distinct tables, and an additional three variable
effect ( ODTijk) pertaining to the variation in
origindestination association in the different
Let us think of T as a number of tables from
different periods within one country, although
it could also be tables from different countries
or a combination of periods and countries (the
model can also be further extended to take
period and country into account as distinct
variables). A first model is the constant social
fluidity (CnSF) model that assumes no varia
tion in the odds ratios OD across the tables (all
0). Erikson and Goldthorpe (1992) and
Xie (1992) have proposed an elaboration of the
CnSF model to test for trends, the UniDiff
(uniform difference) or log multiplicative layer
effect model. UniDiff takes an intermediate
position between CnSF (same pattern and
strength of association in all tables) and the
saturated model (different pattern and different
strength of association for all tables) by using as
a constraint that the set of odds ratios in one
table differs from the set of odds ratios in the
next table only by a log multiplicative scaling
factor: ln ijk k ln ij , where 1 1 by
convention. In this case ln ij refers to the set
of log odds ratios in the first table.
The UniDiff model does not model the pat
tern of mobility in the tables, but simple exten
sions to do so can be made by elaborating
on the scaled association model presented ear
lier: ln ijk k i1 i j1 j. In this
model, scalings i and j are assumed to be
equal across tables and the association k is
allowed to differ (in a similar way as k in the
UniDiff model). Both k and k can be con
strained linearly or curvilinearly.
General statistical programs like SPSS, SAS,
and STATA can be used to estimate most of
the models presented here. To estimate the log
multiplicative scaled association and UniDiff
models, specialized programs such as LEM
(Vermunt 1997) are more appropriate.
Although published more than 20 years ago,
Houts Mobility Tables (1983) is still one of the
more comprehensive introductions to the log
linear analysis of mobility tables. A more recent
work in which both substantive and methodo
logical aspects of mobility analysis are pre
sented is the collection of country papers in
Breen (2004), which also includes a compara
tive analysis of eight nations over three decades.
SEE ALSO: Educational and Occupational
Attainment; Income Inequality and Income
Mobility; Intergenerational Mobility: Core
Model of Social Fluidity; Mobility, Horizontal
and Vertical; Mobility, Intergenerational and
Intragenerational; Mobility, Measuring the
Effects of; Occupational Mobility; Occupa
tional Segregation; Transition from School
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(Ed.), Social Mobility in Europe. Oxford University
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