Discrete-Time Hazard of Migration
Also known as: Person-Period Logit Migration Model, Allison Discrete-Time Event-History Model, Annual-Data Hazard of Moving, Complementary Log-Log Migration Model
The discrete-time hazard model analyzes the timing of migration when the data arrive in chunks of time — usually person-years — rather than as exact dates. Paul Allison's 1982 formulation showed that an event history measured in discrete periods can be analyzed by a remarkably simple device: expand each person into one record per period they are at risk, mark whether the move happened in that period, and fit an ordinary binary regression (logit or complementary log-log) for the conditional probability of moving. The baseline period enters as a set of terms capturing duration dependence — how the risk of moving rises or falls with time elapsed — and covariates can change from period to period. Because annual migration data are the norm in panels and registers, this person-period approach has become the standard event-history tool in migration research, sitting alongside the continuous-time Cox model and extending naturally to competing destinations and repeat moves. Its great practical virtue is that the entire apparatus reduces to a logistic regression any analyst can run.
Key highlights
- Turns event-history analysis into a familiar binary regression on person-periods, so it runs in any logit or cloglog software at scale.
- Handles tied event times naturally, which is exactly the situation created by annual or interval-censored migration data.
- Models duration dependence explicitly and flexibly through baseline period terms rather than assuming a functional form.
- Extends cleanly to competing destinations and to repeat moves, letting the analyst study where as well as when people migrate.
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
Reach for the discrete-time hazard model when migration timing is recorded in coarse intervals — annual panel waves, register years, or census-based duration data — so that exact event times are unavailable or tied. It is the natural choice when you want duration dependence modeled flexibly, when covariates change between periods and should enter as period-specific values, and when moves come in distinguishable types that call for competing-risks or destination-choice modeling. It is also attractive simply because it reduces to a logistic or cloglog regression that integrates with standard software and large datasets. Prefer a continuous-time Cox model instead when exact dates are available and ties are few, and use a dedicated repeat-events design when the object of study is the rate of multiple moves rather than the timing of a single transition.
Strengths & limitations
- Turns event-history analysis into a familiar binary regression on person-periods, so it runs in any logit or cloglog software at scale.
- Handles tied event times naturally, which is exactly the situation created by annual or interval-censored migration data.
- Models duration dependence explicitly and flexibly through baseline period terms rather than assuming a functional form.
- Extends cleanly to competing destinations and to repeat moves, letting the analyst study where as well as when people migrate.
- The person-period expansion can produce very large datasets when many individuals are followed over many periods.
- Results can be sensitive to the width of the time interval, since coarser periods blur within-period timing and lump distinct moves together.
- As with continuous-time models, unobserved heterogeneity can masquerade as duration dependence unless a frailty term is included.
- Within-person correlation across periods must be addressed in the standard errors, or inference will be overstated.
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
Why does a discrete-time hazard model end up being just a logistic regression?
Because once you expand each person into one record per at-risk period with a move/stay indicator, the likelihood of the whole event history factors into a product of Bernoulli terms — exactly the likelihood of a logistic regression on those records. Allison's contribution was to make this equivalence explicit, so that estimating the conditional period probability of moving requires no special survival software, only a logit (for proportional odds) or complementary log-log (for proportional hazards) routine. The one thing you must add is a baseline term for the period or duration, which plays the role of the baseline hazard.
When should I use cloglog instead of logit?
Use the complementary log-log link when you want your discrete-time estimates to approximate continuous-time proportional-hazards ratios, for example to compare with or interpret as a grouped Cox model. The cloglog model arises exactly when an underlying continuous-time proportional-hazards process is observed only in intervals, so its coefficients estimate the same hazard ratios. The logit link gives proportional-odds interpretations and is fine when the hazard is small or when odds-ratio interpretation is acceptable; in practice, with low per-period move probabilities the two links give similar results.
How do I model where people move, not just when?
Treat destinations as competing risks. You either fit a separate discrete-time hazard for each destination type, censoring moves to other types, or, conditional on a move occurring, fit a multinomial logit that allocates the move across destination categories. This lets covariates have different effects on different destinations — for instance, a job offer might raise the hazard of a long-distance move while leaving short-distance moves unchanged. Blossfeld and Rohwer present competing risks as a standard extension of the event-history framework, and it is the right way to keep when and where in one coherent model.
Sources
- 1.Allison, P. D. (1982). Discrete-Time Methods for the Analysis of Event Histories. Sociological Methodology, 13, 61-98.
- 2.Blossfeld, H.-P., & Rohwer, G. (2002). Techniques of Event History Modeling: New Approaches to Causal Analysis (2nd ed.). Lawrence Erlbaum.ISBN 9780805840919
You have read it. What now?
Cite this page
ScholarGate. (2026, June 23). Discrete-Time Hazard of Migration. ScholarGate. https://scholargate.app/migration-studies/discrete-time-hazard-of-migration