PaperlayerView exact revision on arXiv

Source-linked AI summary

Luxury resale volume and composition shifted during the COVID-19 tourism shock, but co-purchase network tests were inconclusive and construction-sensitive

Tengfei Shao

arXiv:2609.36825v1cs.SIstat.ME

TL;DR

The paper asks whether the 2020 tourism shock restructured one resale intermediary’s brand co-purchase network. It compares annual projections using a five-metric battery and Portrait Divergence against permutation nulls that rebuild both graphs. The primary tests did not distinguish the full years, while planted-effect tests show a detection floor specific to the tested redirection.

  • Problem

    The paper asks whether the tourism shock restructured one resale intermediary’s brand co-purchase network.

    Source: Discussion · p. 9

  • Method

    The study compares annual co-purchase projections using five label-invariant graph summaries and Portrait Divergence against two permutation nulls that rebuild both graphs.

    Source: The primary tests did not separate… · p. 4, Discussion · p. 9

  • Results

    The primary battery did not distinguish the full-year graphs, while it detected a planted 30% two-block redirection with power 0.83–0.92 across 11 random brand partitions.

    Source: Discussion · pp. 9, 12

  • Takeaways & Limitations

    The case supports reporting rebuilt-graph nulls and a detection floor, while interpreting non-detection against the tested alternative rather than as evidence that all changes were absent.

    Source: Discussion · p. 11

Abstract

from arXiv · show

Japan's 2020 tourism shock coincided with 27% fewer buyers and 35% lower gross merchandise value at one second-hand luxury resale intermediary. We compared 2019 and 2020 co-purchase projections of recorded brand labels with a Holm-corrected battery of five label-invariant metrics and Portrait Divergence against two permutation nulls rebuilding both graphs. Neither test separated the full years (smallest Holm p 0.407; 0.097 under the design-matched paired-swap null). For one random two-block split of brands, the battery detected a planted redirection of 30% of multi-brand baskets (178 of 10,399 second-group baskets, 1.7%) in 83 of 100 simulations (83-92 of 100 across 11 splits, all at least 80); Portrait Divergence reached 80% power only at full redirection. Observed falls in mean degree and clustering resembled those of 20-30% redirection, but the planted rise in degree assortativity was absent. A composition-only model of the observed attrition would be detected in only 15 of 100 simulations. Results moved with construction: without residual and material labels (post hoc), mean degree separated the years under the paired-swap null (Holm p = 0.030), and Portrait Divergence fell below 0.05, unadjusted, at the widest construction and within April-December. Shock-period network comparisons need rebuilt-graph nulls and a per-metric detection floor.

Results

The primary tests did not distinguish the full-year 2019 and 2020 co-purchase graphs, although a planted redirection was detectable at a stated floor. The shock coincided with lower buyer volume and GMV, while results varied with graph construction.

A concentrated network with shallow communities

  • The 2018–2021 network contained 42,962 buyers and 133 brand labels; 6.5% of buyers accounted for 58.3% of GMV.Brand strength, sale values, and per-buyer spend were also highly concentrated.Source: A concentrated network with shallow… · p. 3
  • The pooled projection had three communities but weighted modularity Q=0.1381; annual community counts were 3, 2, 2, and 3.The watch-community partition was less stable in earlier years than later ones.Source: A concentrated network with shallow… · pp. 3–4

The shock was large in volume and composition

  • From 2019 to 2020, buyers fell 27% and GMV fell 35%, while duty-free and cross-border purchasing also declined.Cross-border buyers fell from 5,449 to 2,016; only 938 buyers were active in both years.Source: The shock was large in volume and… · p. 4

The primary tests did not separate 2019 and 2020

  • The five-metric battery did not separate 2019–2020 (smallest Holm p=0.407); PD was nonsignificant under relabel (p=0.259) and paired-swap (p=0.118) nulls.Under the paired-swap null, the battery's smallest Holm p was 0.097.Source: The primary tests did not separate… · pp. 4–5
  • Post hoc removal of residual and material labels yielded mean degree 6.39 to 4.65 (paired-swap Holm p=0.030) and PD p=0.037; April–December PD was p=0.019.The named-brand April–December comparison did not separate the years; at the widest construction, PD p-values were 0.0445 and 0.0225 under the two nulls.Source: The primary tests did not separate… · pp. 5–6

What the battery could detect

  • Across 11 random brand partitions, the battery detected 30% planted redirection in 83–92 of 100 simulations; PD reached 80% power only at full redirection.For the original random partition, 178 of 10,399 second-group baskets (1.7%) were redirected at f=0.3.Source: What the battery could detect · p. 6
  • The observed falls in density, clustering, mean degree, and modularity resembled planted redirections of 10–30%, but the predicted assortativity rise was absent.Degree assortativity changed by −0.005, below the no-planting mean of +0.007.Source: What the battery could detect · pp. 6–7

The two-community core recurred in every year

At the recorded-label construction, the full-year tests did not distinguish 2019 and 2020, although the battery detected a planted 30% redirection across tested brand partitions. Detection was construction-sensitive, and a composition-only model of observed attrition was rarely detected.

The two-community core recurred in every year

  • Across years, the recurring watch-versus-leather core is descriptive rather than evidence of structural change; 2019–2020 partition agreement was partly attributable to both partitions having two communities.The 2019–2020 ARI was 0.854.Source: The two-community core recurred in… · pp. 7–8

Decomposition by exposure cell, reported as found

  • Domestic buyers generated 64.4% of co-purchase pair mass, while removing cross-border buyers retained 0.755 of edges, less than the 0.827 mean for size-matched domestic removals.The pooled difference was Δ = −0.071; breadth-matched D′ reversed the sign pooled and in 2018, but was diagnostic and identified no mechanism.Source: Decomposition by exposure cell,… · p. 8

The protocol transferred at an adapted threshold

  • The protocol transferred to a public retail benchmark using an adapted threshold, with battery MDE 0.2 and PD MDE 0.45.The literal thresholds produced complete graphs; the fallback selected τ* = 93.Source: The protocol transferred at an adapted… · p. 9

Discussion

  • The authors recommend rebuilding both graphs through the same pipeline, reporting an MDE under the same correction, and stating which alternatives the test does not cover.The evidence is bounded to one firm, one projection-rule family, and annual B2C snapshots.Source: Discussion · p. 11
  • At the recorded-label construction, the tests did not distinguish the full-year networks, while the battery detected planted 30% redirection with power 0.83–0.92 across 11 brand partitions.A composition-only model of the observed size was detected in only 15 of 100 simulations.Source: Discussion · pp. 9, 12

Methods

The study compares annual brand co-purchase projections from one Japanese resale intermediary, using five label-invariant statistics and Portrait Divergence (PD). It treats the firm's B2C market—not the national market—as the target population.

Study design and inference target

  • The primary contrast is 2019 versus 2020; the design has no control market, so changes are reported as coinciding with the shock, not as identified effects.Calendar-year 2020 includes January–March, before the closure took full effect.Source: Study design and inference target · p. 12

Data source, period and sample

  • The data are one Japanese intermediary's 2018–2021 B2C sales records, filtered to positive-price transactions with buyer and brand fields.The brand field was standardised, including mapping five duplicate spellings before counts, rankings, or baskets were built.Source: Data source, period and sample · p. 12

Unit of analysis and target population

  • The unit of analysis is the annual brand co-purchase projection, linking brands by the number of buyers who bought both.The target is this firm's B2C market, not the national market or business-to-business sourcing.Source: Unit of analysis and target population · p. 13

Variables and exposure cells

  • PD is the base-2 Jensen–Shannon divergence between k-weighted network-portrait distributions; the battery covers density, mean degree, clustering, modularity, and degree assortativity.PD uses the unweighted projection.Source: Variables and exposure cells · p. 13
  • Four exposure cells classify buyers by channel and cross-border status using pooled 2018–2021 sales; duty-free marks exposure, not tourist identity.Cell assignments use whether at least half of a buyer's sales are offline and cross-border; composition is also measured by duty-free share and sale-price comparisons.Source: Variables and exposure cells · p. 13

Buyer identity and pseudonymisation

  • Buyer names are unverified strings: near-duplicate names occur at 0.7%, while the exact-homonym rate is unmeasured.The measured near-duplicate rate sets ε = 0.007; the battery result holds up to simulated identity-merge rates of ε = 0.20.Source: Buyer identity and pseudonymisation · pp. 13–14

Time windows and the permutation unit

Network construction

  • The primary projection keeps each year's top 60 recorded labels, links pairs sharing at least three buyers, and removes isolates.It includes residual and material labels; Louvain modularity is weighted, while PD uses unweighted shortest paths.Source: Network construction · pp. 14–15

Rationale for the inference protocol

The protocol compares rebuilt annual graphs against two group-size-preserving permutation nulls and uses a planted alternative to quantify what changes the tests could detect. Robustness checks and a shared-menu control further delimit how results should be read.

Rationale for the inference protocol

  • At these graph sizes, the battery's minimum detectable effect is f = 0.3 for one random brand partition, while PD reaches its detection floor only at f = 1.0.The battery's point power crosses 0.8 between f = 0.2 (0.33) and f = 0.3 (0.83).Source: Rationale for the inference protocol · p. 15

Two permutation nulls

Primary family

  • The five-metric family uses Holm-adjusted two-sided permutation tests; PD is a one-sided diagnostic, and the largest-component fraction was removed after its values were constant.Under the original six-metric family, neither null separated the years: the smallest Holm p-values were 0.489 under relabeling and 0.117 under paired swaps.Source: Primary family · pp. 15–16

Statistical reporting

  • The study reports Monte Carlo and binomial uncertainty conventions, while subsampling bands and several other analyses are explicitly descriptive.The reporting rules specify α = 0.05 and Clopper–Pearson 95% intervals for binomial proportions.Source: Statistical reporting · p. 16

Robustness constructions

  • Robustness checks vary node sets, shared-buyer thresholds, rank ties, and comparison windows; the April–December comparison addresses pre-closure months in 2020.The tie rule was fixed after earlier sweep values had been seen, so the sweep is reported under both rules.Source: Robustness constructions · pp. 16–17

Named-brand sensitivity analysis

  • The named-brand sensitivity removes six non-brand labels and reruns both nulls, the seasonal comparison, and a planted-effect curve; it is post hoc, not a second primary test.Its protocol was written after primary results and descriptive metrics had been seen, but before the sensitivity runs.Source: Named-brand sensitivity analysis · p. 17

Per-year uncertainty

  • Per-year subsampling bands are descriptive, not guaranteed-coverage intervals; centering on each estimate makes inclusion of that estimate automatic.An n-out-of-n buyer bootstrap is shown only for contrast because duplicating buyers inflates shared-buyer counts.Source: Per-year uncertainty · p. 18

Positive control

  • The exposure-cell control tests whether the pipeline separates buyer populations sharing the firm's menu, but it is a discrimination check, not ground truth.Observed PD between cells ranged from 0.45 to 0.81.Source: Positive control · p. 18

Planted-effect power

The planted-effect analysis redirects selected multi-brand baskets between two brand blocks, then tests rebuilt graphs with the primary procedure. Additional checks examine continuity, identity noise, community structure, and buyer-removal comparisons.

Planted-effect power

  • At f = 0.3, an average of 178 second-group baskets—1.7% of 10,399—were redirected in the planted alternative.The curve uses random splits of the pooled 2019–2020 baskets, and the reported qualifying points are conditional on the tested partitions and planting mechanism.Source: Planted-effect power · pp. 18–19

Degree-preserving continuity

  • The degree-preserving continuity test compares observed PD with rewired-graph PD in both directions; continuity is secondary evidence.Rewirings use degree-preserving double-edge swaps, with a test becoming unevaluable if the swap budget is exhausted.Source: Degree-preserving continuity · pp. 19–20

Identity-noise sensitivity

  • At ε = 0.20 under merging, 5 of 20 identity-noise draws could not be rewired within the swap budget.Those continuity tests are reported as unevaluable.Source: Identity-noise sensitivity · p. 20

Community detection and partition indices

  • Consensus community counts were 3, 2, 2, and 3 across 2018–2021, respectively.Communities were formed by pooling 100 Louvain seeds, linking brands co-assigned in at least half of runs, and taking connected components.Source: Community detection and partition… · p. 20

Decomposition and size-matched removal

  • The pre-specified size-matched removal contrast had the opposite sign from its expected direction on every object.The diagnostic D′ was unavailable for 2019 and neither contrast identifies a mechanism.Source: Decomposition and size-matched removal · p. 21

Public-benchmark transfer

The public benchmark transfers the network-comparison protocol to UK online-retail transactions, adapting the graph threshold where literal thresholds yield complete graphs. The supplied evidence describes the transfer design and its eligibility caveat.

Public-benchmark transfer

  • The benchmark uses cleaned UK online-retail customer transactions in two consecutive annual windows, with customers treated as buyers and products as brands.The literal shared-buyer thresholds 2, 3, and 5 produced complete graphs, so the pre-specified rule selected τ* = 93 to keep W1 density at most 0.60.Source: Public-benchmark transfer · p. 21
  • At equal f, the redirected share is not comparable across datasets: 74.2% of benchmark second-group units were eligible, versus 5.7% on the proprietary data.Eligibility requires 2 to 30 anchor products; 48 benchmark units exceeded 30 and were not redirected.Source: Public-benchmark transfer · p. 21
  • The benchmark curve applies a two-part battery criterion: MDE below 1 and no greater than PD's MDE.Undefined battery results count as non-rejections, and the UK-versus-non-UK positive control was unevaluable.Source: Public-benchmark transfer · p. 21

Pre-specification and exploratory analyses

The primary construction and metric battery were fixed in a dated internal plan, but not publicly registered, after an initial comparison had found no separation. Benchmark gates passed, while the size-matched removal gate failed; several analyses were exploratory or post hoc.

Pre-specification and exploratory analyses

  • The primary construction and battery were fixed in a July 2026 written plan after an initial comparison at that construction found no separation; no protocol was publicly registered.“Pre-specified” means fixed in a dated internal written protocol before analysis ran.Source: Pre-specification and exploratory… · p. 21
  • Feasibility, size and power, removal, resolution-sweep reporting, and identity-noise analyses were specified in dated protocols before their corresponding analyses ran.Source: Pre-specification and exploratory… · p. 22
  • Supplementary Table S6 logs specifications, criteria, outcomes, deviations, and the change from six metrics to five; protocol copies are available to editors and reviewers.Source: Pre-specification and exploratory… · p. 22
  • Corrected power designs were specified after discovery of the fixed-base defect but before their results were seen; implementation corrections followed earlier results, and named-brand analysis was post hoc.The further-block planted curve, year-specific exposure-label composition model, and residual-label description were also post hoc, though their protocols preceded those analyses.Source: Pre-specification and exploratory… · p. 22
  • Benchmark gates passed, but the size-matched removal gate failed; D′, the W1-versus-W2 comparison, and resolution-sweep interpretation were exploratory..Source: Pre-specification and exploratory… · p. 22

Ethics statement

The study used pseudonymised archival commercial records from one unnamed resale intermediary under a research-use agreement. It involved no participants, intervention, individual contact, or research data collection from individuals.

Ethics statement

  • The analysis used archival business transaction records from one unnamed resale intermediary, provided under a research-use agreement in pseudonymised form.Source: Ethics statement · p. 22
  • The study involved no human participants, intervention, individual contact, or data collected from individuals for the research.Source: Ethics statement · p. 22
  • Buyer names were replaced with non-invertible pseudonyms in every data product leaving the analysis environment, and no personal identifier was published.Source: Ethics statement · p. 22

Use of large language models

Claude was used only for English-language polishing. The author states that the analysis and results are their own work, were not AI-generated, and that they take full responsibility.

Use of large language models

Software

Analyses used Python with NetworkX, NumPy, SciPy, and pandas, alongside libraries for Leiden partitioning, partition indices, plotting, and workbook reading. Random procedures used documented seeds, and two scripts reproduced output byte for byte under different Python hash seeds.

Software

  • Analyses used Python 3.12.6 with NetworkX 3.2.1, NumPy 2.4.6, SciPy 1.17.1, and pandas 2.3.3.Source: Software · p. 22
  • Leiden partitions used leidenalg and python-igraph, partition indices used scikit-learn, figures used matplotlib, and the benchmark workbook used openpyxl and pyarrow.Source: Software · p. 22
  • Random procedures used documented seeds with base seed 20260703, and modularity-null and continuity scripts reproduced output byte for byte under different Python hash seeds.Supplementary Fig. S1 network layouts used ForceAtlas2.Source: Software · p. 22

Data Availability

The resale-firm transaction data are restricted and the firm is not publicly named. Review access may be arranged under specified conditions; the public benchmark is separately available under a CC BY 4.0 licence.

Data Availability

Figures

The figures show the transaction-to-network construction and tourism shock, then assess year-to-year network differences, detection power, exposure-cell composition, and benchmark transfer.

Fig. 1

  • The construction pipeline projects transaction records into annual top-60 brand co-purchase graphs, retaining edges supported by at least three shared buyers.Annual buyer totals, gross merchandise value, duty-free shares, and sale prices provide context for the 2020 tourism shock.Source: Figure 1 · p. 29

Fig. 2

  • No primary battery metric separated 2019 and 2020 under either null; the smallest Holm-adjusted p-values were 0.407 and 0.097.Portrait Divergence was 0.673, below the 95th percentile for both nulls.Source: Figure 2 · p. 30

Fig. 3

  • At f = 0.3, the battery had 0.83 power for one random brand partition, while Portrait Divergence reached its MDE at f = 1.0.The battery's f = 0.3 power ranged from 0.83 to 0.92 across 11 partitions.Source: Figure 3 · p. 31

Fig. 4

  • Cross-border buyers generated 35.6% of co-purchase pair mass, and removing them retained 75.5% of the pooled graph's edges.Size-matched removal produced lower edge retention than random domestic-buyer removal on every object.Source: Figure 4 · p. 32

Fig. 5

  • On UCI Online Retail II, the battery's same-window half-split rejection rate was 0.027 and its planted-effect MDE was f = 0.2.Portrait Divergence's rejection rate was 0.043 and its MDE was f = 0.45.Source: Figure 5 · p. 33

Tables

The tables compare the primary 2019–2020 tests with construction-sensitive results; the supplied table passages chiefly document the primary metrics and resolution-sweep findings.

Table 1

  • Table 1 presents the five-metric battery and PD for 2019 versus 2020 under the primary construction (top-60 recorded).Source: Table 1 · p. 34

Table 2

  • At the primary threshold of three shared buyers, no battery metrics separated the years, and forward continuity had z = 2.35 (p = 0.015).The threshold sweep reports node and edge counts and observed Portrait Divergence alongside separating metrics and continuity.Source: Tables · p. 35
  • At top-111 with one shared buyer, Portrait Divergence p-values were 0.0445 and 0.0225 across the two nulls, but neither was adjusted across the eight tests.The alternative tie rule retained values below 0.05 for both nulls, while the smallest Holm p-value was 0.095.Source: Tables · p. 35, Table 2 · p. 35

Supplementary information

Supplementary analyses assess detection thresholds and robustness across planted network changes, partitions, benchmarks, buyer-removal checks, and named-brand graph constructions. They distinguish descriptive subsampling bands from permutation-null tests and document how conclusions vary with graph construction.

Network construction

  • The annual graphs had 40 nodes and 137 edges in 2019 versus 33 nodes and 84 edges in 2020; only this annual contrast was tested.The pooled 2018–2021 projection was descriptive only, and the weighted static partition had three communities with Q = 0.1381.Source: Supplementary information · pp. 37–38, Figure S1 · p. 37

Partition persistence

  • 2019-to-2020 consensus-partition ARI was 0.854, the highest year-over-year value, partly because both years resolved to k = 2 communities.The 2019 individual Louvain seeds yielded k = 2 in 69 of 100 runs.Source: Supplementary information · p. 38, Figure S2 · p. 38
  • Observed unweighted modularity exceeded the degree-preserving null for every graph (all empirical p = 0.002), although z values depended on Louvain node order.Across tested orderings, pooled static modularity exceeded the null maximum and annual modularity exceeded the null mean; earlier-ordering 2020 modularity fell below the null maximum.Source: Figure S2 · p. 38, Supplementary information · p. 39
  • Consensus stability was 0.68, 0.70, 0.97, and 0.98 from 2018 through 2021, while Leiden–Louvain ARI was 0.373, 0.876, 1.000, and 1.000.The lower 2018–2019 values indicate comparatively greater sensitivity to Louvain seed and community-detection algorithm.Source: Supplementary information · p. 39

Per-year metrics

  • The m-out-of-n subsampling bands are descriptive uncertainty summaries, not the permutation-null distributions used for the Holm battery.Each band is centered on its full-sample estimate and therefore contains that estimate by construction.Source: Supplementary information · p. 49, Table S2 · p. 49

Planted-effect power

  • Battery MDE was f = 0.3, while Portrait Divergence MDE was f = 1.0, using the smallest tested redirection with power ≥ 0.8.At f = 0, the empirical size was battery 5/100 and Portrait Divergence 2/100; the prespecified stop rule was not triggered.Source: Table S3a · p. 51, Supplementary information · p. 52

Supplementary information

  • At f = 0.3, battery power was at least 0.8 across all 11 random partitions (0.83–0.92; median 0.85) and was 0.90 under the category partition.For every partition, f = 0.3 was the first tested level with battery power at least 0.8 and defined share at least 0.95; partition results shared groups, movers, and inner draws, so their spread is not an interval over partitions.Source: Table S3e · p. 56, Supplementary information · p. 59
  • On the UCI benchmark, the battery MDE was f = 0.2 versus PD MDE f = 0.45, meeting the pre-specified two-part criterion.On average, 74.2% of second-group units were eligible; f is a share of eligible units and is not comparable across datasets.Source: Supplementary information · p. 64
  • Every object in the size-matched buyer-removal comparison showed the opposite sign to the hypothesized positive Δ, so the pre-specified gate failed.The breadth-matched D′ comparison was diagnostic and was unavailable for 2019.Source: Supplementary information · p. 65

Named-brand sensitivity

  • The post hoc construction removed six non-brand labels before top-60 ranking while retaining the primary test’s units and group sizes.Baskets emptied by filtering remained as units without brands; the analysis was not a second primary test.Source: Supplementary information · p. 76
  • Residual labels contributed −0.373 of the −1.759 mean-degree difference between 2019 and 2020; edges among other labels contributed −1.386.In the primary graphs, “Other” had degree 17 in 2019 and 9 in 2020, while “No Brand” had degree 5 and 4. Edges incident to either label numbered 22 of 137 in 2019 and 12 of 84 in 2020, corresponding to 1.100 and 0.727 of mean degrees 6.850 and 5.091.Source: Supplementary information · p. 77
  • The named-brand full-year comparison separated only on mean degree under the paired-swap null; the relabel null showed no battery separation.Holm correction was applied within each battery.Source: Table S7b · p. 77, Supplementary information · p. 77

10,399 buyer-year baskets per replicate; redirection planted in the second group; 100

For this split, the battery MDE was f = 0.3 and the PD MDE was f = 0.8, meeting the pre-specified two-part criterion.

10,399 buyer-year baskets per replicate; redirection planted in the second group; 100

  • On this construction, battery MDE was f = 0.3 and PD MDE was f = 0.8; at f = 0, empirical size was 3/100 for each and the stop rule was not triggered.Source: 10,399 buyer-year baskets per… · p. 78
  • At f = 0, the whole procedure’s empirical size on this construction was 3/100 for the battery and 3/100 for PD; the stop rule (11 or more of 100) was not triggered.Battery MDE was f = 0.3; PD MDE was f = 0.8.Source: 10,399 buyer-year baskets per… · p. 78
  • The anchor was the pooled named-brand top 60, split once into two blocks of 30; the second group held an average of 561 eligible baskets.The per-metric columns report Holm rejection rates.Source: 10,399 buyer-year baskets per… · p. 79

Related papers

Loading 2609.36825v1…