2378 intergenerational mobility: methods of analysis

(Goodman 1979). The starting point is the
very restricted uniform association model that
assumes all contiguous associations in a table to
be identical: ln ij . This model uses one
parameter to characterize all odds ratios in a
table, which is parsimonious but also often too
restrictive (in these data, L2 224.7; df 35).
The stringent assumption can be meaningfully
relaxed in three ways:

1 By including diagonal density parameters
that represent within class immobility over
and above the association.
2 By scaling the distances between the row
i and column j categories: ln ij
i1 i j1 j; the category scal
ings i and j can be interpreted as measures
of distance between or similarity among social
categories with respect to the mobility
chances. If categories are identically scaled
( 1 2), this suggests that they can be
regarded as a single social class. If the scalings
are very different, this implies not only that
mobility between the classes is extremely dif
ficult, but also that they have very different
mobility exchanges with other classes.
3 As a useful special restriction in this model
we can introduce equal scalings for origins
and destinations: i i.
This model is known as the Goodman
Hauser model after its principal inventors
(Goodman 1979; Hauser 1984). This model
yields a very good fit to the data (L2 12.0;
df 23). In Table 5 we present the scaling and
immobility parameters.
Although not equidistant, we see from the
scaling measures that the distance between
the classes is ordered except for the farmers
(IVc), who are better placed between unskilled
manual workers (VIIa) and agricultural workers
(VIIb). The immobility data show that inheri
tance is strong not only for farmers (IVc) and
the self employed (IVab), but also for the ser
vice class (I II).
In the GoodmanHauser model the distance
between the classes is estimated. An attractive
alternative is the measured variable approach in
which known characteristics are used as scal
ings for the classes. In Houts (1984) SAT
model, he scales origins and destinations using
socioeconomic status (S), on the job autonomy
(A), and specialized training (T). Breen and
Whelans (1994) AHP model scales origins
and destinations with origin and destination
specific measures for agriculture (A), hierarchy
(H), and property (P).

COMPARATIVE ANALYSIS

The measures presented here for absolute
mobility can also be used to compare the level
of absolute mobility between countries and per
iods. An important prerequisite is that tables
are comparable (of same dimension and using
similar class categories). Dissimilarity indices
can be computed to compare origin and desti
nation distributions between tables, and in this
way divergence or convergence between coun
tries and periods can be assessed (see, e.g.,
Breen & Luijkx 2004).
For the comparative analysis of relative
mobility, log linear models are extremely well
suited. To compare tables, we need to extend
the log linear model defined earlier:

ln Fijk Oi Dj Tk OTik DTjk
ODij ODTijk;
for all i 1; :::; I; j 1; :::; J; k 1; :::; K
We now have an additional one variable effect
( Tk) pertaining to the table totals, two additional
two variable effects ( OTik; DTjk) pertaining to
the origin and destination distributions for the

Table 5 Parameters for the Goodman Hauser model
Class I II III IVab IVc V VI VIIa VIIb
Scaling 0.48 0.35 0.23 0.38 0.08 0.11 0.66
Immobility 0.69 0.21 1.13 2.82 0.41 0.21 0.20