Graphics Reference
In-Depth Information
Identity Linking
heeasiestandmostcommoncaseofsamplepopulationlinking,whichisalsoknown
asempiricallinking,usestheidentitymapping id
Ω.hislinkingschemeorig-
inates fromthe goal tovisualize the connection between observations that have been
taken at the same individual orcase.It providesthe means tousethe natural connec-
tion between features observed on the same set of cases. It is intrinsically built into
the common data matrices used in statistics in which each row represents one case
and each column a variable that has been measured for this case. Identity linking is
not necessarily restricted to identical sample populations. Whenever two variables
have the same length they can be bound together in a single data matrix and then
all sotware programs will treat the variables as if they have been observed with the
same individuals. However, one has to be careful when interpreting such artificially
linked variables.
Ω
Hierarchical Linking
In practice, databases to be analyzed come from different sources and use different
units of analysis. Nevertheless, data bases that are to be analyzed together typically
show some connection between the various sample populations. A quite common
case is some kind of hierarchy for the various sample populations. his hierarchy can
result from different aggregation levels ranging from the micro level of individual
persons via different social groups up to the macro level of different societies. Simi-
lar situations arise quite common with spatial data which are measured on different
geographical grids, like on the local, the regional, the country and the continental
level. For such kind of data it is convenient to visualize the connection obtained by
the hierarchical aggregation also in the displays. heconnection between the sample
population spaces has then to be established by a relation m
Ω
for which
each element of Ω
is mapped to an element of Ω
in such a way that some kind of
filtration is generated.
Ω
Neighborhood or Distance Linking
A special case arises when we work with geographic data where quite oten the most
important display is a (chorochromatic) map and the focus is on investigating local
effects. It is thus quite oten desirable to see differences between one location and its
various neighbors. So here the linking scheme points also toward the same display
and establishes a self-reference to its sample population. A variety of neighborhood
definitions are used in spatial data analysis, each one leading to a somewhat different
linkingrelation ofthekind m
ω
ω
, ω
.Each
definition of neighborhood or distance leads to a new variant of linking relation, but
the main principles remain the same.
Ω
Ω
, m
(
)=
ω
Ω
dist
(
)
d
Linking Models
8.2.2
AspresentedinWilhelm(
)modelsaresymbolsforvariable termsanddefinethe
set of observations that shall be represented in the displays. Models are the central
