232
M. Fattore and A. Arcagni
i.e. the identification and severity functions, respectively. The following code
produces their frequency and cumulative distributions, depicted in Fig. 3.
ord <- order(res$idn_f)
plot(
res$idn_f[ord], res$prof_w[ord],
type = "h",
xlab = "Identification",
ylab = "Frequency"
)
plot(
res$idn_f[ord], cumsum(res$prof_w[ord]),
type = "s",
xlab = "Identification",
ylab = "Cumulative frequency"
)
ord <- order(res$svr_abs)
plot(
res$svr_abs[ord], res$prof_w[ord],
type = "h",
xlab = "Severity",
ylab = "Frequency"
)
plot(
res$svr_abs[ord],
cumsum(res$prof_w[ord]),
type = "s",
xlab = "Severity",
ylab = "Cumulative frequency"
)
3.3 Comparing Populations Over Posets
When two or more populations must be compared on a MIS, the easiest approach is
to score each statistical unit on the latent trait underlying the indicators and then
to compare the resulting distributions, either by using some synthetic indicator
(typically in the class of power means), or in terms of stochastic dominance. In
any case, some information get lost, when multidimensional data are “compressed”
to unidimensional scores, prior to the comparison. A more efficient and powerful
approach is to compare the distributions directly over the poset generated by the
indicator system, extending stochastic dominance to partially ordered structures.
In its essence, the idea is quite simple. Let π be the poset generated by the MIS
M. Fattore and A. Arcagni
i.e. the identification and severity functions, respectively. The following code
produces their frequency and cumulative distributions, depicted in Fig. 3.
ord <- order(res$idn_f)
plot(
res$idn_f[ord], res$prof_w[ord],
type = "h",
xlab = "Identification",
ylab = "Frequency"
)
plot(
res$idn_f[ord], cumsum(res$prof_w[ord]),
type = "s",
xlab = "Identification",
ylab = "Cumulative frequency"
)
ord <- order(res$svr_abs)
plot(
res$svr_abs[ord], res$prof_w[ord],
type = "h",
xlab = "Severity",
ylab = "Frequency"
)
plot(
res$svr_abs[ord],
cumsum(res$prof_w[ord]),
type = "s",
xlab = "Severity",
ylab = "Cumulative frequency"
)
3.3 Comparing Populations Over Posets
When two or more populations must be compared on a MIS, the easiest approach is
to score each statistical unit on the latent trait underlying the indicators and then
to compare the resulting distributions, either by using some synthetic indicator
(typically in the class of power means), or in terms of stochastic dominance. In
any case, some information get lost, when multidimensional data are “compressed”
to unidimensional scores, prior to the comparison. A more efficient and powerful
approach is to compare the distributions directly over the poset generated by the
indicator system, extending stochastic dominance to partially ordered structures.
In its essence, the idea is quite simple. Let π be the poset generated by the MIS