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L. S. Alaimo and P. Conigliaro
and then move on to the synthesis of the three dimensions of the SWB. Finally,
we propose an analysis of the differences in the SWB level between different subpopulations of respondents.
We identified the sub-populations according to the self-defined labour status. The
relationship between labour status and SWB is widely established in the litera-ture
(Gallie et al. 2012; Diener et al. 2018).
Our analysis intends to safeguard the multidimensionality of the phenomenon,
applying the Partially Ordered Set (hereinafter: poset) methodology to the microdata analysis.
2 The Issue of Subjective Indicators Synthesis
Methods to synthesize subjective measures expressed with ordinal characters have
become more and more sophisticated, while the possibility of making increasingly
complex calculations with simple computers has made such methods more accessible to scholars. There are two main kinds of synthesis approaches: aggregativecompensatory or non-aggregative (Maggino 2017).
The synthesis of the indicators of ES that uses the arithmetic mean is an example
of aggregative-compensatory approach (Ware et al. 1993; Eurostat 2016). This
approach is based on a reflective measurement model and it assumes that the five
questions measure one and only one latent variable. According to this model, it
is admissible to aggregate information allowing a value of an indicator that is
consistent with the concept to be compensated by a value of another indicator
that appears to be reverse. The model supposes the existence of a high correlation
between the indicators that concur to detect the latent variable, which can be
interpreted as an expression of a high internal consistency. Thus, in a compensatory
approach using, for instance, the arithmetic mean to synthesize different measures,
a respondent expressing the [5, 3, 1] combination on a set of three ordinalscale responses from 1 to 5 would be assimilated without distinction to another
responding [3, 3, 3]. It is evident how the use of an aggregative method flattens
the differences between the two different combinations, making equal two profiles
that are actually different (Alaimo and Maggino 2020). Furthermore, the use of
arithmetic mean for the synthesis is conceptually wrong if we consider each affect
as a partially independent element of the emotional status, but primarily because
the five variables expressing affects are ordinal and not cardinal. In brief, statistical
tools for the synthesis of indicators based on an aggregative approach are inadequate
for describing and dealing with multidimensional systems of ordinal data (Fattore
et al. 2011). For this reason, the choice of a non-aggregative method for the
synthesis of SWB variables is the most correct choice. In this work we adopted
the poset methodology. It grounds on partial orders as an application of discrete
mathematics and it is not compensatory. It identifies response profiles basing on
possible combinations of modalities and defines sorting criteria for these profiles.
L. S. Alaimo and P. Conigliaro
and then move on to the synthesis of the three dimensions of the SWB. Finally,
we propose an analysis of the differences in the SWB level between different subpopulations of respondents.
We identified the sub-populations according to the self-defined labour status. The
relationship between labour status and SWB is widely established in the litera-ture
(Gallie et al. 2012; Diener et al. 2018).
Our analysis intends to safeguard the multidimensionality of the phenomenon,
applying the Partially Ordered Set (hereinafter: poset) methodology to the microdata analysis.
2 The Issue of Subjective Indicators Synthesis
Methods to synthesize subjective measures expressed with ordinal characters have
become more and more sophisticated, while the possibility of making increasingly
complex calculations with simple computers has made such methods more accessible to scholars. There are two main kinds of synthesis approaches: aggregativecompensatory or non-aggregative (Maggino 2017).
The synthesis of the indicators of ES that uses the arithmetic mean is an example
of aggregative-compensatory approach (Ware et al. 1993; Eurostat 2016). This
approach is based on a reflective measurement model and it assumes that the five
questions measure one and only one latent variable. According to this model, it
is admissible to aggregate information allowing a value of an indicator that is
consistent with the concept to be compensated by a value of another indicator
that appears to be reverse. The model supposes the existence of a high correlation
between the indicators that concur to detect the latent variable, which can be
interpreted as an expression of a high internal consistency. Thus, in a compensatory
approach using, for instance, the arithmetic mean to synthesize different measures,
a respondent expressing the [5, 3, 1] combination on a set of three ordinalscale responses from 1 to 5 would be assimilated without distinction to another
responding [3, 3, 3]. It is evident how the use of an aggregative method flattens
the differences between the two different combinations, making equal two profiles
that are actually different (Alaimo and Maggino 2020). Furthermore, the use of
arithmetic mean for the synthesis is conceptually wrong if we consider each affect
as a partially independent element of the emotional status, but primarily because
the five variables expressing affects are ordinal and not cardinal. In brief, statistical
tools for the synthesis of indicators based on an aggregative approach are inadequate
for describing and dealing with multidimensional systems of ordinal data (Fattore
et al. 2011). For this reason, the choice of a non-aggregative method for the
synthesis of SWB variables is the most correct choice. In this work we adopted
the poset methodology. It grounds on partial orders as an application of discrete
mathematics and it is not compensatory. It identifies response profiles basing on
possible combinations of modalities and defines sorting criteria for these profiles.