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A BAYESIAN BELIEF NETWORK MODEL OF
A VIRTUAL LEARNING COMMUNITY
Ben K. Daniel and Richard A. Schwier
Virtual Learning Community Research Laboratory
28 Campus Drive
University of Saskatchewan
Saskatoon, Saskatchewan Canada S7N 0X1
306-966-7641
ben.daniel@usask.ca, richard.schwier@usask.ca
Please cite as: Daniel, B.K., & Schwier, R.A. (in press). A bayesian belief network model of a
virtual learning community. International Journal of Web-Based Communities.
Abstract
This article proposes a Bayesian methodology for modeling a virtual learning community, and illustrates one
application of the multi-step approach. The article describes metrics and techniques for modeling
fundamental variables that constitute a virtual learning community. The variables used for constructing the
Bayesian model were drawn from a grounded theory analysis of transcripts of online discussions and an
empirical study that used Thurstone analysis to assign weights and rankings to variables based on their
comparative significance according to participants in the communities. The results of the Thurstone analysis
were then used to infer causality among the variables and to assign the strength of relationships among the
variables. Finally, scenario-based reasoning, grounded on practice, was used to query the model and
observe its impact on the other constituent variables and how they relate to one major variable of interest—
learning in virtual communities.
Introduction
Community is used in common parlance to describe a wide variety of online gatherings, from
casual social groups, to advertising and marketing, to online classrooms. Is “community” a
useful metaphor for online learning environments, and is there any precision in the application of
the metaphor? This concern has led to a number of studies aimed at identifying and isolating the
fundamental variables of virtual learning communities and with key goal of understanding the
process involved in learning in virtual learning communities and supporting it (Daniel, Schwier
& Ross, 2005; Schwier & Daniel, 2006).
This article describes the use of Bayesian Belief Network (BBN) modeling techniques to
understand the fundamental variables that constitute a model of virtual learning community, and
to predict the interactions among key variables that can influence learning in formal virtual
communities. We are interested in isolating and understanding the most important variables as
they relate to learning in virtual learning communities. We suggest that understanding the
constituent processes of learning in virtual learning communities can reveal instructional
principles that underlay the processes of learning. The article also points out the potential for,
and the limitations of, employing Bayesian techniques in domains in the social sciences and the
humanities.
In this article, we present analytical procedures for eliciting data to build a BBN model. We
present the Bayesian approach and describe how the Bayesian network was developed, including
how a conditional probability table was generated, and we provide examples of scenarios that
were used for querying and tuning the network. We conclude the paper by identifying the
fundamental instructional principles necessary for supporting the process of learning in virtual
learning communities and additional research issues, and we discuss the advantages and
disadvantages of using Bayesian techniques in the social sciences and humanities.
Related Research
Learning has been studied in various contexts and the processes involved in learning appear to be
contextually influenced (Driscoll, 2005; Jonassen, 2004). In a community context, individuals
learn by constructing knowledge, by connecting meaning to their knowledge, and by sharing
these meanings with others in the community (Collay, Dunlap, Enloe & Gagnon, 1998; Kanuka
& Anderson, 1998). Kowch and Schwier (1998) described learning communities as collections
of individuals who are bound together by natural will and a set of shared ideas and ideals.
Learning communities are also considered cohesive entities embodying a culture of learning, in
which all members are involved in a collective effort of understanding (Bielaczyc & Collins,
1999; Rovai, & Lucking, 2003). Essentially, learning communities exist when learners share
common interests about acquisition of knowledge in a domain or set of issues and subjects.
Currently, virtual learning communities are gaining wider recognition among researchers as
vehicles for knowledge creation and transformation (Daniel, Schwier, & McCalla, 2003; Palloff
& Pratt, 1999; Preece, 2000; 2002; Daniel, Schwier & Ross, 2006). Related literature has
identified the general contribution of virtual communities in facilitating information exchange
and knowledge creation, thereby enriching the work of the collective (Brown, & Duguid, 1991;
Hildreth, Kimble & Wright, 1998; Lesser & Prusak, 2000). These positive outcomes of learning
in virtual environments have caught the interest of scholars in both academia and the corporate
sector. But despite this growing interest, there are limited theories informing our understanding
of what comprises a community online. In addition, the over-reliance by researchers on
transcript analysis to the exclusion of other methods of evaluation results in a limited lens
through which to view community (Schwier & Daniel, in press). Several studies suggested that
the metaphor of community enables educators to discuss richer, deeper, more complex types of
interplay among learners (Schwier, 2001; Schwier & Balbar, 2003; Schwier & Dykes, in press).
Fundamental to all kinds of virtual learning communities is learning, however, the process
involved in learning in various kinds of communities can differ significantly and can be
influenced by a number of uncharted factors (Daniel, Schwier & Ross, 2005; McCalla, 2000).
Learning theories regard the process of learning in various ways, although they share common
assumptions about what constitutes learning. Learning according to many learning theories is
viewed as persistent change in performance brought about by learners’ experiences and
interactions with the world (Daniel, Scwhier & Ross in press; Driscoll, 2005). Learning can also
be regarded as changes in behavioural patterns that might have implicit or explicit impact on
performance outcomes, including the means to stimulate the conditions that can promote
learning (the process) and the results from that process (the outcomes).
Learning has been studied in many contexts and the processes involved in learning differ. In
a community context, individuals learn by constructing knowledge and connecting meanings to
their understanding, and by sharing these meanings with others in the community (Collay,
Dunlap, Enloe & Gagnon, 1998; Daniel, Schwier & Ross, 2005; Kanuka & Anderson, 1998;,
Wilson, 2004). Research suggests that most learning activities in communities are informal,
involving the exchange of personal experiences, lessons and information (Brown & Duguid,
1991). Wenger (1998) further suggested that sharing tacit knowledge (knowledge drawn from
personal experiences) within a community yields higher success than sharing explicit knowledge.
Daniel, Schwier and Ross (2005) noted that despite growing research into virtual learning
communities, there is limited theoretical support informing our understanding of the nature of
discourse that can ultimately influence learning in these communities. Further, there is little
comparative research on what actually constitutes a community in virtual settings. We contend
that community can be best understood through the members of the community and more
specifically through combined analyses of their perceptions, interactions and artifacts, and by
creating and tuning dynamic models of communities to interpret the interactions among
constituent community variables. Understanding the fundamental variables of a virtual learning
community enables us to employ alternative methods to study how they interact to influence
learning.
In this article we offer new approaches to the study of learning in virtual learning
communities. The combination of Thurstone and Bayesian techniques in the article are novel
ways of moving toward an eclectic set of approaches employed to examine virtual learning
communities and various ways of supporting learning in them.
Methods and Procedures
The formal learning communities analyzed in this article were formed out of five graduate
courses in Educational Communications and Technology at a western Canadian university. The
courses were blended online and face-to-face seminars on the theoretical and philosophical
foundations of educational technology and the principles and practices of instructional design.
Each course spanned an entire semester or academic year. The courses were small graduate
seminars with enrolments from six to thirteen students, and each class met primarily online, but
with monthly group meetings. Most of the students completed both courses, although not at the
same time, nor with the same group in each course. While most students were able to attend the
group meetings regularly, class cohorts had members who participated exclusively or mostly
from a distance.
Data were drawn from transcripts of online discussions, email records, interviews with
individual students and focus groups. One experimental protocol—a paired comparison study,
described below, was also completed with volunteers from each of the courses. A total subjects
completed the Thurstone comparison exercise in the results reported here, and these participants
had participated in either or both of the courses. We did not discriminate between them, as we
were gathering comparative judgments of generic features of community that were evident in
both environments, and also. We were not looking for responses from people who had identical
or highly similar experiences, but rather drawing data from a group that had various mixtures of
community experience within their graduate programs, so they could make critical judgments
about which characteristics were more important than others. Given the blended nature of all of
the courses, and the fact that they were populated by mature and motivated students, we confine
our conclusions to similar environments, and acknowledge that these results cannot be
generalized to environments that are entirely online, entirely face-to-face, or comprised of
different types of students and content. We suspect factors such as students’ level of maturity,
age, gender, prior experience and knowledge of the domain might have influence on the results.
But the purpose of using the approach was to obtain a reasonable starting point for making
decisions about relationships among variables for developing the Bayesian Belief network, so we
were less concerned about statistical precision or possible contamination, as these concerns are
reconciled as the model is tuned over time.
Schwier and Daniel (in press) identified fourteen characteristics of a virtual learning
community that grew out of a theoretical model of a virtual learning community proposed by
Schwier (2001), from the analysis of interactions among participants, from a content analysis of
transcripts of communication among community participants, and from interviews and focus
groups. 1An operational definition of each of these characteristics is given in Table 1. The
theoretical model of virtual learning communities was developed as a framework for understanding
the operation of virtual learning communities in higher education.
Table 1. Characteristics of Formal Virtual Learning Communities and Operational Definitions
(Schwier & Daniel, in press).
Characteristic Operational definition
Awareness Knowledge of people, tasks, environment –or some combination of these.
Social
Protocols
Rules of engagement, acceptable and unacceptable ways of behaving in a community.
Historicity Communities develop their own history and culture.
Identity The boundaries of the community—its identity or recognized focus.
Mutuality Interdependence and reciprocity. Participants construct purposes, intentions and the types of
interaction.
Plurality "Intermediate associations" such as families, churches, and other peripheral groups – other
communities that individuals use to enrich the new community.
Autonomy Individuals have the capacity and authority to conduct discourse freely, or withdraw from
discourse without penalty.
Participation Social participation in the community, especially participation that sustains the community
1 See Schwier & Daniel (in press) for a comprehensive discussion of preliminary data analyses that were used to
generate and understand characteristics of virtual learning communities. These data were ultimately used to populate
the BBN described in this article, but given that the focus of this article is on the BBN and not on VLC models, we
refer the reader to our earlier work for a more detailed account of those procedures.
Trust The level of certainty or confidence that one community member uses to assess the action of
another member of the community.
Trajectory The sense that the community is moving in a direction, typically toward the future.
Technology The role played by technology to facilitate or inhibit the growth of community.
Learning Formal or informal, yet purposeful, learning in the community.
Reflection Situating previous experiences, postings in current discussions, or grounding current
discussions in previous events.
Intensity Active engagement, open discourse, and a sense of importance or urgency in discussion,
critique and argumentation.
Thurstone Analysis
In order to discriminate among the variables, Schwier & Daniel (in press) developed a paired-
comparison treatment that required participants to compare each characteristic of a VLC to every
other characteristic and choose the characteristic they believed was more important to the
community. This was based on Thurstone's method of paired comparisons, a method of analysis
that generates a scale ranking and scale points among variables that can be used to plot a visual
representation of distances between and among variable.
Thurstone (1927) postulated that for each of the items being compared and among all
subjects, a preference will exist, and that for each item the preference will be distributed
normally around that item's most frequent or modal response. A person's preference for each
item versus every other item is obtained, and the more people that select one item of a pair over
the other item, the greater the preference for, or perceived importance of, that item, and thus the
greater its scale weight. Thurstone's Law of Comparative Judgment circumvents potential ceiling
effect problems by forcing individuals to rank items two at a time rather than all at once
(Manitoba Centre for Health Policy, 2005). Given the results of all possible paired comparisons
of the variables under study, scale values can be plotted on a line to provide a graphic illustration
of the relative value of each variable, represented by its relative distance from the other variables
(the greater the distance between any two variables on the scale, the greater the differences
between those two variables).
The scale is descriptive, and there are no post-hoc tests available to identify significant
differences among variables. But the scale values provide a convenient metric for assigning
initial weights to variables in modeling exercises.
In the study of the fundamental variables of virtual learning communities, Schwier and
Daniel (in press), compared each VLC characteristic with the others, following procedures
outlined by Misanchuk (1988). The data were then converted into a line drawing that depicted
differences between elements along a line. Greater differences were shown spatially as larger
distances between points on the line. The outcome of the comparison and the ranking of the
variables are shown in Table 2 and Figure 1 below.
Table 2. Thurstone Scale rankings and scale points for each of the fourteen VLC variable.
Characteristic Thurstone Scale
Ranking
Thurstone Scale Point
Trust 1 0.7341
Learning 2 0.5806
Participation 3 0.3182
Mutuality 4 0.2671
Intensity 5 0.2425
Social Protocols 6 0.1852
Reflection 7 0.1523
Autonomy 8 0.0155
Awareness 9 -0.0785
Identity 10 -0.1939
Trajectory 11 -0.2474
Technology 12 -0.5033
Historicity 13 -0.7309
Plurality 14 -0.7701
Figure1. Thurstone scale points for fourteen VLC characteristics.
As a result of the Thurstone analysis, measures that could be used to understand the
association and interplay of community characteristics in a VLC were obtained. Reviewing the
results of the Thurstone analysis, it is apparent that there were at least three clusters of
characteristics. Trust and learning were considered by the participants to be the most important
characteristics of a VLC. A large cluster of characteristics gathered around the mean scale point,
and while they differed from each other, they can be treated as a group because of their central
position relative to the other points. Technology, historicity and plurality were ascribed much
lower status than the other characteristics, and one might argue as a result that they should be
eliminated from the model entirely. However, the results also show that some variables are
ranked low but their influence are obvious and participants might have taken them for granted. In
fact, follow-up interviews with participants confirmed this suspicion, so characteristics that were
rated low were still included in the BBN.
Bayesian Modeling
A Bayesian Belief Network (BBN) is one of several techniques for building models, but one that
has particular strengths for modeling virtual learning communities. BBNs are graphs composed
of nodes and directional arrows (Pearl 1988). Nodes in BBNs represent variables and the
directed edges (arrows) between pairs of nodes indicate relationships between the variables. The
nodes in a BBN are variables usually drawn as circles or ovals. The arrows between pairs of
nodes that indicate relationships between the variables can be assigned different states, such as
positive, null or negative. Research show that a BBN modeling techniques is a mathematically
rigorous way to model a complex environment, and it is flexible, able to mature as knowledge
about the system grows, and computationally efficient and can be applied in many domains
(Daniel, Zapata-Riviera, McCalla & Schwier, 2006; Druzdzel & Gaag, 2000; Rusell & Norvig,
1995). Given characteristics of virtual learning communities from earlier studies that can act as
nodes, and given Thurstone scale values that can provide a method of weighting the variables,
the BBN provides a useful tool for sharpening our understanding of how VLC variables interact.
It also provides a method of modeling VLCs that can mature as additional data are acquired.
Technically, Bayesian statistics, the expression of prior beliefs about a given situation
(before collecting any data) is required. This degree of belief is normally expressed in terms of a
probability distribution, and then Baye’s theorem is used to update the beliefs in the light of the
information provided by the data. BBNs enable reasoning when there is uncertainty and they
combine the advantages of an intuitive visual representation with a sound mathematical basis in
Bayesian probability. The use of a Bayesian Network makes it possible to articulate experts’
beliefs about dependencies between different variables and naturally and consistently propagate
the impact of the evidence on probabilities of uncertain outcomes.
The structure of a Bayesian network model is also be viewed as a graphical, qualitative
illustration of the interactions among a set of variables within a network. The interactions of the
variables in a network model can be quantified to predict the consequences of observable
behaviors in a model. Research suggests that BBN techniques have significant power to support
the use of probabilistic inference to update and revise belief values (Pearl, 1998). They can
readily permit qualitative inferences without the computational inefficiencies of traditional joint
probability determinations (Niedermayer, 1998). The causal information encoded in BBN
facilitates the analysis of actions, sequences of events, observations, consequences, and expected
utility (Pearl, 1998).
The common problems, which can prevent the wider use of BBN in other domains and
indeed in the social sciences and the humanities, can be summarized as follows:
• Building BBNs requires considerable knowledge engineering effort, in which the most
difficult part of it is to obtain numerical parameters for the model and apply them in
complex, which are the kinds of problems social scientists are attempting to address.
• Constructing a realistic and consistent graph (i.e., the structure of the model) often
requires collaboration between knowledge engineers and subject matter experts, which in
most cases is hard to establish.
• Combining knowledge from various sources such as textbooks, reports, and statistical
data to build models can be susceptible to gross statistical errors and by definition are
subjective.
• The graphical representation of a BBN is the outcome of domain specifications.
However, in situations where domain knowledge is insufficient or inaccurate, the
model’s outcomes are prone to error.
• Acquiring knowledge from subject matter experts can be subjective.
Despite the problems outlined above, BBNs still remain a viable modelling approach in
many domains, especially domains which are quite imprecise and volatile such as weather
forecasting, stock market etc. This article extends the use of BBN approaches to model complex
social systems. We use virtual learning community as an example but the approach can also be
used to model similar social systems. We believe this can help experts and researchers escially
those in the social sciences and humanities build and explore initial social computational models
and revise and validate them as more data become available. We think that by providing
appropriate tools and techniques, the process of building Bayesian models can be made less
complex.
Building a Bayesian Model of a Virtual Learning Community
The first step in building a BBN is to identify key variables that represent a domain (Druzdzel &
Gaag, 2000; Pearl, 1988; Rusell & Norvig, 1995). The variables identified in our model are
drawn from an analysis of online transcripts, interviews and email traffic that were subjected to
grounded theory analysis, and the identified variables were then subjected to a Thurstone
analysis to identify their relative weights. The motivation to build the Bayesian model of a
virtual learning community is to be able to perform a number of simulations and observe the
influence of variables in the network with the goal of determining and understanding those
variables that are critical to virtual learning communities as well as their interactions in the
processes of learning. In building the model, once variables were identified, the second step
involved mapping the variables into a graph (see Figure 2) based upon coherent qualitative
reasoning.
Druzdzel and Henrion (1993) proposed a transformation of a causal Bayesian network into a
qualitative probabilistic network (QPN), in which the relation between two adjacent nodes is
denoted as positive (+), negative (-), null (0) or unknown (?); there are also relations that involve
more than two nodes, such as positive or negative synergies. The main advantage of QPN's is that
they simplify the construction of models, because they do not require the elicitation of numerical
parameters; as a consequence, their main disadvantage is the lack of precision in the results,
especially because very often the combination of "positive" and "negative" influences leads to
"unknown" relations. The motivation for this approach is based on the fact that people usually
reason in qualitative terms.
In our case, we used the Thurstone analysis as a starting point to identify relative positions of
variables of virtual communities, and we then used qualitative reasoning to subjectively identify
those variables that are of interest and influence in the model and isolate those that are less likely
to have an impact on the overall performance of the model. We caution the reader that our
reasoning is based on our teaching and research experience into virtual learning environments, and
it may contain epistemological, contextual and personal bias. However, the initial precision of the
relationships among variables is less important to developing a model than is the identification of
key variables that was accomplished by using the grounded theory approach mentioned earlier.
Precision is built by tuning the model and observing how variables interact over time and across
contexts in the BBN. In other words, a BBN is built iteratively, and as the number of iterations
increase, the model is tuned to render an increasingly accurate network of relationships among key
variables
In this study, we used qualitative reasoning to infer causal relationships among the variables
identified in the study, resulting in relationships among variables that could be charted. For
instance one can qualitatively and inductively reason that in virtual learning communities,
participation and learning are essentially variables whose interactions are mediated by another
technology as another variable, (i.e., it is hard to imagine learning online without any
participation and equally participation is often mediated by technology), and therefore,
technology is assigned to be a parent of participation. Similarly, participation can influence
awareness in various ways, which in turn can lead to the development of trusting relationships.
Since awareness can contribute to trust and distrust, trust is set to be a child of awareness.
Furthermore, one can reason that technology influences awareness in different ways. For
example, imagine a learning environment in which each individual has a profile (electronic
portfolio) and the information is made available to others in the community; this can create sense
of awareness about who is who, or who knows what, in that community. Similarly, technology
may influence intensity in a weak positive manner. For example, poor technology might have
negative outcomes on engagement. In other words, people might not be willing to use technology
that does not work well for them, or they find awkward to use.
Extending this type of qualitative reasoning resulted in the BBN shown in Figure 2. In the
model, those nodes that contribute to causality align themselves in “parent” to “child”
relationships, where parent nodes are causes and child nodes are effects. For example, trust is the
child of mutuality; awareness and intensity, which are in turn children of participation and
technology (see Figure 2). The criterion for determining causality among the variables is a
reflection of our qualitative reasoning process (soft data), which can be validated using empirical
evidence (hard data). We have only provided few examples of the causal relationships among the
variables to show the qualitative nature of the Bayesian approach. We believe this kind of
inferential qualitative reasoning can be validated with alternative approaches. For instance if a
model predicts that there exists relationships between identity and awareness, correlation
analysis can be conducted. But additional validation needs to be performed when additional data
becomes available.
Figure 2. BBN representation of relationships among virtual learning community variables.
The third step in building the model involved assigning initial probabilities to the network.
In general, BBN initial probabilities can be obtained from domain experts, secondary statistics or
they can be taken from observations and subjective intuition. It is also possible that initial
probabilities can be learned from raw data. In addition to learning prior probabilities, it is
sometimes necessary to examine the structure of the network. In our case, the initial probabilities
were obtained using approached discussed in Daniel, Zapata-Revera and McCalla (2003) and the
structure and the degree and strength of influence among the variables was determined by
examining the distances between the variables of virtual learning communities along the
Thurstone Scale. This approach enabled us to cluster those variables that were closely aligned on
the Thurstone scale and use weighted threshold values (Daniel, McCalla, & Schwier, 2005) to
generate the conditional probability table. The relationships and the degree of influence among
the variables were further described qualitatively. In the results of Thurstone scaling, those
variables that cluster around the mean scale point was observed were given high degree of
influence.
Generating the Conditional Probability Table
The initial conditional probabilities were generated by examining qualitative descriptions of the
influence between two or more variables and the strength of their relationships in the model
(Daniel, Zapata-Revera, McCalla, 2003; Daniel, McCalla, & Schwier, 2005). Each probability
describes the strength of relationship. For instance, various degrees of influence among variables
are represented in the model by the letters S (strong), M (medium), and W (weak). The signs +
and - represent positive and negative relationships. The elicitation of the initial probability
approach for the variables was based on the approach discussed in Daniel, Zapata-Revera and
McCalla (2003), but the strengths of the relationships and the influence of each variable was
based on the results of the Thurstone scaling and the relative positioning of each variables along
the scale. For instance, technology was ranked to be last and so it carries a threshold probability
value of 0.6 and the symbol weak (W+) was assigned to it. The sign means that there is some
kind of influence, but because of its low ranking along the scale, the influence is a weak one.
The probability values were obtained by adding weights to the values of the variables
depending on the number of parents and the strength of the relationship between particular
parents and children. For example, if there are positive relationships between two variables, the
weights associated with each degree of influence are determined by establishing a threshold
value associated with each degree of influence. The threshold values correspond to the highest
probability value that a child could reach under a certain degree of influence from its parents, i.e.
assuming that Participation and Technology have positive and strong relationships with
Awareness, evidence of good technology and high participation will result into a conditional
probability value of 0.98 (i.e., Awareness=Exist). This value is obtained by subtracting a base
value (1 / number of parents--0.5 in this case with two parents) from the threshold value
associated to the degree of influence (i.e., threshold value for strong = 0.98) and dividing the
result by the number of parents (i.e., (0.98 - 0.5) / 2 = 0.24). Table 3 lists threshold values and
weights used in this example. The value ! = 0.02 leaves some room for uncertainty when
considering evidence coming from positive and strong relationships.
Table 3. Threshold values and weights with two parents
Degree of
influence
Thresholds Weights
Strong 1-! = 1 - 0.02 = 0.98 (0.98-0.5) / 2 = 0.48 / 2 = 0.24
Medium 0.8 (0.8-0.5) / 2 =0.3 / 2 = 0.15
Weak 0.6 (0.6-0.5) / 2 =0.1 / 2 = 0.05
Daniel, Zapata-Revera and McCalla (2003)
This assumes that participation and technology have positive strong relationships with awareness
and there is evidence of positive participation and technology in a particular community. Given
these assumptions, weights will be added to the conditional probability table of awareness every
time participation = high or technology = good. For example, the conditional probability value
associated with awareness given that there is evidence of participation = high and technology =
good is 0.98. This value is obtained by adding to the base value the weights associated with
participation and technology (0.24 each). Table 4 shows a complete conditional probability table
for this example.
Table 4. An example of conditional probability table for two parents with strong, positive
relationships
Participation High Low
Technology Good Bad Good Bad
Awareness Exists 0.98 0.74 0.74 0.5
Awareness Does Not Exist 0.02 0.26 0.26 0.5
The calculation of the various states of the relationships among the three variables
(awareness, participation and technology), and their corresponding values used in Table 3. Given
below:
P (Awareness= Exist | Participation= high & Technology= Good) = 0.5 + 0.24 + 0.24 = 0.98
P (Awareness= DoesNotExist| Participation= high & Technology= Good) = 1 - 0.98 = 0.02
P (Awareness= DoesNotExist | Participation=High & Technology= Bad) = 1 - 0.74 = 0.26
P (Awareness= Exist| Participation= Low & Technology= Good) = 0.5 + 0.24 = 0.74
P (Awareness= DoesNotExist | Participation= Low & Technology= Good) = 1 - 0.74 =0.26
Querying the Network
Querying a BBN refers to the process of updating the conditional probability table and
making inferences based on new evidence. One way of updating a BBN is to develop a detailed
number of scenarios that can be used to query the model. A scenario refers to a written synopsis
of inferences drawn from observed phenomenon or empirical data.
Druzdzel and Henrion (1993) described a scenario as an assignment of values to those
variables in Bayesian network which are relevant for a certain conclusion, ordered in such a way
that they form a coherent story—a causal story which is compatible with the evidence of the
story. The use of scenarios in Bayesian network is drawn from psychological research
(Pennington & Hastie, 1988). This research shows that humans tend to interpret and explain any
social situation by weighing up the most credible stories that include hypotheses to test and
understand social phenomena. In Bayesian modeling, a hypothesis is the assignment of a value to
a discrete variable or group of variables.
Although a scenario can describe all of the nodes a model, it is more reasonable to include
only the nodes relevant for a certain situation. If there is a certain focal hypothesis, say for
instance H, selected by the user, the relevant nodes are those that affect the posterior probability
of H given the observed evidence e. Otherwise, the relevant nodes are all those whose
probabilities depend on e. The explanation of the model therefore, consists of showing the
evidence (i.e., the scenarios that are most compatible with the hypothesis and those that are
incompatible with the hypothesis.
Furthermore, updating a BBN using scenarios is an attempt to understand the statistical
significance of various relationships among variables in a network. Based on the results of
Thurstone scaling we have observed a large cluster of variables around the mean scale point.
These were then chosen to construct the Bayesian Belief network.
Although, the variables obtained in the earlier analysis can be treated as a group because of
their central position relative to the other points, it is difficult to measure their individual relative
importance to others in the same cluster or in other clusters in the VLC model. We build simple
scenarios to further infer their relative influence and significance to learning within the network.
The approach described in table 3 uses both qualitative and quantitative data in building the
Bayesian Network to model imprecise and nebulous domains (Daniel, Zapata-Revera &
McCalla, 2003). In addition, the probability distribution enables us to query the model and
observe changes as they propagate to generate new posterior probability values (P), which we
can then use to make logical inferences about the state of the model from changes in its
variables.
Changes in the model were observed by querying the network using practical and intuitive
scenarios. For example, imagine a community where there is reasonably high level of
participation among individuals (e.g., p=0.98), and a high presence of mutuality, implying
learners are constantly engaged in reciprocal relationships through exchanging messages, sharing
experiences, stories, information and knowledge. Querying the model (presented in figure 2)
with this scenario reveals increased learning with a posterior probability value of P (l=0.763).
Another scenario we employed to tune the model involved a formal virtual learning
community in which an effective level of participation guided by explicit social protocols was
observed. In addition, individuals were constantly engaged in open discourse (mutuality), and the
issues were addressed in both depth and breadth (intensity). Further, assuming that there is a high
intensity in discourse encouraged individuals to reflect deeply on the issues being discussed.
Results of the query of the model using this scenario revealed a higher probability of learning p
(l=0.779) with a significant difference of 0.016 compared to the probability of learning in the
presence of effective participation and mutuality alone. This result is intuitively appealing, given
interview data that suggested that a combination of these factors encouraged depth in the
discussion and in learning (Schwier & Daniel, in press).
In practice virtual learning communities should encourage freedom of expression, mutual
respect and they should value diversity. Building on the notion of individual freedom in a virtual
learning community, we were interested in observing the impact of autonomy on trust and
learning, given effective participation and good technology. Autonomy seems to be very
influential; the network revealed higher probability of trust P (t=0.924) and correspondingly high
probability of learning P (l=0.794) when autonomy was elevated.
Given the central position that social capital plays in our research, and the importance of
trust as a prerequisite condition of social capital and learning, we were interested in
understanding the impact of all the variables on trust and learning. In this scenario all the
variables in the first layer (technology and participation) and second layer (mutuality, intensity,
social protocols, reflection, autonomy and awareness) in the model were set to their highest
probability values. This scenario increased the values of posterior probabilities of trust (P:
(t=0.944) and learning (P: l=0.810). This result suggests that the variables in the network can
collectively have considerable and yet varying effects on trust and learning, depending on
differing scenarios.
Although the results of the Thurstone analysis ranks trust to be the most important variable
in a virtual learning community, our analysis suggests that when trust is associated directly with
learning, but without the positive influence of its parent variables (mutuality, intensity, social
protocols, reflections, autonomy and awareness), the probability of learning remains low P
(l=0.629). This result holds even in the presence of good technology and effective participation.
Previous research has emphasized the value of trust in enhancing the sense of a community.
Prusak and Cohen (2001) suggested that trust enables people to work together, collaborate, and
smoothly exchange information and share knowledge without time wasted on negotiation and
conflict. In virtual learning communities however, we argue that without mutuality, intensity,
social protocols, reflections, and awareness; the impact of trust on learning may be minimal.
Based on different experiences, experts’ knowledge, intuition and hunches, a large number
of scenarios can be developed to query this model. Querying the model using logical scenarios,
whether based on empirical data or experts’ experiences, offers a disciplined method of
examining the cumulative effect of making changes anywhere in the network and also for
speculating about how any particular change can alter the values of related variables. The BBN is
still, at its core, a tool for speculation, but over time and as data are added to inform the variables
and their interrelationships, the network can be "tuned" to provide robust and precise ways to
make decisions about how to support learning in virtual learning communities.
Discussion
Building a model of a virtual learning community using this approach enables us to isolate those
variables critical to the process of learning in virtual learning communities. Saying that learning
is an important variable of a virtual learning community is tautological, but also an important
reminder that the central intent of this type of community is different from many others
(Schwier, 2001; McCalla, 2000). We suggest that process of learning in VLCs can be better
understood by examining the impact of several variables on learning and this can, in turn,
illuminate how we can support learning in online settings. We believe that there is a need to find
robust ways of identifying fundamental instructional principles that can be used to support the
process of learning in virtual learning communities.
We have observed changes in the posterior probability values of trust and learning as a result
of changes in variables that have both direct and indirect relationships with them. As one would
expect, some of the changes are significant while others are minimal. Some of our findings to
date are consistent with previous research into understanding the process of learning in virtual
learning communities. For instance, findings show that mutuality has some critical influence on
the process of learning. Mutuality connotes reciprocal relationships among learners involving
exchange of messages, sharing stories, experiences and knowledge. Other findings qualify
previous research, in particular, our research suggests that there are several prerequisite
conditions necessary before an increase in trust will result in an increase in learning.
Most of the variables in this model have significant, and complex, implications for
pedagogy. We will use “sharing experiences” to illustrate one complex set of relationships.
Previous study suggests that sharing experiences in virtual learning communities is an expression
of mutual interdependence which can ultimately influence the process of learning in
communities (Daniel, Schwier & Ross in press). In addition, sharing resources, information,
experiences and problems is seen to be a key feature of developing social capital in virtual
learning communities.
When people share their experiences with others in a community they exhibit a sense of
belonging to a community, and feel that they are contributing useful knowledge that can benefit
others in the group. Sharing experiences can therefore, shape collective identity, promote
effective engagement and participation in community events, activities and rituals leading to the
collective accumulation of knowledge or skill by the group. It is also likely that when people
share experiences they develop a sense of trust, which is critical to the process of learning in
virtual learning communities, when combined with other constituent variables.
However, although sharing experiences is critical to generating tacit knowledge, it is
informal, and typically voluntary. This means individuals need to be highly motivated to share
their personal life experiences with others. And so, the need to provide individuals with the
capacity and authority to conduct discourse openly, or withdraw from discourse without penalty
is critical—a key feature of autonomy. Indeed our findings suggest autonomy has high impact on
trust and learning. This creates a significant challenge in the design of online learning
environments. If sharing experiences is critical to learning, but the authority to participate is left
in the hands of autonomous participants, how can an instructor ensure that meaningful sharing
happens? Certainly instructors can encourage participation and direct it; something as simple as
asking students to share experiences may be sufficient in some cases. Indeed, students don’t
always know how to participate in online learning environments, or understand what is expected
of them; so clear direction can be welcome. But it does not ensure that candid, thoughtful
sharing will occur, so instructors who feel a need to control a learning environment and learning
outcomes, may find themselves in a pedagogical wonder-world, where their authority threatens
to interfere with the very outcome they want to promote.
Model Implications and Conclusions
Regardless of the impact of individuals and collective variables on learning as discussed in the
article, in general, we also suspect that learning will manifest itself differently depending on the
context of the community in which it is created, such as whether communities are formal or
informal, the nature of domain in which learning is pursued, instructional roles and the maturity
of participants. While we acknowledge these contextual issues are important, our model does not
address them at this point. Instead we are interested in understanding the fundamental features of
a virtual learning community and how they relate to learning in general.
An important lesson we have learned is that we need to use a variety of methods to analyze
anything as complex as virtual learning community. The literature we have reviewed is replete
with assumptions about what comprises a virtual learning community, often without any
substantial theoretical framework for research that is conducted. While many useful metrics
have been developed to examine specific elements of community, these are typically focused on
few variables, or take little account of interactions among variables in complex learning
environments. The methods we propose flow from definition to analysis to prediction, so they
have some intuitive and practical appeal. But we recognize that we are at the beginning of
learning about how to understand online learning communities as organisms, and so we make no
claim that these methods represent a definitive set of tools for that job. But regardless of the
specific tools used to determine whether virtual communities exist, our experience has led us to a
few key ideas. First, considering the full cycle from definition to modeling is important; much of
the research to date looks closely at a few variables in communities and much of the literature is
speculative.
We think there is a need to isolate features of communities, to try to determine their relative
importance to learning and their interrelationships, and then build Bayesian models that can be
used to test inferences in new environments and inform design science in distance learning. The
Bayesian Belief Network approach introduced in this article is one tool that can enable
researchers to study various influence of variables in virtual learning communities, given
concrete scenarios drawn from empirical evidence.
The virtual learning model presented in this article contains fundamental variables grounded
in practice. The knowledge used to map the relationships among the variables is based on expert
knowledge on research and teaching in virtual learning environments. We believe the initial
model presented here can be further validated by and its precision can attune to different
contexts.
In the future we plan to run sensitivity analysis to determine the fit of the model to the
assumptions made during its development and use the results to improve them model. In
addition, we will gather a panel of experts in virtual learning communities to validate usefulness
of the model using their own experiences.
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