intergenerational mobility: methods of analysis 2379

distinct tables, and an additional three variable
effect ( ODTijk) pertaining to the variation in
origindestination association in the different
tables.
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
ODT
ijk
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
to Work

REFERENCES AND SUGGESTED
READINGS

Blau, P. M. & Duncan, O. D. (1967) The American
Occupational Structure. Wiley, New York.
Breen, R. (2004) Social Mobility in Europe. Oxford
University Press, Oxford.
Breen, R. & Jonsson, J. O. (2005) Inequality of
Opportunity in Comparative Perspective: Recent
Research in Educational Attainment and Social
Mobility. Annual Review of Sociology 31: 223 43.
Breen, R. & Luijkx, R. (2004) Social Mobility in
Europe between 1970 and 2000. In: Breen, R.
(Ed.), Social Mobility in Europe. Oxford University
Press, Oxford, pp. 37 75.
Breen, R. & Whelan, C. T. (1994) Modelling Trends
in Social Fluidity: The Core Model and a
Measured-Variable Approach Compared. Eur
opean Sociological Review 10: 259 72.
Erikson, R. & Goldthorpe, J. H. (1992) The Constant
Flux: A Study of Class Mobility in Industrial Socie
ties. Oxford University Press, Oxford.
Featherman, D. L. & Hauser, R. M. (1978) Oppor
tunity and Change. Academic Press, New York.
Ganzeboom, H. B. G. & Treiman, D. J. (1996)
Internationally Comparable Measures of Occupa-
tional Status for the 1988 International Standard
Classification of Occupations. Social Science
Research 25: 201 39.
Ganzeboom, H. B. G., Treiman, D. J., & Ultee, W. C.
(1991) Comparative Intergenerational Stratification
Research: Three Generations and Beyond. Annual
Review of Sociology 17: 277 302.
Goldthorpe, J. H. (1980) Social Mobility and Class
Structure in Modern Britain. Clarendon Press,
Oxford.
Goodman, L. A. (1979) Multiplicative Models for
the Analysis of Occupational Mobility Tables and
Other Kinds of Cross-Classification Tables. Amer
ican Journal of Sociology 84: 804 19.