Multiplicity Sampling of Migrant Stock
Also known as: Network Sampling of Migrants, Multiplicity Survey of Emigrants, Sirken Multiplicity Estimator, Relative-Report Migrant Sampling
Multiplicity sampling, introduced by Monroe Sirken in 1970, is a survey design for counting rare and hard-to-reach populations by letting respondents report not only about themselves but about eligible relatives living elsewhere. For migration research the appeal is direct: emigrants and dispersed migrants are, by definition, absent from the sampling frame of the place that wants to count them, so an ordinary household survey misses them. Under multiplicity sampling a sampled household reports its migrant relatives — say, children or siblings who have moved abroad — according to an explicit counting rule, which dramatically raises the effective coverage of the rare group because many households can each contribute reports. The price of this expanded reach is that the same migrant may be reportable by several households, so each reported migrant must be weighted by the inverse of the number of households eligible to report them, the migrant's 'multiplicity.' Sirken showed that this multiplicity-weighted estimator is unbiased and that, by enlarging the set of reporters, it can sharply reduce the sampling variance for rare populations compared with conventional surveys.
Key highlights
- Reaches rare and dispersed populations, including emigrants absent from the local frame, by counting them through social ties.
- Yields an unbiased estimator of totals and characteristics once each migrant is weighted by the inverse of its reporting multiplicity.
- Can substantially reduce sampling variance for rare groups relative to conventional residence-based surveys by enlarging the reporter set.
- Flexible: the counting rule can be tuned to trade off coverage against reporting burden and proxy-error risk.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use multiplicity sampling when the population you must count is rare, geographically dispersed, or absent from the available sampling frame — emigrants, return migrants, or migrants of a specific origin — but is socially connected to a reachable population through well-defined relationships. It is appropriate when you can write an unambiguous counting rule and credibly measure each migrant's reporting multiplicity, and when raising the effective coverage of the rare group is worth the added complexity of proxy reporting. It is less suitable when the counting rule cannot be made clear, when respondents cannot reliably report the existence or attributes of distant relatives (introducing severe proxy-response error), or when the multiplicity of each migrant cannot be determined, since without accurate multiplicities the estimator loses its unbiasedness. It also assumes the migrant is connected to the frame; truly isolated migrants with no reporting relatives remain uncounted.
Strengths & limitations
- Reaches rare and dispersed populations, including emigrants absent from the local frame, by counting them through social ties.
- Yields an unbiased estimator of totals and characteristics once each migrant is weighted by the inverse of its reporting multiplicity.
- Can substantially reduce sampling variance for rare groups relative to conventional residence-based surveys by enlarging the reporter set.
- Flexible: the counting rule can be tuned to trade off coverage against reporting burden and proxy-error risk.
- Requires accurate measurement of each migrant's multiplicity (the number of eligible reporters), which is hard to obtain in practice.
- Relies on proxy reports about absent relatives, so response error in identifying and describing migrants can be large and bias-inducing.
- Misses migrants with no eligible reporting relatives in the frame, so isolated or family-less migrants are systematically undercounted.
- Gains from reduced sampling variance can be offset by increased response and measurement error introduced by the multiplicity reporting.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What exactly is the 'multiplicity' of a migrant?
It is the number of sampled-frame units — usually households — that are eligible, under the counting rule, to report that migrant. If the rule lets parents and siblings report an emigrant, and an emigrant has two relevant households (one parental, one sibling), their multiplicity is two. Because such a migrant could be picked up through either household, counting them once per report would over-state the total, so each report is weighted by one over the multiplicity. Knowing the multiplicity accurately is therefore essential to the estimator's unbiasedness.
How is this different from snowball or respondent-driven sampling?
Snowball and respondent-driven sampling chain from one member of a hidden population to the next and rely on referral, producing non-probability or specially weighted samples of the hidden group itself. Multiplicity sampling instead starts from a conventional probability sample of an accessible frame (households) and uses fixed kinship relationships to report on the rare group from outside it, with exact multiplicity weights derived from the counting rule. It is a probability design with a network-based reporting rule, not a referral-driven recruitment of the migrants themselves.
Why does multiplicity sampling reduce variance for rare populations?
In a conventional survey a rare migrant can only be counted if their own (often absent) household is selected, so the chance of capturing any given migrant is tiny and the estimate is volatile. By letting several relatives report the same migrant, multiplicity sampling raises the probability that the sample captures information about each migrant, which lowers the sampling variance of the total. Sirken formalized this gain, while cautioning that it can be eroded by the extra response error involved in reporting about absent relatives.
Sources
- 1.Sirken, M. G. (1970). Household Surveys with Multiplicity. Journal of the American Statistical Association, 65(329), 257-266.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 23). Multiplicity Sampling of Migrant Stock. ScholarGate. https://scholargate.app/migration-studies/multiplicity-sampling-migrant-stock