intergenerational mobility: methods of analysis 2377

multiplied by a constant, the odds ratios remain
the same. This property is useful in the case of
stratified samples: the odds ratios are not sensi
tive to an over or underrepresentation of a
certain category. Even more important is the
fact that it makes comparison of the origin
destination association possible between tables
with different marginal distributions. This ori
gindestination association or relative mobility
is also known as social fluidity.

Log Linear Models to Constrain the Odds
Ratio Patterns

The full set of contiguous odds ratios (Table 4)
constitutes a complete account of the association
pattern, the so called saturated model or uncon
strained association model. Log linear models
are used to constrain the odds ratios in the satu
rated model to a more parsimonious set in order
to find a sociologically more meaningful and
statistically more powerful account of the data.
We define the following log linear model:

ln Fij Oi Dj ODij; for all
i 1; :::; I; j 1; :::; J
where Fij is the (under the model) expected
frequency in the ijth cell of the table; is the
grand mean; oi and Dj are the one variable
effects pertaining to the origin and destination;
and ODij is the origindestination association.
Identifying restrictions on the parameters have
to be defined. As fit measures, the conventional
log likelihood ratio 2 statistic (L2), and the
BIC statistic (Raftery 1986) are mostly used.
Which patterns of social fluidity can be
modeled using log linear analysis? The simplest
pattern would be the one with no origin
destination association, the already presented per
fect mobility model (in that case all ODij 0).
But such a model does not fit our data well
(L2 336.9; df 36). A next model is that of
quasi perfect mobility. It assumes that people
have a higher propensity to stay in their own
class than moving to other classes (and that this
propensity is different for each class), but that
for people who are mobile, there is perfect
mobility. We display this model as a matrix
showing which association parameters of the
model affect which cell of the table:

This model fits the data much better, but
is still not statistically significant (L2 65.4;
df 29). The highest immobility parameter
belongs to class IVc (farmers), followed by
VIIb (agricultural workers) and IVab (self
employed). Another pattern that improves
the fit of the model further is the core model
of social fluidity.

Scaled Association Models

Scaled association models have turned out to be
very useful for summarizing relative mobility

2 1 1 1 1 1 1
1 3 1 1 1 1 1
1 1 4 1 1 1 1
1 1 1 5 1 1 1
1 1 1 1 6 1 1
1 1 1 1 1 7 1
1 1 1 1 1 1 8

Table 4 Odds ratios for the mobility table
Destination
Origin (I II):III III:IVab IVab:IVc IVc:(V VI) (V VI):VIIa VIIa:VIIb
(I II):III 2.35 0.69 2.25 0.67 1.09
1.38
III:IVab 0.93 4.50 0.22 1.31 1.24
0.62
IVab:IVc 1.12 0.56 99.00 0.03 1.62
3.58
IVc:(V VI) 0.87 0.69 0.01 140.25 0.43
0.17
(V VI):VIIa 1.34 0.90 2.91 0.34 1.76
1.25
VIIa:VIIb 1.43 0.97 5.50 0.24 1.24
8.83