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M. Fattore and A. Arcagni
identification function idn(x) of a profile x ∈ π is computed as the fraction of
linear extensions where x is ordered below at least one element of τ . The severity
function svr(x) is computed as the average of the distances of x from the least
element above the threshold in each linear extension of π , normalized to [0, 1]
(for details and formulas, see Fattore 2016).
5. Each statistical unit in the dataset then inherits the identification and severity
scores of the profile it shares.
6. Finally, synthetic indicators of various kind can be computed at population level,
starting from the individual scores.
Remark At first, the above procedure can seem somehow “artificial” and deserves a
short comment on the “naturality” of the posetic approach. The sequence of steps 1−
6 can be seen as a composition of actions, each of which is “natural”, i.e. inherently
consistent with its input (e.g., we structure input data as a poset, we apply algorithms
that are consistent with the poset structure. . . ). Assuming that “the composition of
consistent actions is overall consistent”, we can consider the described procedure
as a “natural” way to approach the evaluation of multidimensional deprivation or
similar socio-economic traits.
The procedure just outlined can be tuned to different contexts and modified
according to the needs of the study, as done in Arcagni et al. (2019), where a
“welfare” threshold has been added to the poverty one, to better assess and compare
populations’ deprivation.
3.2.1 Real Example
To exemplify the above procedure, here we report part of the analysis developed
in Arcagni et al. (2019), about deprivation of migrants in Lombardy (Italy). Data
come from the 2014 ORIM 2 Survey, which involved 4000 subjects, from different
countries of origin, and pertain to migrants’ socio-economic conditions.
Among other social traits, the cited paper focuses on migrants’ social fragility,
described through a MIS comprising the following four ordinal attributes:
• Working dynamics, coded on a 6-degrees scale: 1 – Persistent unemployment; 2
– Run into unemployment; 3 – Worsening condition 4 – Non-active status; 5 –
Improving condition; 6 – Stable condition.
• Legal status, coded on a 2-degrees scale: 1 – Illegal; 2 – Legal.
• Dependent family in country of origin, coded on a 2-degrees scale: 1 – Yes; 2 –
No.
• One-income family, coded on a 2-degrees scale: 1 – Yes; 2 – No.
2 ORIM stands for “Osservatorio regionale per l’integrazione e la multietnicità” (“Regional
observatory on integration and multiethnicity”).
M. Fattore and A. Arcagni
identification function idn(x) of a profile x ∈ π is computed as the fraction of
linear extensions where x is ordered below at least one element of τ . The severity
function svr(x) is computed as the average of the distances of x from the least
element above the threshold in each linear extension of π , normalized to [0, 1]
(for details and formulas, see Fattore 2016).
5. Each statistical unit in the dataset then inherits the identification and severity
scores of the profile it shares.
6. Finally, synthetic indicators of various kind can be computed at population level,
starting from the individual scores.
Remark At first, the above procedure can seem somehow “artificial” and deserves a
short comment on the “naturality” of the posetic approach. The sequence of steps 1−
6 can be seen as a composition of actions, each of which is “natural”, i.e. inherently
consistent with its input (e.g., we structure input data as a poset, we apply algorithms
that are consistent with the poset structure. . . ). Assuming that “the composition of
consistent actions is overall consistent”, we can consider the described procedure
as a “natural” way to approach the evaluation of multidimensional deprivation or
similar socio-economic traits.
The procedure just outlined can be tuned to different contexts and modified
according to the needs of the study, as done in Arcagni et al. (2019), where a
“welfare” threshold has been added to the poverty one, to better assess and compare
populations’ deprivation.
3.2.1 Real Example
To exemplify the above procedure, here we report part of the analysis developed
in Arcagni et al. (2019), about deprivation of migrants in Lombardy (Italy). Data
come from the 2014 ORIM 2 Survey, which involved 4000 subjects, from different
countries of origin, and pertain to migrants’ socio-economic conditions.
Among other social traits, the cited paper focuses on migrants’ social fragility,
described through a MIS comprising the following four ordinal attributes:
• Working dynamics, coded on a 6-degrees scale: 1 – Persistent unemployment; 2
– Run into unemployment; 3 – Worsening condition 4 – Non-active status; 5 –
Improving condition; 6 – Stable condition.
• Legal status, coded on a 2-degrees scale: 1 – Illegal; 2 – Legal.
• Dependent family in country of origin, coded on a 2-degrees scale: 1 – Yes; 2 –
No.
• One-income family, coded on a 2-degrees scale: 1 – Yes; 2 – No.
2 ORIM stands for “Osservatorio regionale per l’integrazione e la multietnicità” (“Regional
observatory on integration and multiethnicity”).