Is this the same as snowball sampling?

No. Recruiting contacts through referrals does not automatically supply the probability design and multiplicity information used here.

Can duplicates be removed correctly?

Yes, with an estimator using the target entities' appropriate inclusion probabilities. Deduplication alone is not that estimator.

Can AI find the links?

It may assist record matching, but mistaken links change counts and weights. Evaluate that measurement process separately.

AI Glossary / Statistics and probability / Advanced

Network sampling

Definition

Network sampling is a survey approach in which a target item can be reported through several linked sampling units. This entry uses the survey-statistics meaning associated with multiplicity counting rules, rather than sampling vertices for a graph-learning algorithm.

What it means

Imagine estimating how many specialist devices are in use by asking repair centers about the devices they maintain. One device might appear in several centers' records. Counting reports as separate devices inflates the result; simply removing duplicates does not necessarily produce the right population estimate either.

The design must distinguish the centers selected for questioning from the devices being counted. Their links explain why different devices have different chances of appearing.

How it works

Specify the population, eligible links and sampling frame before collection. Select reporting units with known probabilities. Record each reported item's multiplicity: the number of eligible frame units linked to it, including units not sampled.

One multiplicity estimator gives each report a fraction equal to one divided by its item's multiplicity, then applies the reporting unit's sampling weight. Under complete coverage, correct links and appropriate probability sampling, these fractions support unbiased total estimation. Reporting errors, missing links and nonresponse require separate attention.

Three practical examples

1. Device-support planning: centers A and B both maintain device V. If its multiplicity is two, each center's report carries half a device before sample expansion. V's serial number alone does not explain its chance of selection.

2. Supplier research: a specialist workshop supplies several distributors. A distributor sample can reach that workshop through multiple routes. The study defines eligible distributor relationships for a fixed reference period, rather than treating every historical contact as a current link.

3. Training evaluation: one learner attends two participating centers. A center-based survey distinguishes unique learners from registrations. If the desired total is registrations, collapsing those two records would answer a different question.

Think of it this way

Think of a device's count as a cake divided among its reporting centers. A device linked to three centers assigns one-third to each. Across all eligible centers, the pieces sum to one device. Sampling observes some pieces and expands them according to the center-selection design. Cutting the cake using only the centers that happened to respond gives the wrong pieces.

Worked example

Consider a completely fictional population of four centers, A, B, C and D, and three devices, U, V and W. U links only to A; V links to A and B; W links to B, C and D. Their multiplicities are one, two and three.

Select two centers uniformly without replacement. Each center has selection probability one-half, so its expansion weight is two. The adjusted report totals are A: 1 + 1/2 = 3/2; B: 1/2 + 1/3 = 5/6; C: 1/3; and D: 1/3.

If A and B are selected, the estimate is 2 × (3/2 + 5/6) = 14/3, approximately 4.67 devices. This exceeds the true total of three: unbiasedness does not mean every sample is exact.

The six possible center pairs AB, AC, AD, BC, BD and CD give estimates 14/3, 11/3, 11/3, 7/3, 7/3 and 4/3. Their average is exactly three. This exhaustive calculation demonstrates design unbiasedness for this small example.

Expanding raw report counts instead gives an average of six, because the full population contains six links. Deduplicating each sample and then multiplying its unique-device count by two gives an average of 14/3, still too high. W appears in every possible pair, whereas U appears in only half. Equal device weights therefore misrepresent their unequal inclusion chances.

Illustrative case study

Fictional Willow Equipment wants to estimate the installed base of a specialized sensor. Its analysts initially label every center record a separate installation. A pilot shows that some sensors move between authorized service centers during the year.

The team defines a device-center link as an eligible maintenance relationship during the reference quarter. It tests whether respondents can report the total number of qualifying centers for each sensor, rather than just those visible in the survey extract.

Before estimating a total, Willow compares a small fully enumerated test population with every possible sample of its centers. The exercise catches both duplicate inflation and an incorrect deduplication rule. The team also records that devices outside the service network remain outside coverage. This is an invented illustration, not evidence of measured commercial results.

Common misconceptions and mistakes

“The network is necessarily a social network.” The worked example uses device-service relationships, without friendships or referrals.

“Multiplicity means sampled reports.” V's multiplicity remains two even when only A is selected. Replacing it with one would change its contribution incorrectly.

“An unbiased estimate must be an integer.” The estimate 14/3 is a weighted total, not a claim that a physical device is fractional.

“More reporting routes always improve precision.” Link configurations and collection costs matter. An estimator's valid weighting does not guarantee that this design is the most efficient choice.

Business use

Use the approach when a practical reporting frame reaches target entities indirectly and overlapping relationships are measurable. Agree whether the business question concerns devices, customers, relationships or transactions before setting counting rules.

For the example, a dashboard should show the reference quarter, center-selection procedure, coverage limits and estimate uncertainty. Displaying only “4.67 devices” hides the sampling variability that produced it. A larger real study needs variance estimation appropriate to its actual design, including any stratification or clustering.

Check your understanding

Why is W always observed in the example?

Answer: Any two-center sample contains at least one of B, C or D.

What is W's contribution when B and C are sampled?

Answer: Its two reports contribute 2 × (1/3 + 1/3) = 4/3 to the expanded estimate.

Does one sample prove unbiasedness?

Answer: No; the six-pair enumeration establishes the expectation here.

Related terms

Horvitz - Thompson estimator
Coverage error
Record linkage
Multiplicity weighting
inclusion probability
sampling frame
snowball sampling

Learn next

Recalculate the six samples after linking U to D as well. Update both its multiplicity and each center's adjusted total before comparing estimates. Then investigate how missing center responses would change the analysis.

Sources

OECD, Glossary of Statistical Terms, “Network sampling”: https://www.oecd.org/content/dam/oecd/en/publications/reports/2008/09/oecd-glossary-of-statistical-terms_g1gh9ad7/9789264055087-en.pdf

Monroe G. Sirken, Network Sample Surveys of Rare and Elusive Populations: A Historical Review, Statistics Canada Symposium 2004, especially Sections 1.2 and 2.2: https://www150.statcan.gc.ca/n1/pub/11-522-x/2004001/8614-eng.pdf

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