CVEN9405 Chap.4 OD Matrices and Cross-Classification
OD Matrices and Cross-Classification
An origin-destination matrix counts movement between zone pairs, while cross-classification calculates different trip rates for groups of people or households. Both methods depend on disciplined data handling. The chapter follows the workshop workflow from raw person and trip records through stable identifiers, origin and destination counts, pivot tables, category assignment and rate calculation.
It distinguishes row productions from column attractions, preserves intrazonal trips, checks excluded or missing zones and reconciles matrix totals with eligible records. Category examples show why the overall rate must be denominator-weighted and why very fine classifications can create unstable cells.
What this chapter covers
- 01
OD cell counts, row productions and column attractions
- 02
Zone keys, selected-zone subsets and missing-code audits
- 03
Intrazonal trips and the influence of zone resolution
- 04
Person-trip joins and uniqueness on the person table
- 05
One-way and multi-way cross-classification rates
- 06
Survey weights, sparse cells and total reconciliation
Worked example · free
Reconcile a small origin-destination matrix
- +1Productions are row totals: O1 = 24 + 16 = 40 and O2 = 10 + 30 = 40.
- +1Attractions are column totals: D1 = 24 + 10 = 34 and D2 = 16 + 30 = 46.
- +1Grand total = 40 + 40 = 80 trips, matching 34 + 46 = 80.
- +1Intrazonal trips are diagonal cells 24 + 30 = 54, so share = 54/80 = 67.5%.
Key terms
- OD Matrix
- A table with origin zones on one dimension, destination zones on the other and trip counts in the cells.
- Intrazonal Trip
- A trip whose recorded origin and destination lie within the same analysis zone, represented on the matrix diagonal.
- Marginal Total
- A row or column sum describing productions from an origin or attractions to a destination.
- Cross-Classification
- A rate method that groups observations by selected attributes and computes a separate average within each category.
- Expansion Weight
- A survey factor used to scale a sampled record toward the population it represents under the survey design.
OD Matrices and Cross-Classification FAQ
Why do OD matrix row and column totals have different meanings?
A row collects every destination reached from one origin, so its sum is production from that origin. A column collects every origin feeding one destination, so its sum is attraction to that destination. Both sets must reconcile to the same grand trip total.
Should intrazonal trips be removed from a matrix?
Not automatically. Diagonal flows are real records under the chosen zone system, though their size depends on zone resolution. Report their treatment explicitly because removing them changes totals and can bias later distance, distribution or assignment analysis.
Why can a detailed cross-classification become unreliable?
Adding dimensions divides the sample into more cells. Some categories may contain few people or be dominated by unusual travellers, producing unstable rates. Inspect cell counts and uncertainty, combine categories for a substantive reason, or choose a model that uses continuous predictors more efficiently.
What should be checked before comparing two OD matrices?
Confirm that both matrices use the same zone boundaries, trip purpose, direction convention, time period, mode coverage and expansion basis. A cell-by-cell difference is meaningless when one matrix counts linked person trips and the other counts vehicle movements. Reconcile definitions and totals first, then investigate spatial changes.
Why can matrix balancing alter apparently reliable cells?
Balancing adjusts seed values so row and column totals meet externally supplied constraints. Even a well-observed cell may change because the algorithm must satisfy the entire system simultaneously. Report the seed, target margins and adjustment factors, and inspect cells with unusually large changes rather than treating the balanced matrix as directly observed truth.
How should empty cross-classification cells be handled?
An empty cell provides no direct estimate of its trip rate. Borrowing a neighbouring rate, combining categories or fitting a smoother model can be defensible, but each choice imposes structure. Record the rule, verify that combined groups remain behaviourally coherent and test how much the forecast depends on the imputed cell.
Exam move
Build a small OD matrix by hand before relying on a pivot table. Label rows as origins and columns as destinations, calculate both marginal sums and reconcile the grand total to eligible trip records. Then add one missing-code category and one selected-zone restriction so you learn how a subset differs from the complete system. For cross-classification, write the numerator and denominator in words before division.
Link person and trip tables on a stable identifier, verify uniqueness on the person side and count unmatched records in both directions. Practise weighted and unweighted overall rates to see why an average of category rates is usually wrong when categories differ in size. When categories are sparse, explain whether you would merge them, collect more data or use a regression form.
Keep raw record counts, weighted totals, denominators and rates in separate columns. Finish every exercise with the unit, such as trips per person per weekday, and a statement about whether the category rates are suitable for the forecast population.
