, treatment assignment, campaign exposure, stock measure, or price control in the regression. R²=0.472 therefore does not mean that one additional contact causes repeat purchase, nor that the model explains 47% of incremental sales.
The script names the shifted value freq_t1, but the shift points to the previous recorded quarter. Quartile membership is calculated from purchase volume in each quarter rather than from a fixed pre-period. These choices allow outcome-related grouping and make the Q1–Q4 comparison partly mechanical. A causal or predictive follow-up must define a fixed baseline cohort, preserve time direction, hold out later periods, and introduce the exposure whose effect is being estimated.
The archived Amazon run processed 1,000,000 review rows and wrote 256 aggregate rows covering 58 ASINs. It reported Pearson r=-0.280 between total review count per ASIN and mean lexical hit rate.
That coefficient is not evidence of language bias. The audit log shows one retained language (en) and 27 excluded language codes. The run therefore did not compare 27 languages.
Two schema mismatches change the meaning of the output.
language → dimension → terms, while the parser expects dimension → language → terms. The output consequently records en as the sole CEP category rather than quality, value, innovation, sustainability, and convenience.The variable named penetration is total review count, not buyer penetration. The value r=-0.280 is a correlation between ASIN review volume and the malformed lexical-coverage output.
No logged result or archived output contains a before/after test showing bottom-five CEP coverage rising from 38% to 52%. The previous edition converted two percentages into an intervention result without an observed intervention. That claim, and the associated <5% Δaccuracy statement, are removed.
The archive also reports NBD parameters and R²≈-7×10⁻⁶. The fitting routine estimates NBD parameters, but the evaluation path predicts the same sample mean for every user. The resulting R² evaluates a constant-mean predictor, not the fitted NBD distribution and not a full NBD-Dirichlet model. It cannot be used to claim that the Dirichlet model fits poorly.
This section describes what the archived scripts did. Labels such as "specification-compliant" and "BCa" are not adopted where the implementation does not meet those definitions.
Counts reported in this document are post-filter counts from the audit logs, not source-dataset totals.
The chosen dunnhumby run applied these conditions:
beautyThe script reduced the data to one row per user-label pair and formed a binary user-label matrix. For each off-diagonal pair it calculated a conditional overlap rate. It then copied the upper-triangle value into the lower triangle. The summary statistic was the weighted mean absolute deviation of upper-triangle values from their weighted mean, using the outer product of retained label counts as weights.
The script ran 5,000 percentile resamples of off-diagonal matrix cells, a within-user week permutation, and a random label-assignment negative control. The output calls the first procedure BCa. It does not calculate bias correction or acceleration and does not resample the primary sampling unit.
For each retained UCI label, penetration was the number of unique buyers divided by total unique users. Average frequency was row count divided by unique buyers. Pearson and Spearman correlations were computed across labels.
The stationarity routine aggregated weekly penetration and frequency, measured first-to-last relative drift, and combined it with Kendall trend tests. The bootstrap routine attempted 5,000 user resamples, but replacement multiplicity was lost through membership filtering and its penetration denominator differed from the point-estimate denominator.
Transaction rows were aggregated to user-quarter observations. Purchase-volume quartiles were recomputed within each quarter. Within each quartile, the script standardized the current transaction count and regressed the shifted adjacent-quarter count on it using ordinary least squares. Reported confidence intervals are t-based slope intervals from that regression.
The parser detected review language, required at least 20 rows per ASIN-language cell, searched configured substrings, computed Wilson intervals for hit proportions, and correlated total review count with mean lexical coverage. The parser/configuration mismatch described in Finding 4 invalidates the intended dimension and multilingual interpretation.
| Run | Input identification | Timestamp |
|---|---|---|
| dunnhumby DoP | SHA prefix e2470f224f7f0609 |
2025-09-27 14:12:31 |
| Instacart DoP | SHA prefix fa486f16bde1d909 |
2025-09-27 01:01:06 |
| Amazon CEP | SHA prefix faa6eadcba54534f |
2025-09-27 01:22:17 |
| UCI DJ | recorded only as loaded; commit unknown |
2025-09-23 00:55:12 |
| UCI buyer frequency | recorded only as loaded; commit unknown |
2025-09-23 13:28:06 |
| UCI NBD diagnostic | recorded only as loaded; commit unknown |
2025-09-23 13:28:45 |
The absence of hashes and commit identifiers for the UCI runs prevents exact provenance reconstruction.
The analyses use grocery orders, household retail transactions, giftware invoices, and product reviews. Market boundaries, buyer identifiers, observation windows, and label construction differ. Agreement or disagreement across these outputs cannot be attributed to one common consumer process without a harmonized design.
The UCI source is a UK giftware retailer. Its bodycare category and brand-like labels were created by project heuristics; retained labels include product-description tokens rather than verified beauty brands. The Amazon pipeline retained ASINs rather than normalized brands. These transformations weaken every claim that depends on a stable brand or category unit.
These conditions prevent the near-miss from functioning as a confirmatory statistical test.
The point estimate and bootstrap use different penetration denominators. Bootstrap draws with replacement are collapsed to membership, so repeated users receive no additional weight. The logged interval excludes the point estimate and is not interpretable. The stationarity check also failed.
Purchase-volume quartiles are defined from contemporaneous outcomes, and the model contains no intervention. Higher Q4 R² can arise from the larger variance and persistence of high-volume buyers. No budget allocation or contact-frequency recommendation follows from this regression.
The CEP parser and lexicon schemas disagree, leaving one malformed category and one retained language. The NBD evaluation compares observations with a constant mean instead of predictions from the fitted distribution. Neither result can confirm or reject the corresponding theory.
The raw data are not bundled with the public report. Instacart and dunnhumby require account- or terms-mediated acquisition. The local analysis folder is not tied to a recorded Git commit, three logs record the input only as loaded, and the advertised one-hour end-to-end guarantee was never evidenced by a clean-room run.
No peer review, preregistration, or independent replication occurred. Thresholds were project-defined and should not be treated as universal theory tests.
The archive supports only this claim: a 2025 exploratory pipeline recorded a near-miss DoP summary and several negative or uninterpretable diagnostics, while preserving enough logs to identify what must be rebuilt. It does not support causal marketing recommendations, validation of the Ehrenberg-Bass laws, or a published failure-to-replicate conclusion.
The current archive is not reproducible from the public report alone. This checklist defines the work required before the study can be described as a replication.
The September 2025 audit trail identifies these primary outputs:
results/dop_dunnhumby_beauty_spec_q90_b2_m20.csvresults/dop_instacart_shampoo_specification_compliant.csvresults/dj_bodycare.csvresults/moderation_bodycare.csvresults/cep_coverage_complete.csvresults/dirichlet_bodycare.csvThese filenames identify the historical snapshot. They are not evidence that the current pipeline reproduces from a clean checkout.
These sources define empirical regularities and model structure. They do not supply the project-specific MAD≤0.015 or Pearson r≥0.80 gates.
The numerical values in this report were checked against the September 2025 JSONL logs and CSV files named in the reproduction checklist. The logs for the dunnhumby, Instacart, and Amazon runs include input-hash prefixes. The UCI logs do not include a recoverable input hash or source commit.
This report is provided for informational and educational purposes. It does not constitute professional, investment, or marketing advice. The archived analyses have not been peer reviewed and should not be used to make budget, targeting, or portfolio decisions.
The source datasets remain subject to their respective licenses and access terms. This report does not redistribute restricted raw data.
Contact information submitted through the distribution form is retained for up to 12 months for document delivery and research updates. Deletion requests may be sent to support@visageaiconsulting.com.