Assessing Subjective Well-being in Wide Populations. A Posetic Approach. . .
251
5 Application of the Partial Ordering Methodology
The exploratory analysis confirms that the three main dimensions of SWB cannot
be summarised in a single measure using aggregative compensatory approaches
without losing significant information. This synthesis involves a very delicate twostep process. The first step defines the ES by synthesizing the five affects; in the
second one, the ES becomes an input variable, together with LS and Mol, to define
a SWB measure, which allows us to assess the level of SWB of the population of
respondents. The poset methodology allows creating a non-aggregative and noncompensatory synthesis of the three dimensions of well-being, based on solid
mathematical criteria (Fattore et al. 2015; Fattore and Bruggemann 2017). In
particular, it seems the most suitable approach to synthesize the five variables
(affects) expressing ES. In effect, these variables are weakly correlated, they are
expressed in terms of frequency of subjective experience and their modalities
represent the order and not absolute values (they do not enjoy the properties of
a ratio scale and the different levels are not equidistant). We believe that the five
affects do not lie in a continuum, which identifies a latent variable: we cannot say
that a frequent happiness and an equally frequent depression give rise to an average
level of ES (even if the temporal reference is limited to the last four weeks).
A first problem is the definition of the ES poset, due to the criticality linked to
the number of profiles expected in a set of five variables each with five modalities
(3125). In fact, each partially ordered set that we can draw is one of the possible sets
(linear extensions) generated by the comparison of profiles. The number of possible
linear extensions in a set of 3125 profiles is enormous and makes computation
impossible. Thus, to overcome computational problems, we have recoded all the
five variables in three modalities (Table 1). By doing this, the number of the possible
profiles becomes 243. Figure 2 reports the distribution of the answers according to
each affect. Only 1.2% of profiles are “homogeneous” (i.e. [1,1,1,1,1], [2,2,2,2,2],
[3,3,3,3,3]). The 38% of respondents have a profile of this type (in particular, 26%
of total population present a profile [3,3,3,3,3]) 14 .
A second problem is to know the specific ES value to be attributed to each
respondent, starting from the values assumed by the 5 affects. According to Fattore
Table 1 Recoding of affect variables
Variables
Modalities
Nervous
Down
Calm
Depressed
Happy
Always or most of the time
1
1
3
1
3
Sometimes
2
2
2
2
2
A little or none of the time
3
3
1
3
1
14 For an example of the distribution of homogeneous profiles within the total ones, see: Conigliaro
(2018).
251
5 Application of the Partial Ordering Methodology
The exploratory analysis confirms that the three main dimensions of SWB cannot
be summarised in a single measure using aggregative compensatory approaches
without losing significant information. This synthesis involves a very delicate twostep process. The first step defines the ES by synthesizing the five affects; in the
second one, the ES becomes an input variable, together with LS and Mol, to define
a SWB measure, which allows us to assess the level of SWB of the population of
respondents. The poset methodology allows creating a non-aggregative and noncompensatory synthesis of the three dimensions of well-being, based on solid
mathematical criteria (Fattore et al. 2015; Fattore and Bruggemann 2017). In
particular, it seems the most suitable approach to synthesize the five variables
(affects) expressing ES. In effect, these variables are weakly correlated, they are
expressed in terms of frequency of subjective experience and their modalities
represent the order and not absolute values (they do not enjoy the properties of
a ratio scale and the different levels are not equidistant). We believe that the five
affects do not lie in a continuum, which identifies a latent variable: we cannot say
that a frequent happiness and an equally frequent depression give rise to an average
level of ES (even if the temporal reference is limited to the last four weeks).
A first problem is the definition of the ES poset, due to the criticality linked to
the number of profiles expected in a set of five variables each with five modalities
(3125). In fact, each partially ordered set that we can draw is one of the possible sets
(linear extensions) generated by the comparison of profiles. The number of possible
linear extensions in a set of 3125 profiles is enormous and makes computation
impossible. Thus, to overcome computational problems, we have recoded all the
five variables in three modalities (Table 1). By doing this, the number of the possible
profiles becomes 243. Figure 2 reports the distribution of the answers according to
each affect. Only 1.2% of profiles are “homogeneous” (i.e. [1,1,1,1,1], [2,2,2,2,2],
[3,3,3,3,3]). The 38% of respondents have a profile of this type (in particular, 26%
of total population present a profile [3,3,3,3,3]) 14 .
A second problem is to know the specific ES value to be attributed to each
respondent, starting from the values assumed by the 5 affects. According to Fattore
Table 1 Recoding of affect variables
Variables
Modalities
Nervous
Down
Calm
Depressed
Happy
Always or most of the time
1
1
3
1
3
Sometimes
2
2
2
2
2
A little or none of the time
3
3
1
3
1
14 For an example of the distribution of homogeneous profiles within the total ones, see: Conigliaro
(2018).