# Methodology ## 1. Purpose and inferential boundary SPAN compares possible cycling-network interventions at metropolitan screening scale. Its unit of analysis is an origin–destination (OD) movement assigned to a directed, source-identified network. It estimates how stated scenarios and treatments change route availability, generalized cycling cost, network connectivity, and monetised screening outcomes. The tool does not estimate causal effects from a randomized or quasi-experimental design. Scenario demand is a constrained allocation informed by published PCT propensity functions. Candidate results are conditional model comparisons, not promises of observed patronage or benefit. ## 2. Reproducible analysis contract Every result must be traceable to: - checksummed source snapshots and their licences; - a versioned configuration containing all parameter values and units; - source code version and dependency lock; - deterministic topology and tie-breaking rules; - a recorded random seed for stochastic procedures; - stage-level counts, exclusions, warnings, and failure reasons; and - a release manifest linking the analysis output to the published interface. The pipeline must fail clearly when required fields, coordinate systems, units, or topology identifiers are missing. Silent unit conversion and silent dataset substitution are prohibited. ## 3. Demand and confidentiality treatment ### 3.1 OD observations For OD relation \(i\), let \(E_i\) be total stated journey-to-work trips in the source cell and \(O_i\) the bicycle subset. Both fields can be disclosure-controlled; an eligible total marked `-999` is not a known zero or a known cap. The importer therefore constructs intervals \([E_i^L,E_i^U]\) and \([O_i^L,O_i^U]\), then selects or samples only from the joint feasible set \(0\le O_i\le E_i\). Disclosure-controlled counts are not treated as recovered truth. The principal and bound/sensitivity runs use the same geography and pipeline, and the manifest records the joint selection rule. The importer must preserve the difference between a numeric release and an explicit suppression marker. Under the Stats NZ 2023 Census sensitive-table rules, a suppressed count is below six and is represented as \([0,5]\). Every remaining count is fixed-random-rounded to base three and differs from its confidential source count by no more than two. Accordingly, an unsuppressed numeric release \(r_i\) has the conservative interval \([\max(0,r_i-2),r_i+2]\), while an explicit suppression marker has interval \([0,5]\). In particular, an unsuppressed numeric zero represents \([0,2]\), not the suppression interval. Bicycle bounds are then intersected with the eligible-total bounds through the joint constraint. The selected point or draw is an analysis convention; it is never described as a recovered source count. Product sensitivity and any table-specific exception must be recorded. Stats NZ Datafinder table 121988 version 410594 additionally removes rows whose total population is below six and includes only people whose workplace address is available at SA2. That structural absence is a third state: it is not an explicit suppression marker and not a published numeric zero. SPAN does not materialise a missing OD pair, assign it a destination, or apply the cell interval above. Missing-row and unlocated-workplace mass is retained in a source-coverage ledger as unresolved unless publisher totals support a bounded comparison. Scenario denominators describe the available-address, published OD universe—not all Auckland commuters. The SA2 transport-mode margin and the internal Auckland OD table do not have an interchangeable universe. A direct source audit found 874,065 in the published full-origin margin field `VAR_2_786`, versus approximately 610,101 published internal-Auckland OD total trips plus suppressed and structurally omitted cells. The margin is therefore a bounded, soft validation diagnostic unless a release documents exact universe and category reconciliation; it is not a hard allocation constraint. All source OD records, including outbound records when supplied, and every unsnapped or unreachable internal record remain in a ledger with a scope or route status. A missing outbound universe is reported rather than fabricated. The formal interval definitions are in `../equations/confidentiality.tex`, and the governing source is Stats NZ (2024), ISBN 978-1-99-104974-2. ### 3.2 PCT propensity Published PCT 2020 coefficient sets transform routed distance and hilliness into a relative spatial propensity. The logit contains distance, square-root distance, squared distance, centered gradient, and distance–gradient interactions. Inputs are kilometres and percent gradient. Coefficients and the equation are recorded in `parameters.md` and `../equations/pct-uptake.tex`. The imported coefficient sets describe PCT scenarios developed for England. They are used as transferable prioritisation priors, not as a locally estimated Auckland behavioural model. External validation and sensitivity tests are therefore essential. ### 3.3 Explicit commute-cycling sensitivity The adopted Transport Emissions Reduction Pathway describes a 2030 target of 17% of trips by cycling and micromobility together (and 13% by distance). SPAN's default 8% commute-cycling share is a configurable modelling sensitivity. It is neither a standalone adopted target nor a direct crosswalk from TERP's all-trip denominator to the Census commute denominator. For a declared source-compatible OD universe \(\mathcal I\) and confidentiality draw or point \(b\), required additional cycling is \[ T_b^+=\max\!\left(0,q\sum_{i\in\mathcal I}E_i^{(b)} -\sum_{i\in\mathcal I}O_i^{(b)}\right), \] where \(q\) is the declared cycling share. Additional trips are distributed by iterative proportional allocation with capacity \(K_i^{(b)}=\max(0,E_i^{(b)}-O_i^{(b)})\) and weight \(W_i^{(b)}=K_i^{(b)} p_i f(d_i)\), where \(p_i\) is the selected PCT propensity and \(f(d_i)\) is the declared distance-decay function. Water filling prevents any OD relation exceeding its eligible population and reports any unallocated target. The full declared universe remains in the demand ledger; only routable relations receive path allocation, so routing failures appear as unallocated demand and explicit coverage rather than silently shrinking the denominator. This separates the aggregate scenario constraint from the behavioural propensity used to distribute it. ## 4. Network construction The graph preserves each OSM node identity, source way identity, legal direction, bicycle access, and the layer/bridge/tunnel state of every physical edge. Near-coincident coordinates are never merged merely because they are close: a bridge and road that cross in plan remain disconnected unless the OSM ways explicitly share the same source node. A shared source node remains connected when adjoining ways change layer at a legitimate structure approach. Physical edges have stable IDs; each permitted direction is a separate traversal. Import validation checks, at minimum: - unique node and edge IDs; - endpoints present in the node table; - positive finite length and plausible geometry endpoints; - direction and access consistency; - bridge, tunnel, and layer transitions; - weak components and isolated demand snaps; and - duplicate geometries without conflating legitimate parallel facilities. OD endpoints snap only to source-identified SPAN nodes that have an unambiguous endpoint identity in the reconciled R5 graph and belong to a compatible network component within the documented maximum distance. Routing starts and ends at those exact R5 vertices; it does not ask a coordinate linker to choose a nearby edge. Ambiguous source-node/engine-vertex mappings fail closed and are counted. The result retains SPAN node, component, layer, snap distance, route status, and failure reason. ## 5. Traffic stress and generalized cost Each edge receives a four-level traffic-stress classification from facility type, road class, speed, lanes, volume, and intersection stress. The classifier is inspired by the LTS literature but is an auditable Auckland screening rule, not an assertion that a US threshold transfers without calibration. Missing speed, lanes, or volume are conservatively imputed by road class and recorded per edge. For directed traversal \(e\), generalized cost is \[ c_e=\ell_e\,m_{s(e)} \left(1+w_+\max(0,g_e)+w_-\max(0,-g_e)\right)m_e^{\mathrm{structure}}, \] where \(\ell_e\) is metres, \(m_{s(e)}\) is the LTS multiplier, \(g_e\) is directional rise/run, and the structure term records bridge and tunnel sensitivities. Intersection stress can raise, but not lower, link stress. R5 supplies directed route searches, but the SPAN topology is authoritative for bicycle access, direction, stress, terrain, structure penalties, and exact segment identity. Every R5 directed edge is reconciled through OSM way geometry to an ordered SPAN segment sequence. Unmapped engine edges have bicycle and pedestrian permission removed in the engine-local copy so R5 cannot silently fall back to walking a bicycle. Any path that cannot be reconciled to one contiguous, source-identified SPAN sequence fails closed. The first search minimizes generalized cost and a separate search establishes the shortest physical-distance denominator. Subsequent searches multiply the cost of previously used engine edges by a declared factor. Up to five distinct alternatives are retained after generalized-cost, physical-detour, and shared-edge screens; the Auckland default performs at most four alternative searches after the base path. This is a deterministic link-penalty choice-set generator, not an implementation of Yen's algorithm and not a claim that all behaviourally perceived routes have been enumerated. Demand-support records are selected by deterministic, seeded simple random sampling without replacement within each published zonal OD. The default routes one of the up to 25 spatial disaggregation records in every supported stratum, retains every selected and unselected record in the OD ledger, and uses the exact inverse inclusion probability as a Horvitz--Thompson analysis weight. This is declared probability sampling, not silent truncation. Retained paths receive path-size-logit probabilities, which reduce independent- alternative weight for nearly duplicate paths. The choice set, sampling variance, and utility coefficients remain structural uncertainties until the specified sensitivity and local validation work is complete. ## 6. Existing network and candidate treatments An existing low-stress facility must be supported by declared source attributes or an approved authoritative facility overlay. Painted lanes are not silently classified as protected. Classification conflicts and overlay matching tolerances are reported. Candidate corridors comprise exact physical edge IDs and a declared treatment. The candidate generator may join high-demand gaps, bridge short network gaps, and connect termini to the existing network, but each added connector is visible in the candidate geometry and capital cost. Parallel-facility filtering must consider topology and access as well as planar distance so a nearby but inaccessible path is not mistaken for a substitute. Candidate provenance records seed edges, connectors, excluded duplicates, treatment, length, source IDs, cost basis, and connectivity to existing low-stress components. Candidates are hypotheses for investigation, not engineering alignments. ## 7. Candidate counterfactual For candidate \(C\), only its exact edge set is changed to the proposed treatment; the graph is otherwise held fixed. Generalized costs and shortest paths are recomputed for eligible OD relations. A relation is counted as using the treatment only when the treated path traverses an edge in \(C\). The model reports baseline and treated path cost, distance, changed edges, and whether a path was unavailable in either state. A continuous, bounded odds-elasticity response translates generalized-cost change into cycling probability. For baseline probability \(p_0\), baseline cost \(C_0\), treated cost \(C_1\), and elasticity \(\eta\): \[ \operatorname{logit}(p_1)=\operatorname{logit}(p_0)+ \eta\log(C_0/C_1). \] The result is bounded to the eligible population and produces no benefit when cost does not improve. A declared small probability floor makes the logit finite for a disclosure-controlled zero, while the increment is still measured against the published baseline count so the floor itself is not counted as cycling. Elasticity and floor are explicit and sensitivity-tested. Benefits are credited only to modelled incremental activity under this response model; scenario trips that merely reroute are not automatically counted as newly induced trips. The reference graph algorithm performs exact-edge rerouting. The current Auckland research snapshot instead recomputes generalized costs and path-size probabilities over each OD's retained set of up to five plausible paths. It can therefore represent substitution among those paths, but it cannot discover a new route outside that set. Candidate outputs and the evidence profile identify this limitation; no full-network connectivity result is substituted. ## 8. Low-stress connectivity Let \(\Omega\) be a declared analysis set of OD relations. A pair passes when a directed path exists using edges at or below the LTS threshold and its physical length is no more than \(\delta\) times the unrestricted feasible route length. When the full-network calculation has executed, unweighted and demand-weighted **SPAN OD low-stress connectivity shares** are defined as: \[ \mathrm{LS}_{\mathrm{OD}}=|\Omega|^{-1}\sum_{i\in\Omega}I_i,\qquad \mathrm{LS}_{\mathrm{OD},w}=\frac{\sum_{i\in\Omega}w_i I_i}{\sum_{i\in\Omega}w_i}. \] The current Auckland snapshot withholds both point estimates because the production full-network reroute has not executed. In a completed calculation, the denominator includes unreachable pairs unless the release explicitly reports a second, conditional measure. The selection rule for \(\Omega\), its size, coverage of total demand, snap failures, and geographic composition are published to prevent a top-demand subset being read as a population statistic. The metric is not labelled as a universal network connectivity index and is not compared across cities unless geography, demand set, weights, routing coverage, stress threshold, and detour threshold are harmonised. ## 9. Portfolio comparison and cumulative evaluation Candidate comparison has two transparent views. The Network, Equity, School, Everyday, Transit, and Appraisal presets apply published weights to min–max-normalised indicators relevant to the named purpose. A Pareto frontier separately identifies candidates for which no other candidate is at least as good on every declared objective and strictly better on one. The interface shows every component and weight used by a preset. For the current Auckland snapshot, every cumulative step reapplies all selected exact-edge treatments and recomputes costs, path probabilities, demand response, and appraisal over the affected retained path market. This captures overlap and some complementarity without repeatedly crediting static candidate totals, but it is not full-network rerouting and cannot reveal paths absent from the retained choice set. The reference full-network algorithm is separately tested, but the Auckland full-network connectivity result is intentionally reserved for the separate sabbatical research integration. No Auckland point estimate is reported here. Presets and Pareto membership are decision aids, not proof of a globally optimal programme. Budget, dependency, deliverability, and geographic constraints remain explicit scenario inputs. ## 10. Economics Screening benefits are annualised from incremental quantities on a documented ramp and discounted over a 40-year default horizon. For a non-commercial public-sector activity, the principal real discount schedule follows NZTA General Circular 25/01: 2% in years 1–30 and 1.5% in years 31–40, with the required constant 8% sensitivity also reported. Capital, operations, maintenance, renewals, treatment life, and residual value are separate cash-flow fields in a common real price base. Benefit categories are not double-counted. A research snapshot may report an indicative lifecycle benefit–cost ratio and interval for its declared evidence scenario, not a formal appraisal BCR. The capability is labelled `research_only`; provisional local cost, maintenance, renewal, residual, benefit, e-bike, price-base and demand-response inputs must pass expert review before decision use. Candidate BCRs are not additive and do not form a programme BCR. The applicable Waka Kotahi Monetised Benefits and Costs Manual is authoritative for a formal appraisal. Historical default values retained for reproducibility are labelled by source version and price base. A current release must not claim MBCM compliance merely because it uses one value from an older manual. MBCM v1.7.5 applies to calculations commencing on or after 29 May 2026; General Circular 26/01 records that version update, while General Circular 25/01 is the authority for the discount schedule above. ## 11. Validation, uncertainty, and reporting Validation distinguishes present-day observed cycling from future scenario flows. Counter comparisons use aligned periods, directional definitions, coverage checks, and spatial matching rules; a future uplift scenario is not presented as a current-flow prediction. Diagnostics are reported without using a global ratio as automatic calibration unless that transformation is pre-registered and out-of-sample performance improves. Parameter, structural, data, scenario, and spatial uncertainty are different objects. Principal results are accompanied by confidentiality-bound, target-share, PCT scenario, stress, response, cost, and discount-rate sensitivities. Seeded Latin-hypercube parameter designs and rank stability summarise the declared model space; they do not claim to span every possible future. See `validation.md`, `uncertainty.md`, and `limitations.md`. Candidate evidence is communicated as a profile rather than a single summary grade. The profile reports data completeness, routing coverage, frontier or rank stability, parameter sensitivity, and explicit warnings. No one component is presented as a probability that a project will succeed. ## 12. Core references The main methodological precedents are Lovelace et al. (2017), Goodman et al. (2019), Mekuria et al. (2012), Lowry et al. (2012), Furth et al. (2016), Lowry et al. (2016), Buehler and Dill (2016), Yen (1971), Ben-Akiva and Bierlaire (1999), and Woodcock et al. (2018, 2021). Current appraisal rules are documented by NZTA's MBCM v1.7.5, General Circular 26/01, and General Circular 25/01. Area-deprivation interpretation follows Atkinson et al. (2024), with NZDep treated as contextual geography rather than individual identity. Full records are in `../references/library.bib`.