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5.1.4 Precedence Plots
Based on computation of AA and SS for a particular district, the
structure in the lower part of the subordination schematic can be
used to prepare a ‘precedence plot’ for visualization (Figure 5).
The precedence plot is a plot for AA (ascribed advantage) as Yaxis
and SS (subordinate status) as the X-axis. The prominent
position declines from top (upper-left) to toe (lower-right).
Primary prominence varies vertically showing that there is a
larger percentage of ascribed advantage (greater severity) with
increasing height. Horizontal variation on a given level shows
clarity of comparison. Farther to the right is greater clarity as
more definite (less severe) with a larger percentage of subordinate
status versus indefinite instances among the couplets where
ascribed advantage (greater severity) is lacking. In other words,
more indefinite instances constitute increased lack of clarity
(incomparability in the usual parlance of partial ordering).
Scheme 3 in [8] Function Facilities gives an R function named
PrecPlot which accepts the output of the ProdOrdr function and
produces a precedence plot.
5.1.5 Representative Ranks
Representative ranks show descriptive order statistics of indicator
rankings for each district. Representative ranks are concerned
with the rank distribution for any particular district. The rank
numbers received by a given district across all criteria can be
placed in a single array and sorted in ascending order. The
minimum, median, and maximum ranks for the district are
conveniently informative.
5.2 Upper Level Set (ULS) Scan statistics
By definition, a hotspot is a zone characterized by a high response
rate, it makes intuitive sense that ULS method search for a hotspot
begin with a cell with the highest response rate and annex to it
other cells with high response rates. The need to bring a definite
order for the search leads one to the concept of the ULS scan tree
or just the ULS tree. Denoting for cell a the response rate ga =
ya/na, a ∈ T over the connected region R, we define the ULS tree
as follows:
Let G = {ga | a ∈ T}
Suppose r1 > r2 > … > rm are all distinct members of G.
Define for i = 1, 2, …, m,
Ti = { a ∈ T | ga = ri },
and the upper level sets as unions of Ti’s,
Ui = T1 ∪ T2 ∪ … ∪ Ti
= { a ∈ T | ga ≥ ri }.
Let Ci = set of connected components of Ui, i = 1, 2, …, m, and
the reduced parameter space ΩULS = C1 ∪ … ∪ Cm.
The ULS tree = (ΩULS) is a tree whose nodes are members
of Ω ULS. The root of the ULS tree is Um = R. Let Z be a node
belonging to the ULS tree. If all cells belonging to Z have the
same response rate, then Z is a leaf node. Thus, members of C1 are
leaf nodes. If not all cells in Z have the same rates then let e =
min{ ga | a ∈ Z} and connected components of Z – {a ∈ Z: ga =
e} are members of Z. [13]
Since our search for a hotspot is based on cellular response rates,
we assign a unique level to each node of the ULS tree in terms of
its response rate and then scan the tree by level starting with nodes
level 1 down. Members of C1 are level 1 nodes. The root is the
level m node. In general, for 1 ≤ i ≤ m, the level of a zone Z is i if
and only if min{ ga | a ∈ Z } = ri. Since each cell is introduced in
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a unique node in the ULS tree, the ULS tree has at most N nodes.
Hence |ΩULS| ≤ N, the equality holding if and only if m = N. [13]
Several geometric properties should be satisfied by a collection of
cells from tessellation of study area before it could be considered
as a candidate for a hotspot cluster
1) the union of the cells should comprise a geographically
connected subset of the region R. Such collections of cells
will be referred to as zones and the set of all zones is denoted
by Ω. A zone Z∈Ω is a collection of cells that are connected.
2) the zone should not be excessively large. This restriction is
generally achieved by limiting the search for hotspot to zones
that do not comprise more than fifty percent of the region.
[14]
6. RESULTS AND DISCUSSION
6.1 Correlation Analysis and Descriptive
Statistics
Paired scatter plots make a simple way to see and get information
about the strength of the relationship between two indicators.
Scatter plots of pairs of infant health indicators are shown in
Figure 2. If the observation points tend to be in a straight line,
there is a correlation (relationship) between two variables
(indicators). Table 2 shows the correlation coefficient between
two indicators. Through this table it can be seen how strong the
relationship between the two indicators is. According to Figure 2,
there are tendencies of linear relationship between indicators infd
and pov, infd and lbw, and pov and lbw. Table 2 shows that the
correlation between infant death and poverty is 0.567. It can be
said that there is a positive statistical association between those
two indicators because it has p-value of 1.621e-10 (less than
0.05). In statistics, if a parameter estimation (in this case is the
coefficient correlation) has p-value of less than 0.05, it means the
error probability of making conclusion is less than 5 percent. This
is also true regarding infant death and low birth weight (r =
0.4163; p-value = 7.425e-06); and for poverty and low birth
weight (r = 0.399; p-value < 0.0001). There are positive
relationships between infant death (infd) and absence of health
personnel (abhp) and also between infd and average education
shortfall (avedsf), even though both relationships are weaker. The
relationship between infant death and births without health
personnel (abhp) is stronger (r = 0.319; p-value = 0.0007531)
than the relationship between infant death and average education
shortfall (r = 0.290; p-value = 0.002375).
Variability of the infant health indicators is shown by Figure 3a
and 3b. Figure 3a shows boxplots of infm, pov (in thousands), and
lbw. Thus, lbw is more variable than the other two indicators and
contains outliers. Figure 3b shows boxplots of births without
health personnel (%) and education shortfall.
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