rivista italiana di economia demografia e statistica - Sieds

Rivista Italiana di Economia Demografia e Statistica 165
like leisure or sport clubs. The subjective perceptions of social exclusion and of
social usefulness are captured by the EB questions: “Do you feel left out of
society?” and “Do you feel to have the chance to play a useful part in society?”.
Finally, for the institutional dimension, the EB survey provides data about the
subjective evaluation and satisfaction of the respondents about the medical services,
their social entitlements in case of sickness, invalidity and unemployment, and the
presence of vandalism and theft in the place where they live.
In Latent Class models, covariates are used to predict the membership to latent
classes, thus improving their description. The individual level covariates we used
are the age and the occupational status of the respondents. Referring to the regional
level covariates, we considered the gross domestic product (GDP), and we defined
an indicator given by the ratio between the amount of taxes, social contribution and
transfers paid, and the primary income, representing a proxy of the social
protection expenditure of the region. Finally, using an individual response of
Eurobarometer, we computed an indicator that quantifies, for each European region,
the percentage of people attributing the responsibility of poverty and social
exclusion either to individual or to societal failure.
3. A multilevel latent class model to study social exclusion
We analyse the condition of social exclusion for the individuals. However,
sharing the same environmental conditions, individuals within a region tend to be
more alike than individuals coming from different regions. The approach followed
to deal with the intra-region correlation is the so-called multilevel approach
(Skrondal and Rabe-Hesketh 2004). First level units are individuals, and the first
level model corresponds to a standard LC analysis (Hagenaars and McCutcheon
2002). Based on the observed indicators, individuals are classified in latent classes,
representing the levels of exclusion. The regions where individuals live represent
the second level units: the regional differences in the distribution of the latent
variable are modelled allowing some parameters to vary across regions.
Consider individuals i= 1,..., nj
originated from an international sample of 77
European regions, j = 1,...,77 . Y
ijk
represents the response to item k (with
k = 1,...,12
) of person i coming from region j , whereas Y ij
is the full K × 1
n × K × vector
Y is the full ( ) 1
vector of responses of the same individual i , and
j
j
of responses of all individuals in region j . All the K = 12 indicators used in the
analysis are categorical. Z ij
and
g
Z denote respectively the individual and the
j