Log-Linear Mobility Model
Also known as: log-linear model for mobility, topological mobility model, quasi-independence model, levels model
Log-linear mobility models analyze an origin-by-destination mobility table by modeling the logarithm of its expected cell counts as a sum of terms: separate effects for the origin and destination marginals plus interaction terms that capture the origin–destination association. By specifying that association parametrically — through diagonal, level, or scaled terms — these models test precise hypotheses about the structure of social fluidity independent of the changing sizes of classes.
Key highlights
- Separates the origin–destination association from the marginal distributions, isolating relative mobility.
- Encodes substantive hypotheses (diagonal inheritance, class barriers, level structure) as testable, parsimonious parameter sets.
- Nested-model comparison via G² and BIC gives a rigorous way to choose among competing fluidity structures.
- Enables formal cross-national and cross-cohort comparison of social fluidity through multi-table layer models.
Intuition
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How it works
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When to use it
Use log-linear mobility models when you have a contingency table of categorical origins and destinations and want to model the origin–destination association explicitly — testing specific structural hypotheses (diagonal inheritance, class barriers, symmetry) and comparing fluidity across groups or time net of marginal change. They are the standard tool for relative-mobility analysis. They are not appropriate when origin or destination is continuous (use intergenerational elasticity), when categories are ordered and a scaled association is wanted (the Goodman association model is more apt), or when cells are so sparse that maximum-likelihood estimates are unstable. They describe association, not causal mechanism.
Strengths & limitations
- Separates the origin–destination association from the marginal distributions, isolating relative mobility.
- Encodes substantive hypotheses (diagonal inheritance, class barriers, level structure) as testable, parsimonious parameter sets.
- Nested-model comparison via G² and BIC gives a rigorous way to choose among competing fluidity structures.
- Enables formal cross-national and cross-cohort comparison of social fluidity through multi-table layer models.
- Requires categorical class schemes; choice of categories and their number strongly affects results.
- Sparse or zero cells in detailed tables destabilize estimates and complicate degrees-of-freedom accounting.
- Topological-level designs encode the analyst's theory; a poorly chosen design matrix can misrepresent the association.
- The models describe statistical association, not the causal processes (education, networks) that generate mobility.
Common pitfalls
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Applications
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Frequently asked
What is the 'perfect mobility' model?
Perfect mobility is the model of statistical independence between origin and destination: the destination distribution is identical for every origin class, so where you start carries no information about where you end. It is the baseline against which all association is measured. Real mobility tables always reject it, and the interesting question is which structured departures from independence best describe the data.
How is a topological (levels) model specified?
The analyst supplies a design matrix that assigns each cell of the table to one of a small number of 'levels' reflecting a theory about where mobility barriers lie — for example separating the diagonal, near-diagonal moves, and long-range moves, or manual versus non-manual boundaries. The model estimates a single association parameter per level, capturing structured fluidity with few parameters. The design matrix is a theoretical input, not an estimate.
Why is BIC preferred over the chi-square G² test in mobility research?
Mobility tables are usually built from very large samples, in which the G² likelihood-ratio test rejects even substantively trivial misfit. The BIC penalizes model complexity relative to sample size, favoring parsimonious models and providing a more useful criterion for choosing among competing association structures when N is large.
Sources
- 1.Hauser, R. M. (1978). A structural model of the mobility table. Social Forces, 56(3), 919–953.
- 2.Goodman, L. A. (1979). Simple models for the analysis of association in cross-classifications having ordered categories. Journal of the American Statistical Association, 74(367), 537–552.
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ScholarGate. (2026, June 22). Log-Linear Mobility Model. ScholarGate. https://scholargate.app/sociology/log-linear-mobility-model