3.2. Method: family variance decomposition
In order to estimate the impact of paternal and maternal status
on the socioeconomic status of their children, we used a family
variance decomposition method. The justification of this approach
in studying the influence of the family background follows the
same reasoning as in the case of sibling similarities: the more siblings
are alike, the greater the impact of the shared background
is expected to be. This shared family variation reflects anything
common among siblings, including their living surroundings in
childhood and youth, parental resources, and the shared genetic
background.
To estimate the family variances needed for the decomposition,
we fitted three-level random-effects (mixed-effects) linear
regression models in which the observations are clustered according
to families and individuals (random effects). The families have
up to eight children, and there are two observations of occupational
status for each sibling, which allows us to fit models with
random effects for unobserved heterogeneity (unexplained variance)
at the level of both the family and the individual. The model
can be expressed as the following regression equation:
y = ˇ
Xijk + ıi + εij + uijk
Xijk includes observed parental and child characteristics; residual
ıi reflects differences in occupational status due to unobserved
family-level heterogeneity, which does not vary between children
ofthe same family; εij refers to unobserved individual-level heterogeneity,
which is constant over the two observations on occupation
for each individual (at the ages of 25–29 and 30–24); and uijk refers
to the residual (temporal) variance.
We are primarily interested in unobserved family-level heterogeneity
that should include all the sources of background variation
that are not yet controlled for in each model. Controlling for
anything shared among siblings, such as maternal or paternal
education, occupational status, or income, reduces this variation.
The individual heterogeneity component includes the unobserved
individual-level variation in occupational achievement that does
not originate from the shared background; controlling for factors
that are specific to each sibling and are not shared would reduce this
variation. In principle, controlling for parental characteristics could
also reduce the individual level variance. This would be the case,