UNIDIFF Mobility Model
Also known as: UNIDIFF model, log-multiplicative layer effect model, uniform difference model, Xie-Erikson-Goldthorpe model
The uniform difference (UNIDIFF) model, equivalently the log-multiplicative layer effect model, compares the strength of origin–destination association across several mobility tables — countries, time periods, or birth cohorts. It assumes the tables share a common pattern of association ψ_ij but allows the overall strength of that pattern to differ by a single layer-specific multiplier φ_k. A φ_k above one means stronger origin effects (less fluidity) in that layer; below one means greater fluidity.
Key highlights
- Summarizes cross-table differences in association with a single, interpretable parameter per layer.
- Cleanly separates change in association strength from change in the marginal distributions.
- Parsimonious: tests the trend in fluidity with far fewer parameters than full interactions.
- Standard, comparable framework that underpinned landmark comparative-mobility research.
Intuition
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How it works
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When to use it
Use UNIDIFF when you have several mobility (or other association) tables and want to test whether the strength of the origin–destination association differs across them while assuming a common pattern of association — the standard question of whether social fluidity is rising, falling, or differing across countries. It is the workhorse for comparative and trend mobility analysis. It assumes the difference between tables is a uniform scaling of one pattern; if the pattern itself changes shape across layers, UNIDIFF is misspecified and a more flexible (e.g., regression-type or RC-II) model is needed. It describes association, not causal mechanism, and shares the sparse-cell sensitivities of log-linear models.
Strengths & limitations
- Summarizes cross-table differences in association with a single, interpretable parameter per layer.
- Cleanly separates change in association strength from change in the marginal distributions.
- Parsimonious: tests the trend in fluidity with far fewer parameters than full interactions.
- Standard, comparable framework that underpinned landmark comparative-mobility research.
- Assumes a single common association pattern scaled uniformly; it cannot capture changes in the shape of association across layers.
- Requires the analyst to commit to a common pattern, which may not hold across very different societies.
- Inherits log-linear sensitivities to sparse and zero cells.
- Describes the strength of association, not the educational or institutional mechanisms behind it.
Common pitfalls
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Applications
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Frequently asked
What does the φ (phi) parameter mean?
φ_k is the layer-specific multiplier on the common association pattern. With the reference layer fixed at φ = 1, a layer with φ greater than 1 has stronger origin–destination association — less fluidity, stickier class origins — while a layer with φ below 1 is more fluid. The sequence of φ values across layers traces the trend or cross-national pattern in fluidity.
What is the key assumption of UNIDIFF, and when does it fail?
The crucial assumption is that all tables share one common association pattern ψ_ij and differ only by uniformly scaling its strength. If the actual pattern of barriers changes shape across layers — say, a particular class boundary weakens while another strengthens — then a single multiplier cannot represent the difference and UNIDIFF is misspecified, requiring a more flexible model.
How does UNIDIFF relate to ordinary log-linear mobility models?
UNIDIFF is a log-multiplicative extension of log-linear mobility models to multiple tables. A single-table log-linear model describes the association within one mobility table; UNIDIFF stacks tables and adds the φ_k multiplier so that the common association can be scaled per layer, turning the comparison of fluidity across tables into the estimation and interpretation of those multipliers.
Sources
- 1.Xie, Y. (1992). The log-multiplicative layer effect model for comparing mobility tables. American Sociological Review, 57(3), 380–395.
- 2.Erikson, R., & Goldthorpe, J. H. (1992). The Constant Flux: A Study of Class Mobility in Industrial Societies. Clarendon Press / Oxford University Press.ISBN 978-0-19-827383-6
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Cite this page
ScholarGate. (2026, June 22). UNIDIFF Mobility Model. ScholarGate. https://scholargate.app/sociology/unidiff-mobility-model