But
How
Does Place Matter? Using Bayesian Networks to Explore
a Structural Definition of Place
By
Colin Flint
Mark Harrower
Robert Edsall
Department of Geography
Pennsylvania State University
University Park, PA 16802
Paper
presented at "New Methodologies for the Social Sciences: The Development and
Application of Spatial Analysis for Political Methodology." University of Colorado at
Boulder, 10th

12th of March, 2000
.
ABSTRACT
Previous attempts by electoral geographers to
investigate the contextual nature of politics
have focused upon space rather than place.
To further the inquiry of contextual politics a
structural definition of pla
ce is needed.
A
structural view of place requires a
consideration of what constitutes a place, how these elements of place interact, and how
they combine to mediate politi
cal behavior within places. A spatial analysis of the change
in the Nazi party vote between 1928 and 1930 illustrates how the search for spatiality in
aggregate data concentrates attention towards the manifestation of place

specific
behavior in spaces rath
er than the operation of the elements of place. Bayesian networks
are introduced as an alternative technique
that may
examine
a structural definition of
place
. Bayesian networks allow for an examination of how the component parts of place
interact to produce a political outc
ome. Again, the Nazi party vote between 1928 and
1930 is used to exemplify the argument. Bayesian networks show how the institutional
and economic aspects of place interacted to produce support for the Nazi party. Spatial
analyses and Bayesian networks are
complementary techniques that show how space and
place create contextual settings for political behavior.
Keywords: Bayesian networks, spatial analysis, Nazi party, ele
ctoral geography, place,
space.
1
1. Introduction
Geographers have developed structural
notions of place, whereby the practices
and institutions within places mediate political behavior to produce place

specific
outcomes. Place and politics are both the product of group and individual actions, or in
other words, they are socially constructed
. In addition, there is a recursive relationship
between place and politics as political acts create and recreate places and, in turn, the
nature of a place frames future political activity. Electoral geographers have mapped the
geographical variation in p
olitical activity and, more recently, have used spatial analytical
techniques to uncover the place

specific interaction of economic and social processes
with politics. However, spatial

analytical tools have concentrated, up to now, upon
spatial patterns ra
ther than place

specific behaviors. Hence, geographers have been left
with the task of showing that there is a geography, or place does matter, without being
able to investigate how or why.
The two purposes of this paper are to call for a concentration up
on place rather
than space in the contextual analysis of politics and to introduce Bayesian Networks
(BNs) as a technique to explore a structural understanding of place and politics. In order
to make our argument we first discuss differences between compos
itional and structural
conceptions of place, and show the theoretical superiority of the latter. Second, we
describe how spatial regressions have incorporated the spatiality in aggregate data to
show the place

specific nature of political behavior. Third,
spatial regression techniques
are criticized for focusing upon space rather than place. Fourth, we describe BNs and
show how they may be used to identify the complexity of the mediating role of different
2
aspects of place upon political behavior. Analyses
of the growth of the Nazi party vote
between 1928 and 1930 are used to illustrate both the spatial statistical techniques and
BNs.
Bayesian Networks (BNs) provide a way to uncover probabilistic relationships
between variables while also denoting key subse
ts of variables and the interactions
between them (Heckerman et al., 1995). Hence, BNs allow for the evaluation of causal
relationships between the dependent and independent elements of a regression equation,
and also the complexity of relationships within
the explanatory variables. In the
quantitative analysis of political behavior, BNs can be used to explore the complexity of
the relationships identified by a spatial

regression analysis. Such exploration also
provides insights into the way that different
aspects of place interact, or, in other words,
how the mutually constituted elements of place combine to produce place

specific
behavior. The end result is an examination of the relationships
within
places rather than
across
spaces.
Despite the promise o
f BNs to the contextual analysis of politics, we stress that
this is our first attempt at applying this technique to political behavior. Thus, the spirit of
the paper is an exploratory foray into both the technique itself and the analysis of a
mediated and
structurally complex notion of place. The paper is organized in the
following way. First, we outline definitions of place and how place is theorized to
mediate politics. In this section we emphasize the difference between a structural and a
compositional
notion of place. Next, we note how such notions of place have been
modeled using spatial

structural regression techniques to highlight the spatiality in the
data, spatial dependence and spatial heterogeneity. The fourth section of the paper uses
3
the exampl
e of a spatial regression analysis of the growth of the Nazi party vote between
1928 and 1930 to illustrate the focus upon space rather than place. Section five introduces
an alternative focus and an alternative technique by describing the logic and constr
uction
of BN's. Our purpose in adopting BNs is to unpack the results of a spatial

structural
regression to uncover the complex interactions between the different components of a
place and how they combine to influence political behavior. In section six, we
use the
growth in the Nazi party vote between 1928 and 1930 as an example of how BNs can
further our understanding of the contextual influences upon political behavior by
evaluating the causal role of different aspects of place and how they are related to
each
other. In the concluding section, we discuss future steps in the use of BNs as a tool for
contextual analysis to assess its potential as a technique that can provide a systematic
analysis of place rather than space.
2. Defining Place and How It Matte
rs
Place matters because it structures the way we behave (Pred, 1990). Our everyday
experiences and actions are a framed by the institutions, practices and people with whom
we interact. The problems people face, the possible avenues towards solutions, and
the
interpretation of what needs to be done and why differ depending upon the economic
trajectory of a place, how institutions within a place filter information, and the senses of
identity that are developed and given meaning within places. The uniqueness
of a place is
not a matter of the variation in the size of particular socio

economic groups, i.e., the size
of the black population or Muslim populations. Such a compositional view of place
misses the complexity of a place and how its institutionalized pr
actices and customs
mediate behavior.
4
When place is considered a structure rather than an entity composed of different
attributes, it becomes the unit of analysis. Political behavior is place

specific because of
“the intricacies of interaction, the speci
ficity of particular times and spaces, the sense of
living as meeting, the context” (Thrift, 1983, p. 39). An analysis of place

specific
political behavior, at the very least, needs to capture the institutions that are interacting,
the senses of identity,
and the actions of different socio

economic groups. Political
outcomes are place

specific because knowledge is interpreted and acted upon within the
varying contexts of institutionalized memory, interpretation of contemporary events, and
endorsement of pol
itical responses (Thrift, 1983, p. 45). A contextual analysis of political
behavior considers the role of institutions and identity in mobilizing particular groups. In
other words, a structural view of place considers the setting of political actors rather
than
just the attributes of those actors.
Thus, the analysis of place and politics is, at the outset, an ontological issue. The
scale of analysis for a contextual approach to politics is the geographic setting that
mediates the political outcomes of inter
est. The key questions are what are the
components of place that determine political behavior, and how do these components
interact? A number of geographers have established theoretical frameworks to guide us in
an interrogation of these questions.
John Ag
new’s
Place and Politics
(1987) established a theoretical basis for the
analysis of place

specific behavior. Agnew identified three aspects of place; location, the
role a place plays in the world

economy; locale, the institutional setting of a place; and
s
ense of place, identities forged and given meaning within places. Of course, these three
aspects are separated purely for heuristic reasons. Within places, the existence and
5
vitality of institutions such as unions and chambers of commerce is partly a funct
ion of
the type and health of local economic activity. In addition, a sense of what it means to be
working class or a member of an ethnic minority will be developed within institutions,
i.e. within a union, and in relation to the activities of other instit
utions, the police or
religious congregations, for example. Thus, Agnew (1987) provides a view of places as
being constituted by economic, institutional and socio

cultural processes.
Doreen Massey’s (1994) definition of place makes explicit some of the
imp
lications of Agnew’s (1987, 1996) work. For Massey (1994, p.120), places are
“networks of social relations” that are dynamic over time. The current expression of
social relations is, to some degree, a function of the legacy of previous social relations
tha
t have been altered. Places are continually changing as current political actors use the
background of existing social relations to foster change. Also, for Massey the nature of a
place is a product of its linkages with other places and not just a matter o
f its internal
features. Trade, migration flows, and cultural exchanges are examples of how a place
reaches out in ways that alter its economic, institutional and cultural make

up. Thus,
Massey makes explicit the temporal dynamic of a place and the way tha
t it is part of a
broader network of places.
The importance of place in the study of political behavior demands an ontology
that recognizes places as objects of study. Such a structural view of place promotes a
holistic and relational view of place instead
of a compositional perspective that counts the
socio

economic make

up of places. This is where electoral geographers using aggregate
data run into trouble when in dialogue with political science colleagues. “Holistic view”
can translate into an argument t
hat places are “complex” and “unique”. In other words,
6
the idea that “place matters” is often asserted by reference to individual case studies, at
best, or even anecdotal examples. What have been elusive are systematic studies showing
how places matter.
To
conclude this section, we will summarize the components of place that need to
be identified to include a structural definition of place into a systematic analysis. An
operationalization of Agnew and Massey’s definition produces the following measurable
co
mponents of place; economic role, institutional setting, political

cultural identity,
linkages with other places, and changes over time. The historical dynamism of political
behavior within places has been illustrated by a number of studies (Agnew, 1987; A
rcher
and Shelley, 1986; Flint, 1998a; Johnston and Pattie, 1998). Also, studies have shown the
importance of linkages between places at either the local (Flint, 1998a) or extra

local
scale (Cox, 1998). The empirical section of this paper will illustrate h
ow BNs may be
used to identify the relative importance of the other three aspects of place in mediating
political behavior and how these aspects are related to each other. In this way it is hoped
that place can be shown to matter while retaining the integr
ity of a structural notion of
place.
Studies that attempt to uncover the role of place often end up looking at the
spaces created by political behavior. For example, Flint’s (1998b) analysis of the Nazi
party showed that its electoral support varied across
regional spaces. Other studies of the
regional nature of political behavior include O’Loughlin and Bell (1999), Johnston and
Pattie (1988), and Archer and Taylor (1981). Also, the role of linkages between places in
determining political behavior have been
incorporated into contextual analyses by
defining localized pockets, or spaces, of support (Flint, 1998a). In summary, space rather
7
than place has dominated geographer’s contextual analyses of politics. Hence, the
difficulty in substantiating the claim th
at place matters.
The reason for the prioritization of space over place in contextual analyses lies in
the search for spatiality in aggregate data that has driven many studies (O’Loughlin et al,
1994; Flint, forthcoming). The following section describes t
he two forms of spatiality in
aggregate data and illustrates their role in focusing attention upon space rather than place.
An alternative approach is to use spatial

regression analysis as an aid in constructing BNs
that can explore the complexities of pla
ce.
3. Spatiality in Aggregate Data
Electoral geographers commonly use aggregate data. This is an ontological
decision as the purpose of geographic inquiry is to investigate the specificity of place and
its influence upon political behavior. Aggregate dat
a is used to measure attributes of
places, or other geographic units, which, in combination, combine to form structures
mediating behavior. The focus, therefore, is open the geographic setting rather than the
individual. Two aspects of spatiality in aggreg
ate data have been identified and
incorporated into analyses by electoral geographers: spatial dependence and spatial
heterogeneity.
Spatial dependence exists when the value of the dependent variable in one spatial
unit of analysis is partially a function
of the value of the same variable in neighboring
units. The existence of spatial dependence may be a manifestation of diffusion and can
result in "Galton's problem", whereby "certain traits in an area are often caused not by the
same factors operating in
dependently in each area but by diffusion processes"
(O'Loughlin and Anselin, 1992, p.17). In other words, an increase in electoral support for
8
a political party in one place may have been a function of increased support in
neighboring places. The identif
ication of spatial dependence and its incorporation into the
analysis of political behavior operationalizes a key component of place, the importance of
the linkages between places in defining context (Massey, 1994).
Spatial heterogeneity refers to a regio
nal pattern in the data that results in
instability of parameters across the whole study (Anselin, 1988, p.9). In other words, the
slope of any regression equation would not be constant when comparing regions with the
complete data set. The identification
of spatial heterogeneity within the data indicates the
presence of geographical variation in political behavior and its incorporation into
statistical models illuminates the place

specific behavior of voter and party. For example,
white

collar employees m
ay have supported a party in one region while blue

collar
employees supported the same party in a different region.
The application of spatial dependence and spatial heterogeneity to electoral
geography have been detailed elsewhere (O’Loughlin et al, 1994;
Flint, 1998a; Flint,
1998b; Flint, 1999). In this paper, we identify the logic of spatial dependence and spatial
heterogeneity in order to show how, by definition, they allow us to explore the role of
space in electoral behavior rather than the role of pl
ace.
Spatial heterogeneity indicates the existence of regionally specific relationships
across the data. It may exist as a mere statistical nuisance, expressed as lack of constancy
of the regression error variance, or it may be indicative of contextual v
ariation in political
behavior (O'Loughlin and Anselin, 1992, p.27). Structurally significant heterogeneity is
identified in OLS models by diagnostic tests for heteroskedasticity (Anselin, 1992).
Heteroskedasticity is the presence of non

constant variance
of the random regression
9
error over all of the observations. If heteroskedasticity is present, the OLS estimates are
unbiased but inefficient and inference based upon the t and F statistics will be misleading
and the measures of fit will be wrong (Anseli
n, 1988, p. 120).
If diagnostic tests for heteroskedasticity are significant, regional patterns of
political behavior are indicated. In other words, subsets of geographical units, or regional
groupings of counties or census blocks, are identified in which
different explanations for
political behavior are found. After diagnostic tests have identified heterogeneity, previous
studies, theoretical frameworks, and exploratory analysis can be used to identify regions
that display voting behavior different from t
he remainder of the data. The identification
of these regions, called spatial regimes, is then used to estimate structural change models
(Anselin, 1992, p. 32

1). To estimate a structural change model, cases within a particular
region are identified by th
e use of a dummy variable and the structural change estimation
reported separate regression coefficients for the two sets of cases, those in the region and
those that are not. The structural change model is represented by the equation
y
i
= α
i
+ X
i
ß
ij
+ ε
i
for d = 0
y
j
= α
j
+ X
j
ß
ij
+ ε
j
for d = 1
where both the constant terms (α
i
(
j
)) and the slope terms (ß
i
(
j
)) take on different terms
(O'Loughlin & Anselin, 1992, p. 31). To diagnose whether the structural change
estimation captures th
e heterogeneity within the region, tests for heteroskedasticity
should be insignificant.
In addition, a Chow test was reported for the model as a whole and for each of the
explanatory variables. The Chow statistic (Chow, 1960) is a test upon the stability
of
regression coefficients. The Chow statistic is distributed as an F variate with K, N

MK
10
degrees of freedom (with M as the number of regimes). The test is a test of the null
hypothesis
H
0
: g'b = 0
where b is a vector of all the regression coefficients
(including the constant terms) and g'
is a K by 2K matrix [I
k


I
k
], with I
k
as a K by K identity matrix (Anselin, 1992, p. 32

2). The corresponding Wald test may be expressed as the equation
W = (g'b){g'[var(b)]

1
g}

1
(g'b)
where b are the estimates of t
he regression coefficients and var(b) is the corresponding
(asymptotic) variance matrix (Anselin, 1992, p. 32

2). A significant value for the Chow
test measuring the stability of the regression coefficients between the two spatial regimes
indicates that h
eterogeneity existed at the regional scale. In other words, different
political behavior existed within the regions, or contextual settings, defined by the spatial
regimes.
The identification and incorporation of spatial heterogeneity into the analysis
of
political behavior identifies spaces of regionally specific behavior. These spaces are the
product of the combination of relatively similar places and the political behavior that they
mediate. The spatial regimes of a structural change model are the man
ifestation of how
place matters in politics but they are not able to capture the processes that determine the
role of place as a geographic structure. In other words, spatial heterogeneity and
structural change models are a concept and technique that descr
ibes the product of place

specific behavior rather than its operation.
Spatial dependence is also incorporated into the spatial analysis of political
behavior in order to identify a key component of place, linkages to other places (Massey,
11
1994). Spatia
l dependence may be incorporated into models of voting behavior in one of
two ways depending upon the diagnostic tests reported in the initial models. The average
value of the vote in neighboring geographic units in the first of a sequence of two
election
s, referred to hereafter as the
temporal

spatial lag
, was incorporated into the
initial OLS model. If spatial dependence existed after the inclusion of this variable, then
it was replaced by the
spatially lagged dependent variable
, the average value of th
e
dependent variable in neighboring spatial units. In both of these cases, the definition of a
neighbor may be calculated either by distance or contiguity. If the temporal

spatial lag is
positive in sign and statistically significant, it indicates that t
he size of the vote in one
unit
was partially a function of the size in support in the neighboring units in the first of
the two elections in that particular period of change. If the spatially lagged dependent
variable was positive in sign and statistical
ly significant, it indicates that the vote in a unit
was partially a function of the vote in the same election in neighboring units. The
inclusion of either of these variables models the role of the interlinkages between places
in defining the contextual s
etting of the voter. Methodologically, the presence of spatial
dependence produces biased and inconsistent regression coefficients (Anselin, 1988,
p.59).
Spatial dependence can exist in two forms (Anselin, 1988, pp. 11

13). In its
substantive form, sp
atial dependence is interpreted as spatial contagion, whereby the
behavior in one spatial unit is partly explained by similar behavior in neighboring units.
Methodologically,
substantive spatial dependence
is incorporated into the regression
equation by
adding the spatially lagged dependent variable. Formally this may be
expressed by the equation
12
y =
p
WY + Xß + ε
where y is a vector of observations on the dependent variable, X is a matrix of
explanatory variables, including the temporal

spatial lag, ß are the regression
coefficients, e is an error term,
p
is a spatial autoregressive coefficient, and WY
is the
spatial lag, the average of the value of the dependent variable in neighboring units
(Anselin, 1992, p. 27

1).
In addition to the substantive interpretation, spatial dependence may also have to
be controlled for as a nuisance. This form of spatia
l dependence is known as
spatial
error dependence
as it is associated with model specification errors that are not
restricted to one unit but spill across the spatial units of observation. The usual
assumptions of homoskedastic and uncorrelated errors no l
onger hold and so the spatial
error model incorporates a spatial autoregressive process in the error term. To estimate
regression coefficients in the presence of spatial error dependence, a spatial
autoregressive model is estimated which may be stated in
the following equations
y = Xß + ε
ε = We + x
where the notation is the same as above with We being a spatial lag of the errors and x is
a "well

behaved" error term with mean of zero and variance matrix s
2
I (Anselin, 1992,
p.29

1). The presence of both the spatial lag and the "w
ell

behaved" error term creates a
problem of simultaneity. Therefore, a maximum likelihood procedure that includes the
estimation of a nonlinear likelihood function must be executed (Anselin, 1988, p. 59). If
the spatial error dependence is ignored, the
OLS estimates would be unbiased but could
13
result in misleading inference if the variance estimates are not adjusted because the OLS
variance expressions do not account for the dependence among the errors.
Substantive spatial dependence is a means of oper
ationalizing the role linkages
between places play in mediating political behavior. However, though the goal is to
uncover the specificity of place the result is the inclusion of connections across space
between places. Defining neighbors in terms of conti
guity or distance is a spatial
relationship that aims to uncover the nature of places. As with the consideration of spatial
heterogeneity, incorporating spatial dependence into an analysis of contextual political
behavior prioritizes the construction and m
ediating role of spaces rather than places. In
other words, including the spatiality of aggregate data in the spatial analysis of political
behavior shows the manifestations of place

specific behavior but not the mediation of
politics and social processes
within places, a mediation that produces the specificity of
place.
There is a second implication of using spatial regression models to investigate
the recursive interaction between place and politics. Regression analysis partitions the
roles played by p
articular aspects of place. Interrelationships between the independent
variables in a multiple regression analysis are controlled for rather than sought and
incorporated as part of the model. Hence, a compositional view of place is promoted,
whereby place

specificity is a product of the combination of different socio

economic
attributes. These two implications of using spatial regression to explore politics and place
are exemplified through an analysis of the Nazi party vote.
14
4. A Spatial Analysis of the N
azi Party Vote
C
ensus data were used to create variables t
o measure different aspects of place.
1
Location, or the economic role of a place, was investigated by using variables measuring
the proportion of different classes and employment sectors within a county. Specifically,
the following variables were used to me
asure location: BCTRADE, the percentage of the
workforce who were blue collar workers in trade and transport; and TOTSELF, the
percentage of the workforce who were self

employed. Locale, or institutional setting was
engaged by including variables that meas
ured religious affiliation and labor organization.
Specifically, the following variables were used to measure locale: PROT, the percentage
of the population who were Protestant; and MANIND, the percentage of the workforce
who were manual industrial workers
. Finally, sense of place was measured by including
variables that identified alienation. Specifically, the following variables were used to
measure sense of place; UNEMP, the percentage of the workforce who were
unemployed; and TURNOUT, the electoral turn
out as a percentage of eligible voters for
the second of the two elections within the period of change in the Nazi vote. The
dependent variable, NAZI30CH, was the percentage change in the Nazi party vote
between the consecutive
Reichstag
(parliament) elect
ions of May 1928 and September
1930.
It should be noted that these variables are also instruments to test theoretical
frameworks that have been used to explain Nazism. Institutional setting is the place

specific manifestation of Burnham's (1972) theory
of political confessionalism. Burnham
argued that Catholics and the industrial proletariat would not have been attracted to the
Nazi party because of their respective allegiances to the Center party and the Social
15
Democrats and Communists. In other words,
religious and labor institutions would have
been an element of the particularity of places. Sense of place is the manifestation of local
identities generated by alienation (Arendt, 1958; Kornhauser, 1959), and surrogately
measured by unemployment and elect
oral turnout. Finally, the class theory (Lipset, 1960)
argued that the economic policies of the Nazi party attracted the self

employed middle

class, while Flint (1998b) and Ault and Brustein (1998) found that artisans and skilled
workers were also suscepti
ble to the Nazi’s economic policies. The economic role of a
place is investigated by the relative size of these economic groups, measured by the
variables TOTSELF and BCTRADE.
Exploratory analysis is required before the estimation of spatial regression
models. Multiple regression models were specified using the variables discussed above
plus adding others by stepwise regression techniques. Though a theoretically informed
model is preferred, additional variables were considered in order to counter the cr
itique of
electoral geography that contextual influences identified by geographers are a function of
poorly specified models that do not include all the relevant explanatory variables
(McAllister, 1987). The only other significant variable to be found was
TRADJOBS, the
percentage of the workforce employed in the trade and transport sector.
The spatial analysis of the Nazi party was conducted at the national scale in order
to maximize the number of cases and, therefore, assist in facilitating the robustne
ss of the
Bayesian network created later. The results are displayed in Table One. The model
provides evidence for a significant role for all three aspects of place but the direction of
the relationships is surprising. The positive and significant value of
the variable PROT
illustrates, as expected, that places without strong Catholic institutions supported the Nazi
16
party. The negative and significant value of the variable TURNOUT indicates that
political alienation was not a factor in the Nazi party vote. I
nstead, the institutional
setting was one of weakening political parties allowing the Nazis capture their support.
The two variables measuring socio

economic status are harder to interpret. Both
BCTRADE and TRADJOBS measure employment in the trade and tran
sport sector, the
former focusing upon a particular class of employee. BCTRADE displays a negative sign
while TRADJOBS is positive. Other analyses have shown BCTRADE to be positively
related to the Nazi party vote (O’Loughlin et al, 1994; Flint, 1998b). Th
e positive sign of
TRADJOBS may indicate support for the Nazi party in urban transport nodes, but this is
just speculation.
In addition to significant socio

economic variables, regional dummy variables
were included to capture heterogeneity across the nat
ional surface. Germany was divided
into eight historical

cultural regions in order to capture the heterogeneity of German
society and its possible influence upon voting behavior. The regions were Prussia, the
Northwest, Rhineland

Westphalia, Silesia, Centr
al Germany, Baden, Bavaria, and
Württemberg (Figure One). The regions were designed to capture cultural similarities and
historical interactions and political organization. Also, the borders of these regions were
related to the regions created by the Nazi
party to organize their political campaigns. In
sum, the regions are an attempt to capture a similarity in the message being disseminated
by the Nazis and the similarity in the cultural setting within which it was received. The
significant value of three o
f the regional dummy variables indicates the presence of
regional heterogeneity. However, the significant value of the Breusch

Pagan statistic
indicates heterogeneity within the regions.
17
Finally, the regression model is a spatial error estimation to cont
rol for spatial
autocorrelation across the error terms. LAMBDA is the spatial autoregressive coefficient
that controls for the spatial error autocorrelation and allows for the estimation of unbiased
and efficient estimates (Anselin, 1992, p.29

2).
Spatial
regression models are effective in illustrating spatial variation in political
behavior as well as how linkages across space is a factor in defining place

specific
politics. However, the emphasis upon space is to the detriment of the understanding of
how
different elements of place interact to mediate politics. Spatial regression does offer
insights into the attributes of places that mediate political behavior. However, these
attributes, as independent variables in a regression analysis, are treated separa
tely. The
alternative approach offered by BNs has the benefit of exploring the interaction between
different aspects of place and how they combine to mediate political behavior. Spatial
regressions promote a compositional view of place by separating out ad
ditive socio

economic attributes of place. On the other hand, BNs promote a structural view of place
by showing the mutually constituted complexity of place and its mediation of politics.
5. An Overview of Bayesian Approaches
Bayesian networks (BNs) have
recently gained popularity in the modeling of
uncertain relationships among variables. For introductory and accessible texts see Pearl
(1988), Charniak (1991), Heckerman et al (1995), and Jensen (1996). The term "Bayesian
network" encompasses a variety of
graphical models for representing knowledge and
associations within a data set (including Bayesian belief networks, Bayesian inference
networks, and graphical probability networks). However, the term Bayesian network
(BN) is preferred as it is more neutra
l than including the term belief, causal, or inference
18
(Charniak, 1991). Though the theory behind BNs has been in existence for over a
century, only now have the difficult problems of computing probabilities given evidence
and conditional probabilities bec
ome tractable using modern computing and
breakthroughs in algorithms for "propagating" the uncertainty through the related
variables. Indeed, less than ten years ago Charniak (1991) was lamenting the computation
time needed to construct BNs.
A Bayesian net
work is a graph of relationships among variables in a data set. A
network consists of a series of nodes, each representing a variable, and arcs (or edges),
connections (with direction) between nodes representing a causal (but uncertain)
relationship betwee
n the variables in the nodes (Charniak, 1991, p.50). The assignment of
these relationships can be driven either by the data or by the analyst, but most often and
most effectively, the relationships are derived from some combination of the two
(Spiegelhalte
r et al, 1993). A connection between two nodes may be interpreted as either
a causal path from one to the other or evidence that the nodes are correlated (Charniak,
1991, p. 54). Causal relationships are, of course, useful in making predictions given
certa
in information, but learning causal associations is also important in exploratory
analysis, in gaining insight into a data set (and its corresponding problem domain)
(Heckerman, 1996a).
The uncertainty of the cause

and

effect relationship between variable
s (connected
nodes) represents the primary advantage of Bayesian approaches to statistics over other
statistical approaches. Including a measure of uncertainty in the prediction is cited as an
advantage of Bayesian methods over artificial neural networks,
which output the most
likely outcome given evidence with no sense of the confidence in that prediction (Jensen,
19
1999). Bayesian inference enables expert knowledge to be implemented in a
straightforward manner. This knowledge need not be certain: for exampl
e, non

Bayesian
rule

based systems model the relationships between variables as “if a=b then y, but if a=c
then z.” The same relationship in a Bayesian network might be stated "if a=b then there is
a 0.64 probability of y, and if a=c then there is a 0.83 p
robability of z." Thus, Bayesian
methods allow the encoding of the strengths of the causal relationships, involving the
expert user in the analysis.
The expert input may be interpreted as the prior probability of a relationship that
is then judged by the
data to create a posterior probability (Mitchell, 1997, p. 157). A
maximum likelihood approach is used to create the probabilities taking into account the
observations and the assumed probabilistic distribution of the data (Mitchell, 1997, p.
157). Thus, B
ayes theorem evaluates the probability of a hypothesis by considering its
prior probability, the probability of particular observations given the hypothesis, as well
as the actual observations (Mitchell, 1997, p.157). Bayes theorem may be stated
P(hD) =
P
(Dh)P(h)
P(D)
where P(hD) is the posterior probability of our hypothesis (h), P(h) is the prior
probability, P(D) is the probability of observing the data given assumptions of its
distribution without reference to h, and P(Dh) is the probability of
observing the data
given that h is correct (Mitchell, 1997, p. 156).
The type of probabilistic approach of Bayesian methods is in contrast to the
classical approach of statistics, which deals with confidence intervals and levels. Where
classic deductive r
easoning assumes that observation alone can be used to predict
20
unobserved events, Bayesian methods incorporate beliefs about the probability of an
outcome held prior to (and perhaps updated by) the observations. In this way, Bayesian
networks allow inferen
ce without repeated trials by allowing direct construction by a
domain expert of the probability tables associated with each node.
The arcs defined by a BN allow for the evaluation of the conditional
independence of the variables, or nodes (Mitchell, 1997,
p. 185). Three varieties of
conditional independence are defined (see Figure Two, adapted from Henrion et al,
1991). First, marginal independence refers to source variables, those with no predecessors
(Henrion et al, 1991, p. 74), variables U and W for ex
ample. Second, two variables are
conditionally independent if they have “one or more common parent(s) but no arc
between them” (Henrion et al, 1991, p. 74), variables X and V for example. Third, a
variable is “conditionally independent of its indirect pred
ecessors given all the variable’s
immediate predecessors” (Henrion et al, 1991, p. 74), for example Y is conditionally
independent of U given its immediate predecessor V.
The idea of conditional independence produces three types of path (see Figure
Three,
adapted from Charniak, 1991). First, a linear path from node A to node B and on
to node C, second, a converging path as both nodes A and C are predecessors to B, and
third, a diverging path as node B is the predecessor to both nodes A and C (Charniak,
1991
, p. 54). The linear path shows a causal path from A to B and then on to C. The
converging path shows that both A and C are causes of B. The diverging path shows that
B is a causal factor for both A and C.
A BN may include a variety of these paths. It is
from the graphic visualization and
probabilistic calculation of these relations that the structural nature of place can be
21
explored. Variables representing different aspects of place can be included in a network.
The existence of causal paths between these
nodes and one representing political
behavior graphically display the mediation of politics by elements of place. In addition, a
converging path will show that different aspects of place play a role in mediating political
behavior. Linear and diverging pa
ths illustrate the complexity of place by showing how
different aspects of place are related to each other and may have a less immediate impact
upon political outcomes. Another avenue for inquiry, and one not pursued in this paper, is
to reverse the direct
ion of the acyclic arcs to explore the recursive interaction between
politics and place.
Of course, the assumption of prior knowledge about the relationships between
variables is a weakness as well as a strength. A drawback to the construction of Baye
sian
networks is the determination of its structure with respect to causality and dependence
among the nodes. To determine the structure of a Bayesian network, two things are
required: some order of the variables that indicates which variables are causes a
nd which
are effects, and an assessment of the subset of variables that are conditionally
independent of one another. On the one hand, Charniak (1991, p. 61) dismisses the
problems of defining prior probabilities. However, Heckerman (1996b, p. 13

14) has
f
ound that "the causal semantics of Bayesian networks are in large part responsible for
the success of Bayesian networks as a representation of an expert system," and asserts
that, rather than searching through n! different combinations of orders, people "c
an often
readily assert causal relationships among variables, and causal relationships typically
correspond to assertions of conditional dependence." The problems of defining prior
22
probabilities are much more problematic for those considering social behavi
or than, say,
medical diagnoses as the processes being investigated are much more contingent.
A computer, in an unsupervised network generation algorithm, explores all
possible pairs of nodes for conditional dependency (though, in our experience, we have
n
ot encountered a network generation algorithm that explores all possible orderings of the
variables). After the dependencies and causal relationships are in place in a Bayesian
network, the local probability distributions for each node (given specific outc
omes or
values of its parents) is assessed and incorporated into the graph.
It is possible to level a criticism of BNs that often these prior probabilities seem
arbitrary; it is not often easy, even with domain experts, to develop probabilities for every
possible combination of elements in a set of variables. For this reason, the problem (and
its associated computing complexity) is reduced somewhat by discretizing continuous
variables into classes or rankings (Charniak, 1991, p. 51). Even so, the number of
probabilities in a single node with three possible values (low, medium, and high) with p
parent nodes, each having three possible values, is 3p+1. Thus, even the simplest of
models become daunting to input all of the values in the node probability tables
(Agena
Ltd., 1999). However, the complexity of the network is reduced when the conditional
independence of some nodes is found and hence the amount of connections and
probabilistic outcomes is reduced (Charniak, 1991, p. 53).
An alternative to the requirem
ent that the analyst fill in all possible probabilities
of a BN is the network's capacity to develop conditional probability tables from existing
observations. In so doing, the analysis moves away from expert systems and toward data

driven systems by updat
ing prior probabilities (presuming the expert knows some
23
probabilities, as they often do, or if the expert has "nudged" the probabilities according to
his or her prior experiences). Thus, BNs are placed in the middle of the data

to expert

driven continuum
, or by quantifying the probabilities purely from the observations in a
database, thus placing BNs on the left (unsupervised) side of the continuum (and unable
to take advantage of the Bayesian approach).
2
In our application of Bayesian networks, the network structure

that is, the
conditional dependencies among the nodes
of the networks

was not provided in
advance. The construction of linkages establishing conditional dependenc
i
e
s among
variables is a difficult and time

cons
u
mi
ng task because it (most effectively) must be
per
f
o
rmed manually by an expert. How
ever,
with
large data sets or data sets for which an
expert is not readily available, the generation of network structure can be augmented by
unsupervised iterative machine learning methods
(
Cooper and Herskovits
,
1992).
The
machine learning of the network structure
is achieved by
calculat
ing
the probabilities of
possible network li
nkages and selects a model that
maximizes the probability of the
result.
A
network structure
is created
that has a high probability given the data: the
structure itself amounts to a hypoth
esis about the conditional dependencies of the
variables in the data set. The search, then, is for the maximum likelihood hypothesis
given the data set.
T
he relative likelihood of each of the large number of possible network structures
(
Cooper and Herskov
its,
1992)
.
The number of possible structures increases
exponentially with the number of nodes (variables) present,
but
a series of assumptions
cut down on the number of tested solutions (and resulting complexity) without losing
significant explanatory pow
er
(
Cooper and Herskovits
,
1992)
.
A
metric for the likelihood
24
of the structure
is determined
and compared
to a
measure
of the most likely structure
found thus far in the search. If the probability, given the data, of the network presently
evaluated is gre
ater than the previous "best" result, the present network is established as
the most likely structure.
The maximum likelihood measure can be assessed
both locally for each link (thus
showing the most dominant dependencies in the data set), and globally (th
e measure
for
the comparison of one network to another in the search). The log likelihood is given,
since the probabilities (which can range from 0 to 1) are typically very small numbers,
and it is easier
to examine the exponents (usually
large negative n
umbers) of the
likelihood measures rather than the measures themselves. Thus, the most likely
hypotheses (networks) are those with the lowest negative (closest to zero) global log
likelihoods, and those dependencies which are strongest are those with the
lowest
negative local log likelihoods.
Our purpose in using a BN is to identify how diff
erent aspects of place interact to
produce place

specific political behavior. BNs are a tool for the systematic analysis of
probabilistic relationships that geographers cite as being the key mediating factors of
places. The need for expert input into BNs
gives them a role within the electoral
geographer’s toolkit. Theory, case studies and complementary quantitative techniques
can offer evidence for the expert in their construction of the network. In turn, the
relationships found within a BN can be used to
inform theory, case study and further
quantitative analysis.
Following Spiegelhalter et al (1993), the BN of Nazi voting behavior may be
thought of at three levels of representation. First, is the qualitative level to investigate the
25
general relationships
by creating arcs between the nodes (Spiegelhalter et al, 1993, p.
220). The second level, or the probabilistic domain, calculates the joint distribution of the
nodes in terms of probabilities (Spiegelhalter et al, 1993, p. 222). The third level, or the
qu
antitative domain, provides a numerical evaluation of the conditional distributions
(Spiegelhalter et al, 1993, p. 223). A BN uses the conditional distributions of individual
arcs to create a joint probability for the network as a whole. Hence, we end up w
ith a
graphic visualization of the structural relationships creating and place and mediating
political behavior as well as a quantitative evaluation of the combined determination of
that behavior.
6. A Bayesian Network Analysis of Place and Politics
A bal
ance needs to be maintained between illustrating the complexity of place to
such a degree that it becomes unclear or confusing and an over

simplification that
prevents an analysis of the structural qualities of place. To negotiate such a tension, a
network
illustrating the complexity of place and how it mediated support for the Nazi
party was constructed. From the relationships identified in that network two refined
networks were constructed that focused upon the interactions of identity, class
composition,
and institutions in mediating Nazi electoral support. The choice of nodes in
the refined networks was made by reference to relationships found in the complex
network, the earlier regression analysis, as well as theories of place and theories of Nazi
party
support. Hence, we used expert knowledge derived from theory and prior data
analysis to construct the refined network.
The variables used in the BNs are the same as the ones in the previous regression
analysis. The construction of BNs requires discrete d
ata. This is a drawback in the use of
26
BNs as it requires expert intervention in deciding what breaks are used to recode
continuous variables. For this analysis a binary classification was adopted, using the
mean of the variable as the break. The binary cla
ssification produced more robust
networks than those adopting three or four categories did.
The complex network (Figure Four) illustrates, well, the complexity of place. The
different components of place are related to each other and the nodes representin
g
Protestant, manual industrial workers, and blue collar trade and transport workers are all
parents of the Nazi node. The manual industrial workers node has a direct link to the Nazi
node and an indirect link in terms of a linear path through the blue

col
lar trade and
transport workers node. The same is true for the Protestant node as it displays a direct
link to the Nazi node and a linear path via through the blue

collar trade and transport
workers node. Nodes measuring alienation, electoral turnout and u
nemployment, play
different roles. The electoral turnout node is the apex of a diverging path connecting to
manual industrial workers and self employed. On the other hand, unemployment is an
ending node conditionally dependent upon manual industrial worker
s and self employed.
The class node measuring the self employed is at the end of arcs leading from manual
industrial workers, electoral turnout, and protestant. In turn, the self employed node is a
parent to unemployment, measuring economic alienation. Fin
ally, the node measuring
jobs in the trade sector is the end node of two arcs, one from manual industrial workers
and the other, not surprisingly, from through the blue collar trade and transport workers.
T
he
global
log likelihood score for the
network was
–
3488,
allowing for
comparison of
its
explanatory value
with subsequent networks.
27
The network is, perhaps, better thought of as a we
b. The web contains nodes
measuring the institutional, identity, and class composition aspects of place. Sense of
place, or identity within place, may be engaged by noting the level of alienation of the
inhabitants. Economic alienation is measured via the
node measuring unemployment and
political alienation is identified with the electoral turnout node. The institutional setting
of a place was measured by two nodes, religious institutions are measured via the
protestant node and organized labor is measured
via the manual industrial workers node.
The economic role of a place was captured by nodes measuring class composition, self
employed, and blue collar workers in trade and transport.
The arcs between the various nodes show how the different components of
place
are mutually constituted. For example, political alienation is related to the institutions of
organized labor as well as the size of the self employed group. As another example,
religious institutions are related to the size of the self employed gro
up and also to the
presence of blue collar workers in trade and transport. A final example of the relationship
between different aspects of place can be seen in the relationships of organized labor and
self

employment to unemployment, or economic alienatio
n.
When it comes to showing how these aspects of place structure political behavior,
two institutional nodes, protestant and manual industrial workers, and one class node,
blue collar trade and transport workers, explain Nazi party electoral support. In
addition,
the network also shows that the institutional aspects of place are translated through class
composition to explain political behavior. Hence, the two linear paths manual industrial
workers to blue collar trade and transport workers to Nazi party
vote and also protestant
28
to blue collar trade and transport workers to Nazi party vote. In other words, different
aspects of place explain political behavior and these aspects are related to one another.
To try and make the explanation of Nazi party suppo
rt clearer, two refined
networks were created. The construction of these networks was based upon expert
knowledge and the previous complex Bayesian network. Agnew’s (1987) theory of place
suggests that measures of economic role, institutional setting, and
sense of place should
be included in the network. Complementing Agnew’s approach are theories of Nazi party
support suggesting the role of institutionalized political competition (Burnham, 1972),
political and economic alienation (Arendt, 1958; Kornhauser,
1959), and class (Lipset,
1960; Ault and Brustein, 1998). Hence, expert knowledge suggests that variables
measuring identity/alienation, class or socio

economic status, and the role of institutions
should be included in the refined network. The complex ne
twork identified protestant,
manual industrial workers, and blue collar trade and transport workers as parent nodes of
the Nazi vote. In addition, earlier regression analysis had identified electoral turnout as an
explanatory variable. In combination, prev
ious analyses and expert knowledge called for
a network that included alienation (measured by electoral turnout), institutional setting
(measured by manual industrial workers and protestant), and class (measured by blue
collar trade and transport workers)
as potential parents for the change in the Nazi party
vote.
The choice of variables to be entered into the network was determined by
Agnew’s (1987) theory of place. However, different interpretations of Agnew’s theory
produced different ideas of how the a
spects of place interacted. Seeing as the order that
the variables are entered into the network may have an effect upon the relationships that
29
are found (Heckerman, 1996b, p.13), two networks were constructed. In the first refined
network (Figure Five), th
e initial node was alienation, measured by the size of electoral
turnout, which was experienced within institutional settings, measured by the variables
protestant and manual industrial workers, and also interpreted depending upon class
position, measured
by blue collar workers in trade and transport. Of course, the variable
manual industrial workers also measures class position, and may be interpreted either
way. Alienation is related to both blue collar trade and transport workers and manual
industrial wo
rkers which, in turn, converge onto the node measuring change in the Nazi
party vote. Thus the presence of alienation within a place is expressed through class
position and labor institutions to produce political support for the Nazis. In a separate
linear
path, the institutional religious setting displays a relationship with the Nazi vote
independent of the other nodes. In other words, the dominance of the religious
institutional setting in determining political behavior in Weimar Germany is supported by
t
hese results.
Figure Six shows the strength of the relationships in the first refined network. The
figures are log likelihood scores, and the lower the score the greater the probability that
the status of a parent node determines the status of its child.
The log likelihood table
shows that the strongest relationship (

419.39) is a product of considering the religious
and labor institutional settings with class status (or Protestant, with manual industrial
workers and blue

collar trade and transport worker
s). Further support for the role of
institutional setting in mediating political behavior is offered by the next strongest
relationship (

420.33), one that considers just the Protestant and manual industrial
workers nodes. The third strongest relationship
(

430.34) confirms the interaction
30
between class standing and institutional setting in mediating political behavior, by
quantifying the interaction of Protestant and blue collar trade and transport workers and
their relationship to the Nazi party vote. The
log likelihood table also indicates the
relative unimportance of electoral turnout in mediating the Nazi party vote.
The global
log likelihood score for the refi
ned network was
–
2427,
illustrating i
ts greater
explanatory value c
ompared to the complex networ
k
.
The relatively weak role played by electoral turnout in the first refined network
suggested an alternative refined network. The second re
fined network (Figure Seven)
places class position as the initial node, a position from which alienation is experienced
and then interpreted through religious institutions. Hence, the nodes measuring blue

collar workers in trade and transport and manual in
dustrial workers (both deemed to be
measuring class) were entered first, followed by electoral turnout and protestant.
Similar to the first refined network, religious institutional setting (measured by
Protestant), displays relationship to the Nazi party
vote separate from the other variables.
Both the manual industrial workers and blue collar trade and transport workers nodes
display direct relationships with political behavior. Entering electoral turnout into the
network at a later stage confirms the fi
ndings of the first network that it has no
relationship with Nazi party vote. However, there is a relationship from manual industrial
workers to electoral turnout that suggests the role of class standing and/or labor
organization in voter mobilization. Fin
ally, the linkage from manual industrial workers
and blue

collar trade and transport workers probably suggests an obvious correlation
between two measures of class.
31
The log likelihood tables for the second refined network
are, not surprisin
gly, the
same as the previous ones
(Figure Six)
. The second refined network shows the dominant
roles played by institutions and class standing in mediating the Nazi party vote. Religious
institutions in particular, and the interaction between class standing and class
o
rganization, interacted to form settings that either nurtured or frus
trated Nazi electoral
success. The global log
likeliho
od score
for
the
second refined network was
–
2424,
meaning that its explanatory value was almos
t identical to the first refined
network.
A fina
l, complex, network
was created in order to test the robustness
, or
sensitivity,
of the refined networks or, in other words, that the relationships fo
und were
not merely an artifact of the order in which the nodes were entered into the network
(Figure Eight)
. A sensitivity network was created in which all the variables were entered
in a random order
. The acyclic graph illustrates that the same three nod
es (protestant,
manual industrial workers, and blue collar trade and transport workers) have direct
pathways to the change in the Nazi vote. In addition, electoral turnout plays is located in
a linear path, in this case between manual industrial workers an
d protestant. The role of
these four variables in the complex and randomly generated network provides support for
the claim that the relationships in the refined expert networks are not an artifact of the
data.
7. Conclusion
In summary, the refined networ
ks illustrate how different aspects of place are
mutually constituted and, together, mediate political behavior. Sense of place, location
and locale are seen to operate through variables measuring alienation, class position, and
institutions. The arcs of t
he networks illustrate how these aspects of place interact to
32
mediate politics within places. Using expert knowledge derived from theories of place
and theories of political behavior, in conjunction with knowledge gained from previous
analyses, BN’s were c
reated which unpacked spatial regression models to show the
complexity of place and its role in mediating actions.
With respect to the Nazi party vote, institutions and class position were found to
be the most important aspects of place in determining pol
itical behavior. The dominant
role of Protestantism in explaining the Nazi party vote has been a staple of previous
analyses (for example, see Falter, 1991). However, the BN approach conceptualizes
Protestantism as an institutional feature of place rather
than an individual characteristic.
The importance of institutional setting in explaining the Nazi party vote is confirmed by
the role of the manual industrial workers node in the networks. Finally, the
interrelationship between the manual industrial worker
s node and the blue

collar trade
and transport worker illustrates how institutional setting constitutes class standing. In
combination, different aspects of place interacted to form spatial settings conducive to
Nazi party electoral success.
BN’s reorient
the quantitative analysis of contextual politics from a focus upon
space to place. Instead of looking at spatial linkages between places and variation in
political behavior across regional spaces, BN’s provide a systematic way of analyzing the
mechanisms
by which place mediates political behavior. The next step is to incorporate
space into the BN’s. Spatially lagged variables of political behavior may be included in
the networks to capture local political activity. In addition, and once spatial analysis ha
s
identified regions of political behavior, different networks can be created for different
33
regions to engage such spatial heterogeneity. Hence, the mutual construction of place and
space can be included in the same analysis.
The purpose of this paper was
to investigate how places mediate political
behavior. Once the elements of place were identified through theory, the relationships
amongst them were identified graphically and probabilistically. Hence the way that
aspects of place are mutually constituted
was explored. In addition, BN’s show how the
complexity of place aligns to mediate political outcomes. Thus, BN’s offer a fruitful
mechanism for unpacking the components of place to see how they interact to structure
place

specific behavior. Using this te
chnique, place is shown to be more than the sum of
its parts, as it is the way that the elements of place combine that produces place

specific
behavior.
34
1.
There is a wealth of aggregate data allowing for the spatial analysis of voting behavior
in Weimar Germany. Census and election files were obtained from an archive "
Wahl

und Sozialdaten der Kreise und Gemeinden des Deutschen Reiches, 192
0

1933
" at the
Central Archive of the University of Cologne.
The Cologne data were dissaggregated at a
scale of over 6,000 geographic units that included
Kreise
(counties), villages, and
neighborhoods within cities and then aggregated into 743 Kreise in o
rder to match census
and voting data. The explanatory variables were created from the 1925 census data. Areal
boundaries of the
Kreise
were obtained from an OSS (Office of Strategic Services) Map,
#6289 (1944) and digitally coded into a Geographic Informat
ion System (GIS) using the
Arc/Info
software package.
Rusty Dodson, David Fogel and Steve Kirin (Department of
Geography, Univers
ity of California, Santa Barbara) coded the original map into a GIS.
Subsequently, Michael Shin (Department of Geography and Regional Studies, University
of Miami) and Colin Flint revised this map to incorporate the boundary changes and
reduce the number o
f Kreisunits on the map to 743.
The GIS was used to construct a
contiguity or spatial weights matrix based upon first order contiguity to define the
immediate neighbors of the
Kreise.
The election file includes returns for the
Reichstag
elections between 1920 and
1933, and the cens
us file contains socio

economic data collected from a variety of
sources and at a variety of times. Jürgen Falter and Wolf Gruner (1981) have described
how this data set was revised during the 1970's to correct data errors, which were mainly
a result of p
unching errors, and also to compensate for internal political boundary
changes within Weimar Germany in order to make the territorial units within the data set
as consistent and coherent as possible. The changes in internal political borders in
35
Weimar Ger
many were a product of major changes in administrative units between 1919
and 1933 that were partially a result of the incorporation of suburbs into urban areas and
the reform of local government. Falter and Gruner believe that the sources of the data set
are the respective volumes of the
Statistik des Deutschen Reiches
(Statistics of the
German Reich) issued by the
Statistisches Reichsamt
(State Statistical Office) in Berlin.
2
. With the innovations in the computational algorithms for the propagation of evidence
given uncertain relationships among variables, BNs demonstrate their utility as self

contained decision support systems. Once a network
has been defined, and the probability
distribution among the variables inputted (either by the expert, by the data, or some
combination of both), BNs can be used to propagate known evidence, like states of
certain variables, and predict the likelihood of
states of other variables given that
evidence. For example, a BN is an effective representation for the diagnosis of car
problems: given the fact (evidence) that the car doesn't start, but that the radio works and
the lights work, there is a 0.58 (of 1.00)
chance that the likely cause for the failure is a
bad distributor, and a 0.35 chance that the spark plugs need to be replaced. The
assumption is that the certain variables are independent (like the status of the fuel pump
and that of the power windows), b
ut that others are dependent and interrelated (like the
status of the ignition and that of the alternator), and that these conditional dependencies
can be modeled through some combination of prior (expert) knowledge and evidence.
Such potential of the
propagation of uncertainty through a network of relationships to
reveal the conditional probability of a certain outcome makes a BN a very effective
decision support tool. The user presents the network with a "what

if" scenario and the
36
network delivers it
s prediction (with uncertainty and alternatives) for states of unknown
variables.
37
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Table One. Spatial error estimation of the change in the Nazi party vote, May 19
28

September 1930.
OBSERVATIONS = 743
VARIABLES = 12
DEGREES OF FREEDOM = 731
R2 = 0.47
LIK =

2425.92
Variable
Coefficient
Standard Deviation
CONSTANT
26.83*
4.35
PROT
0.14*
0.01
BCTRAD

0.31**
0.16
N309TURN

0.23*
0.05
TRADJOBS
1.02
*
0.25
NORWEST
0.44
1.30
RHINE
0.60
1.30
CENTRAL

3.80*
1.44
SILESIA
2.13
1.64
BADEN
2.09
1.72
WURTBERG

10.37*
1.58
BAVARIA

3.02**
1.50
LAMBDA
0.43*
0.04
* Statistically Significant at the 0.01 Level
** Statistically Significant at
the 0.05 Level
Regression Diagnostics:
Diagnostics for Heteroskedasticity
Random Coefficients
Test:
DF
VALUE
PROB
Breusch

Pagan test
11
120.42
0.000
Spatial B

P test
11
120.42
0.000
Diagnostics for Spatial Dependence
Test:
DF
VALUE
PROB
Likelih
ood Ratio Test
1
91.50
0.000
Test on Common Factor Hypothesis
43
Test:
DF
VALUE
PROB
Likelihood Ratio Test
11
12.96
0.296
Wald Test
11
12.24
0.346
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