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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