Conversion of Revealed Causal Map into Evidential Diagram and Belief
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Propagation
In this section we first discuss how a revealed causal map can be converted to a belief
function evidential diagram and then discuss how beliefs can be propagated through this
evidential diagram. Our example is displayed in Figure 3.
Conversion of Revealed Causal Map into Evidential
Diagram
The conversion process of revealed causal map into evidential diagram can be described
in the following five steps:
1. Identify the main variables (i.e., constructs) in the revealed causal map.
2. Determine the possible values of these variables (such as, ‘true/false’, or ‘high/
medium/low’).
3. Determine the relationships among the variables (see the details below).
4. Connect the variables through the corresponding relationships.
5. Identify potential items of evidence pertaining to the variables in the diagram and
connect these items of evidence to the relevant variables.
The above approach yields the desired evidential diagram for belief-function analysis.
In Steps 1 and 2, we have identified nine variables (i.e., constructs; see Figure 3) and their
corresponding categorical values (Table 4).
Step 3 (determining the relationships among various variables) is a somewhat difficult
process. Expert judgments about these relationships must be rendered. For example, the
relationship R1 defining the relationship between ‘Role Recognition (RR)’ and ‘Job
Security (JT)’ was extremely difficult to model. In this case, the survey data provided only
information on whether the subjects recognize their changing role on the job and did not
specify any details on how this knowledge might influence ‘Job Security’. For IT
personnel, ‘Role Recognition’ might mean that ‘yes’ there is ‘Job Security’, but it also
may mean that there is no ‘Job Security’. Thus, lacking any other information, we assume,
for the present discussion, that when ‘Role Recognition’ is yes, ‘Job Security’ is 50%
‘yes’, and 50% ‘no’. However, when there is no knowledge about ‘Role Recognition’,
there is no knowledge about ‘Job Security’. Such a relationship can be expressed in terms
of m-values as given below.
m-values for R1:
mR1({(yes RR, yes JT), (no RR, yes JT), (no RR, no JT)}) = 0.5,
mR1({(yes RR, no JT), (no RR, yes JT), (no RR, no JT)}) = 0.5.
The above relationship propagates9 50% of mE1(yes RR), the belief on ‘Role Recognition’
being ‘yes’ from evidence E1 (Figure 4), to ‘yesJT’ 50% of mE1(yes RR) to ‘noJT’, and 100%
of mE1(noRR) and mE1({yesRR, noRR}) to ({yesJT, noJT}), as described in the assumed
relationship. In other words, the m-values propagated from variable ‘Role Recognition
(RR)’ to variable ‘Job security (JT)’ are given as:
mJT←RR(yesJT) = 0.5mE1(yesRR), mJT¬RR(noJT) = 0.5mE1(yesRR), and
mJT←RR({yesJT, noJT}) = mE1(noRR) + mE1({yesRR, yesRR})
For the relationship R2 we assume the following. On average, a person with the
knowledge that there is no job security will sign up for job training with 90% belief and
a person with the knowledge that there is no problem with the job security will not sign
up for job training with 90% belief. This relationship can be modeled in the following way:
m-values for R2:
mR2({(yes JT, no ST), (no JT, yes ST)}) = 0.9, and
mR2({(yes JT, yes ST), (yes JT, no ST), (no JT, yes ST), (no JT, no ST)}) = 0.1.
Similar to endnote 9, one can easily show the following m-values to be the result of mvalues
propagated from variable ‘Job Security (JT)’ to variable ‘Sign up for Job Training
(ST)’ through the relationship R2:
mST←JT(yesST) = 0.9mJT(noJT), mST¬JT(noST) = 0.9mJT(yesJT), and
mST←JT({yesST, noST}) = 0.1 + 0.9mJT({yesRR, yesRR}).
We assumed the following m-values for R3 (see Table 4 for the definitions of the
symbols):
m-values for R3:
mR3({(yes ST, yesUS), (no ST, no US)}) = 0.75, and
mR3({(yes ST, yes US), (yes ST, no US), (no ST, yes US), (no ST, no US)}) = 0.25.
The relationship previously discussed implies that if variable ‘ST’ is ‘yes’, i.e., a person
sings up for training, then variable ‘US’ will be ‘yes’, i.e., the person will have the
opportunity to use the new skill with 0.75 belief, and the remaining 0.25 belief is assigned
to ignorance. Similarly, the relationship implies that if ‘ST’ is ‘no’ then ‘US’ is ‘no’ with
belief 0.75, i.e., if one does not sign up for job training then he/she will not have the use
of new skill with belief 0.75. The remaining 0.25 belief represents ignorance.
For the relationship R4, we assume the following m-values:
m-values for R4:
mR4({(yesGS, yesUS), (noGS, noUS)}) = 1.0.
This relationship implies that if ‘GS’ is ‘yes’ then ‘US’ is ‘yes’ with 1.0 belief. Also, if ‘GS’
is ‘no’ then ‘US’ is ‘no’ with 1.0 belief. In other words, if one has the opportunity to gain
new skills on the job then there is 1.0 belief that there is opportunity to use the new skills.
Similarly, if there is no opportunity to gain new skills on the job then there is no
opportunity to use the new skills.
The relationship R5 relates variables ‘US’, ‘FS’, ‘AW’, and ‘CW’ to the variable ‘Job
Satisfaction (JS)’. We have assumed the following relative weights, 0.125, 0.125, 0.25, and
0.5, respectively, for ‘US’, ‘FS’, ‘AW’, and ‘CW’ when propagating information (mvalues)
to the variable ‘JS’.
Step 4 simply represents a diagram with all the variables interconnected through the
assumed relationships (see Figure 4). In Step 5, we identify various items of evidence
pertaining to different variables and connect them to the corresponding variables. Table
4 provides a list of evidence pertaining to the nine variables in Figure 4. Once these items
of evidence are connected to the corresponding variables, we develop the evidential
diagram shown in Figure 4 for the analysis.
Propagation of Beliefs through Evidential Diagram
In order to propagate information in terms of m-values from all the variables to the variable
of interest, say, ‘Job Satisfaction (JS)’ in Figure 4, we need to follow the following steps.
First, gather all the information (m-values) at ‘Role Recognition (RR)’, propagate that
information (m-values) to variable ‘Job Security (JT)’ through the relationship R1 by first
vacuously extending to the space of R1, combining it with the m-values at R1 using
Dempster’s rule, and then marginalizing the resulting m-values to the space of ‘JT’.
Combine this information (m-values) with the m-values at ‘JT’ obtained from evidence
E2.1 and E2.2, again using Dempster’s rule. Next step is to propagate the resulting mvalues
at ‘JT’ through R2 to the variable ‘Sign up for Training to Gain New Skills (ST)’.
This is achieved again by vacuously extending the total m-values at ‘JT’ to the space of
R2, combining them with the m-values at R2 using Dempster’s rule, and then marginalizing
them to the space of variable ‘ST’. Combine this information (m-values) with the m-values
obtained from evidence E3 for ‘ST’. The resulting m-values are then propagated to the
variable ‘Opportunity to use New Skills (US)’. Combine these m-values with the m-values
obtained from the variable ‘Opportunity to Gain New Skills on the Job (GS)’ and the mvalues
from evidence E5 for ‘US’.
In the final step, we need to propagate all the m-values from the four variables, ‘US’, ‘FS’,
‘AW’, and ‘CW’ through the relationship R5 to the variable ‘Job Satisfaction (JS)’ by
vacuously extending the respective m-values to the space of R5, combine these m-values
with the m-values defining R5 and then marginalize them to the space of ‘Job Satisfaction’.
The marginalized m-values on ‘Job Satisfaction (JS)’ can be written as:
mJS(yesJS) = 0.125mUS(yesUS) + 0.125mFS(yesFS) + 0.25mAW(yesAW) + 0.5mCW(yesCW).
mJS(noJS) = 0.125mUS(noUS) + 0.125mFS(noFS) + 0.25mAW(noAW) + 0.5mCW(noCW).
mJS({yesJS, noJS}) = 1 - mJS(yesJS) - mJS(noJS).
These m-values provide the impact of all the variables in the evidential diagram in Figure 4.
Given that the evidential diagram in Figure 4 is a tree, the propagation of m-values from
various variables to the variable of interest, ‘Job Satisfaction’ is much easier than
propagation in a network of variables. We programmed the logic of vacuous extension,
marginalization, and Dempster’s rule of combination in a spreadsheet program in MS
Excel, which then was used to perform various analyses as discussed in the next section.
Decision Analysis of Causal Map Using
Belief Functions
In this section, we discuss how one can analyze the impact of one variable on the other
variables in the network given in Figure 4. Such an analysis allows the decision maker
to isolate an independent variable while holding the rest of the variables in the model
constant. In this example, the overall belief in job satisfaction is 0.803 given the inputs
from the Survey Results and industry data. The above value implies that based on the
subjects responses, on average, employees are satisfied with their jobs in the environment
surveyed with 0.803 level of belief. In order to investigate the impact of a number
of variables on the level of job satisfaction, we use a range of possible responses (0 to
1.0) for the variables while keeping the inputs from other items of evidence fixed at values
obtained from the survey as given in the respective figures.
First, we investigate the impact of ‘Job Security’ on ‘Job Satisfaction’. We vary the input
belief from evidence E2.2 for the negation of ‘Job Security’ from 0 to 1.0, keeping the rest
of inputs fixed. As seen in Figure 5, the impact of ‘No Job Security’ is pretty severe. As
the belief in no job security increases the belief in job satisfaction decreases with
increasing rate. In other words, if an employee sees strong evidence in support of ‘no
job security’ then he/she will have very low job satisfaction.
The second sensitivity analysis is conducted on the impact of having an opportunity to
use new skills on the job. This analysis reveals that the opportunity to use new skills has
© 2005, Idea Group Inc. Copying or distributing in print or electronic forms without written
permission of Idea Group Inc. is prohibited.
Figure 4. Evidential diagram* of the causal map in Figure 3
3. Sign Up For Training to Gain
New Skills (ST) {yesST, noST}
4. Opportunity to Gain New Skills
on the Job (GS) {yesGS, noGS}
1. Recognition of Tech. & Bus. Role
Change (RR) {yesRR, noRR}
2. Job Security (JT)
{yesJT, noJT}
[yes/no]
5. Opportunity to use New
Skills (US) {yesUS, noUS}
Job Satisfaction (JS)
{yesJS, noJS}
7. Challenging work (CW)
{yesCW, noCW}
6. Feedback from Superiors/
Co-workers (FS) {yesFS, noFS}
8. Autonomy of Work (AW)
{yesAW, noAW}
E1. Survey Results: Q51, Q52,
Q53, Q55 (0.63, 0.37)
E2.1: Layoffs reported – in the firm, R1
industry, general public (0.27, 0.73)
E3: Survey Results, Q34
(0.79, 0.0)
R4 R3
E4: Survey Results, Q30
(0.84, 0.0)
R2
R5
E2.2: Survey Results, Q28
(0.83, 0.0)
E6: Survey Results, Q6, Q14-Q22
(0.66, 0.34)
E5: Survey Results, Q35
(0.81, 0.0)
E8: Survey Results, Q2, Q16, Q20
(0.77, 0.23)
E7: Survey Results, Q26
(0.81, 0.0)
*The oval shaped boxes represent variables and the rectangular boxes represent items of evidence.
The numbers in a rectangular box represent the level of support for and against the variable it
is connected to. These numbers were determined from the Survey Results except for E2.1 which
was determined from the industry data.
Belief Function Approach to Evidential Reasoning in Causal Maps 129
Figure 5. Belief in job satisfaction versus belief in no job security*
*The following input m-values in Figure 4 were used for the graph: mE1(yesRR)=0, mE1(noRR)=0,
mE2.1(yesJT)=0.27, mE2.1(noJT)=0.73, mE2.2(yesJT)=0, mE2.2(noJT)=0, mE3(yesST)=0, mE3(noST)=0,
mE4(yesGS)=0, mE4(noGS)=0, mE5(yesUS) varied from 0 - 1, mE5(noUS)=0, mE6(yesFS)=0.66,
mE6(noFS)=0.34, mE7(yesCW)=0.81, mE7(noCW)=0, mE8(yesAW)=0.77, mE8(noAW)=0.23.
Impact of Belief in 'No' Job Security on Belief in Job Satisfaction
0.65
0.67
0.69
0.71
0.73
0.75
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Belief in 'No' Job Security
Belief in Job Satisfaction
Figure 6. Belief in job satisfaction versus belief in opportunity to use new skills*
Impact of Belief in Opportunity to use New Skills on Belief in Job
Satisfaction
0.72
0.74
0.76
0.78
0.80
0.82
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Belief in Opportunity to use New Skills
Belief in Job Satisfaction
*The following input m-values in Figure 4 were used for the graph: mE1(yesRR)=0, mE1(noRR)=0,
mE2.1(yesJT)=0.27, mE2.1(noJT)=0.73, mE2.2(yesJT)=0, mE2.2(noJT)=0, mE3(yesST)=0, mE3(noST)=0,
mE4(yesGS)=0, mE4(noGS)=0, mE5(yesUS) varied from 0 - 1, mE5(noUS)=0, mE6(yesFS)=0.66,
mE6(noFS)=0.34, mE7(yesCW)=0.81, mE7(noCW)=0, mE8(yesAW)=0.77, mE8(noAW)=0.23.
Figure 7. Belief in job satisfaction versus belief in feedback from supervisors and coworkers*
Impact of Belief in Feedback from Supervisors and Co-Workers
on Belief in Job Satisfaction
0.71
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Belief in Feedback from Supervisors and Co-Workers
Belief in Job Satisfaction
*The following input m-values in Figure 4 were used for the graph: mE1(yesRR)=0, mE1(noRR)=0,
mE2.1(yesJT)=0.27, mE2.1(noJT)=0.73, mE2.2(yesJT)=0, mE2.2(noJT)=0, mE3(yesST)=0, mE3(noST)=0,
mE4(yesGS)=0, mE4(noGS)=0, mE5(yesUS)=0.81, mE5(noUS)=0, mE6(yesFS) varied from 0 - 1, mE6(noFS)=0,
mE7(yesCW)=0.81, mE7(noCW)=0, mE8(yesAW)=0.77, mE8(noAW)=0.23.
a significant positive impact on ‘Job Satisfaction’ as seen from Figure 6. As the belief in
opportunity to use new skills increases, the belief in job satisfaction increases. We find
an 8.5% increase in job satisfaction over the range from 0 – 1.0 for belief in opportunity
to use new skills. This impact is linear, unlike the previous case.
The third variable analyzed is ‘Feedback from Supervisors/Co-workers’. As shown in
Figure 7, the results demonstrate a substantial positive impact of feedback on the job
satisfaction. In particular, job satisfaction increases about 19% as we progress from the
lower to higher levels of perceived feedback. It is obvious that feedback is a powerful
variable in predicting job satisfaction.
Next, we conduct a sensitivity analysis with the independent variable, ‘Challenging
Work’. ‘Job Satisfaction’ was extremely sensitive to increases in the perceived level of
challenging work. From no belief that the job is challenging to the higher range of belief,
1.0, the model indicates that the belief in job satisfaction moves from 0.388 to 0.838; a 129%
increase as seen in Figure 8. These results indicate that challenging work is the most
powerful variable in the model in the prediction of job satisfaction.
Finally, a sensitivity analysis was conducted on ‘Autonomy of Work’. The results
indicate that ‘Autonomy of Work’ has a significant impact on the dependent variable,
‘Job Satisfaction’. Job satisfaction was found to be very sensitive to autonomy. As the
perceived autonomy increases from 0 to 1.0, job satisfaction improves from 60% to 85%,
an increase of 41.6%. These results are presented in Figure 9.
These sensitivity analyses have shown the impact on job satisfaction from a broad range
of variables and their corresponding beliefs. However, we do want to point out that the
Figure 8. Belief in job satisfaction versus belief in challenging work*
Impact of Belief in C hallenging W ork on Belief in Job Satisfaction
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Belief in Challenging Work
Belief in Job Satisfactio
*The following input m-values in Figure 4 were used for the graph: mE1(yesRR)=0, mE1(noRR)=0,
mE2.1(yesJT)=0.27, mE2.1(noJT)=0.73, mE2.2(yesJT)=0, mE2.2(noJT)=0, mE3(yesST)=0, mE3(noST)=0,
mE4(yesGS)=0, mE4(noGS)=0, mE5(yesUS)=0.81, mE5(noUS)=0, mE6(yesFS)=0.66, mE6(noFS)=0.34,
mE7(yesCW) varied from 0 - 1, mE7(noCW)=0, mE8(yesAW)=0.77, mE8(noAW)=0.23.
Figure 9. Belief in job satisfaction versus belief in autonomy of work*
Impact of Belief in Autonomy of Work on Belief in Job Satisfaction
0.50
0.60
0.70
0.80
0.90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Belief in Autonomy of Work
Belief in Job Satisfaction
*The following input m-values in Figure 4 were used for the graph: mE1(yesRR)=0, mE1(noRR)=0,
mE2.1(yesJT)=0.27, mE2.1(noJT)=0.73, mE2.2(yesJT)=0, mE2.2(noJT)=0, mE3(yesST)=0, mE3(noST)=0,
mE4(yesGS)=0, mE4(noGS)=0, mE5(yesUS)=0.81, mE5(noUS)=0, mE6(yesFS)=0.66, mE6(noFS)=0.34,
mE7(yesCW)=0.81, mE7(noCW)=0, mE8(yesAW) varied from 0 - 1, mE8(noAW)=0.
interrelationships among the intermediate variables and the relative weights assigned to
‘Opportunity to use New Skills’, ‘Feedback from Supervisors and Co-Workers, ‘Challenging
Work’, and ‘Autonomy of Work’, have direct impact on the results for the
dependent variable, ‘Job Satisfaction’.
In summary, the above analysis provides an example of how an evidential reasoning
approach under Dempster-Shafer theory of belief functions can be used to determine the
impact on a given construct or constructs of other constructs in a revealed causal map.
It should be noted that a revealed causal map of a decision problem is only a static model
while an evidential diagram of a revealed causal map provides a dynamic model for
analyzing the behaviors of various constructs under different conditions.
Conclusions and Future Directions for
Research
In this chapter we have demonstrated the use of evidential reasoning approach under
Dempster-Shafer (D-S) theory of belief functions to analyze revealed causal maps. As an
example, we used a simplified causal map obtained through a Revealed Causal Mapping
(RCM) technique where the participants were from information technology (IT) organizations
who provided the concepts to describe the target phenomenon of ‘Job Satisfaction’.
They also identified the associations between the concepts. After creating the
causal map of the problem being investigated, we developed an evidential diagram. This
diagram consists of the variables or constructs of the causal map, interconnected to the
other variables with some relationships. These relationships were defined by the
decision maker based on experience. Various items of evidence were identified that
pertained to different variables. Estimates of the beliefs in terms of m-values in support
of, or negation of, the variables were made for each item of evidence using survey
questions (Buche, 2003, particularly Appendix C). These m-values were then propagated
through the evidential network to obtain the overall belief of ‘Job Satisfaction’.
To illustrate the usefulness of the evidential reasoning approach under Dempster-Shafer
theory of belief functions, we performed various sensitivity analyses to determine the
impact of different variables on ‘Job Satisfaction’. This technique enables researchers
to predict the level of job satisfaction when given evidence for the other variables in the
model. As further validation for our findings, our results are directly in line with previous
literature on job satisfaction for workers in general. IT personnel are very similar to other
professions and vocations. An evidential diagram similar to the one discussed here
would be useful in predicting whether a specific work environment would be more or less
satisfactory to an employee before joining the job.
In this chapter we have explained the steps necessary to convert revealed causal maps
into evidential diagrams. The analysis of the transformed diagram is useful in forming
predictions about human behavior. This technique incorporates the existence of uncertainty
in the level of belief associated with the evidence. Therefore, the researcher is able
to include in the diagram personal intuition and confidence based on direct experience.
Another advantage of the evidential reasoning approach over a revealed causal map is
that the former provides a dynamic model of a decision problem while the later provides
only a static model. As a limitation, the evidential reasoning approach may become quite
complex especially when variables or constructs in the diagram are highly integrated. For
ease of instruction, the example discussed herein was fairly simplistic, with primarily
linear associations.
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Endnotes
1 See the following references for more discussion on belief functions and their
applications: Bovee et al. (2003), Srivastava (1993), Srivastava and Datta (2002),
Srivastava and Liu (2003), and Srivastava and Mock (2000).
2 For three independent items of evidence, Dempster’s rules can be written as:
-1
1 i 2 j 3 k 1 i 2 j 3 k
i,j,k i,j,k
Bi Bj Bk =B Bi Bj Bk =
m(B) = K . m (B )m (B )m (B ), where K = 1 - m (B )m (B )m (B )
∩∩∩∩∅
.
One can easily generalize the above formula for n independent items of evidence
(see Shafer, 1976, for details).
3 The argument of m-function represents the state for which the value is assigned
and the subscript describes the evidence from which the value is derived. For
example, mX(x) = 0.6 represents 0.6 level of support for ‘x’ from an item of evidence
pertaining to the variable X.
4 Propagation is the process by which m-values on a variable or a set of variables
are moved (mapped) to another variable or a set of variables. For example, m-values
from variable X in Figure 1 can be propagated to the relational variable ‘AND’ that
consist of three variables, X, Y, and Z.
5 Vacuous extension is the process through which m-values on a smaller frame are
extended to a larger frame. For example, m(x) when vacuously extended to the joint
space of X and Y, i.e., the frame {xy, x~y, ~xy, ~x~y}, yields m(x) = m({xy, x~y}).
6 Marginalization of m-values is opposite to the vacuous extension. This process is
similar to marginalization in probability theory; it involves eliminating all the
unwanted variables by summing the m-values over the unwanted variables. For
example, assume that we have the following m-values on the joint space of X and
Y, X,Y = {xy, x~y, ~xy, ~x~y}: m({xy}) = 0.1, m({xy, x~y}) = 0.6, and m({xy, x~y, ~xy,
~x~y}) = 0.3. The marginalized m-values onto the space of X variable are: m({x})
= 0.1 + 0.6 = 0.7, and m({x, ~x}) = 0.3. Similarly, the marginalized m-values onto the
Y space are: m({y}) = 0.1, m({y, ~y}) = 0.9.
7 Through this example we are illustrating the details of the propagation process of
beliefs or m-values through a tree of variables as this is what is needed in our model
of IT job satisfaction obtained through the RCM process. A discussion on the
details of the propagation of beliefs through a network of variables is beyond the
scope of this chapter. Interested readers should see Srivastava (1995) and Shenoy
and Shafer (1990) for this kind of propagation.
8 A Markov tree is characterized by a set of nodes N and a set of edges E where each
edge is a two-element subset of N such that (Srivastava, 1995; see also, Shenoy,
1991):
• (N,E) is a tree.
• If N and N’ are two distinct nodes in N, and {N, N’} is an edge, i.e., {N,N'} ∈E ,
then ∩N’≠∅
• If N and N’ are distinct nodes of N, and X is a variable in both N and N’, then
X is in every node on the path from N to N’.
9 As described in Section IV, in order to propagate m-values from ‘RR’ to ‘JT’ through
the relationship R1, one needs to vacuously extend the m-values from the space
of ‘RR’, {yesRR, noRR}, to the space of R1, which is the joint space of ‘RR’ and ‘JT’,
i.e., {(yesRR, yesJT), (yesRR, noJT), (noRR, yesJT), (noRR, noJT)}, combine the m-values
at R1, and then marginalize to the space of ‘JT’, {yesJT, noJT}.
10 This semi-structured interview guide was also part of NSF grant proposal and
Transition Study research project (Nelson, 2000; Buche, 2003).
Appendix A: Concept Dictionary with
Examples
Construct Description Example
Role not valued Company no longer needs certain skill sets
to support certain roles.
Generalists such as myself…don’t see that
role being valued much.
Role change Expectations of workers experience
transition.
I got into the analyst role, being the leader
and doing the coordination.
Fear of job loss Lack of job security.
Anyone would be worried about their
career.
Sign up for training Training is provided by a company for
workers to develop new skills.
We just look at the classes, sign up for
them.
Opportunity to gain
new skills
Workers are taught new skills in classroom
or self-paced training.
Once you learn programming, and you
have that skill.
Opportunity to use
new skills
The job environment provides the
opportunities for workers to practice the
skills learned during training.
Using new skills to make the company
more competitive.
Feedback form
superiors and coworkers
Direct reaction obtained from supervisors
and co-workers that reduces ambiguity
about perceived performance.
The users let me know if the system meets
their needs.
Challenging projects Work assignments provide an intrinsic
motivation because the problem-solving
aspect takes effort.
Technical challenges of the job.
Autonomy of Work Workers have freedom and independence in
determining relevant job-related decisions.
Nobody really tells me what to do or how
to do it.
Job satisfaction Affective response to the current job
environment.
Pleasant work environment.
Appendix B: Interview Protocol10
1. What motivates you to come to work here every day?
2. What is the best thing about your current work environment?
3. What is the worst thing about your current work environment?
4. What is the most important thing you contribute to this organization?
5. What could you contribute to your organization that you currently are unable to
contribute?
6. What barriers keep you from making this contribution?
7. Where do you realistically see yourself professionally in five years?
8. Where would you ideally like to see yourself professionally in five years?
9. What barriers might keep you from your ideal situation?
10. How much do you like change?
11. How much do you think the IT field, in general, is changing?
12. How much do you think the IT field at your company is changing?
13. How do you feel about this level of change?
14. How is your organization supporting you in personally making these changes?
15. What barriers do you see in making these changes?
16. What is your primary, one year professional goal?
17. How can your organization help you achieve you goals?
18. In summary, how do you see yourself fitting into the organization’s “big picture”?
19. Would you like to add any further comments or observations?
Appendix C: Propagation Illustration in
Figure 1
In this appendix we describe in detail the three steps involved in the propagation of mvalues
from variables X and Y in Figure 1 to variable Z.
Step 1: Propagation of m-values from X and Y to ‘AND’ node:
In order to propagate m-values from variable X, a smaller node with one variable and the
frame X={x,~x}, to the ‘AND’ node, a larger node consisting of three variable X, Y, and
Z with the frame AND= {xyz, x~y~z, ~xy~z, ~x~y~z}, we vacuously extend the m-values
at X to the space {xyz, x~y~z, ~xy~z, ~x~y~z} defined by the ‘AND’ node. This process
yields the following non-zero m-values from X to the ‘AND’ node:
mAND←X({xyz, x~y~z}) = mX(x) = 0.6,
mAND←X({~xy~z, ~x~y~z}) = mX(~x) = 0.2,
mAND←X({xyz, x~y~z, ~xy~z, ~x~y~z}) = mX({x, ~x}) = 0.2.
Similarly, we obtain the following non-zero m-values at the ‘AND’ node when the mvalues
from Y are propagated to the ‘AND’ node:
mAND←Y({xyz, ~xy~z}) = mY(y) = 0.7
mAND←Y({xyz, x~y~z, ~xy~z, ~x~y~z}) = mY({y,~y}) = 0.3
Step 2: Combine m-values from X and Y with the m-values at ‘AND’
We have the following set of m-values at the ‘AND’ node; one from X, one from Y, and
one at the ‘AND’ node defining the relationship.
m-values from X:
mAND←X({xyz, x~y~z}) = 0.6, mAND←X({~xy~z, ~x~y~z}) = 0.2, and
mAND←X({xyz, x~y~z, ~xy~z, ~x~y~z}) = 0.2.
m-values from Y:
mAND←Y({xyz, ~xy~z}) = 0.7,
mAND←Y({xyz, x~y~z, ~xy~z, ~x~y~z}) = 0.3.
m-values at the ‘AND’ node:
mAND({xyz, x~y~z, ~xy~z, ~x~y~z}) = 1.0.
After we combine the above m-values using Dempster’s rule, we obtain the following mvalues:
m({xyz}) = mAND←X({xyz, x~y~z}).mAND←Y({xyz, ~xy~z}).
mAND({xyz, x~y~z, ~xy~z, ~x~y~z}) = 0.6x0.7x1.0 = 0.42,
m({xyz, x~y~z}) = mAND←X({xyz, x~y~z}).
mAND←Y({xyz, x~y~z, ~xy~z, ~x~y~z}).mAND({xyz, x~y~z, ~xy~z, ~x~y~z})
= 0.6x0.3x1.0 = 0.18,
m({~xy~z}) = mAND←X({~xy~z, ~x~y~z}).mAND←Y({xyz, ~xy~z}).
mAND({xyz, x~y~z, ~xy~z, ~x~y~z})
0.2x0.7x1.0 = 0.14,
m({~xy~z, ~x~y~z}) = mAND←X({~xy~z, ~x~y~z}).
mAND←Y({xyz, x~y~z, ~xy~z, ~x~y~z }).
mAND({xyz, x~y~z, ~xy~z, ~x~y~z}) = 0.2x0.3x1.0 = 0.06,
m({xyz, ~xy~z}) = mAND←X({xyz, x~y~z, ~xy~z, ~x~y~z }).
mAND←Y({xyz, ~xy~z}).mAND({xyz, x~y~z, ~xy~z, ~x~y~z}) = 0.2x0.7x1.0 = 0.14,
m({xyz, x~y~z, ~xy~z, ~x~y~z})
= mAND←X({xyz, x~y~z, ~xy~z, ~x~y~z }).
mAND←Y({xyz, x~y~z, ~xy~z, ~x~y~z }).
mAND({xyz, x~y~z, ~xy~z, ~x~y~z }) = 0.2x0.3x1.0 = 0.06.
The above m-values are propagated to variable Z by marginalizing them to Z as described
next.
Step 3: Propagate m-values from ‘AND’ node to Z
The third step deals with propagating beliefs or m-values from ‘AND’ node to variable
Z. Since the “AND’ is a bigger node consisting of three variables, X, Y, and Z, the mvalues
have to be marginalized to variable Z. As discussed in endnote 6, marginalization
of belief functions or m-values is similar to marginalization of probabilities. The unwanted
variables are eliminated by summing the m-values over the variables. We obtain the
following m-values on variable Z as a result of propagation of m-values from X and Y
through the relationship ‘AND’ by marginalization of m-values at the ‘AND’ node:
mZ←AND({z}) = m({xyz}) = 0.42,
mZ←AND({~z}) = m({~xy~z}) + m({~xy~z, ~x~y~z}) = 0.14 + 0.06 = 0.20,
mZ←AND({z,~z}) = m({xyz, x~y~z}) + m({xyz, ~xy~z}) + m({xyz, x~y~z, ~xy~z, ~x~y~z})
= 0.18+ 0.14 + 0.06 = 0.38.
This completes the process. We now know that belief that Z is true is 0.42 (i.e., Bel(z) =
0.42), given that we know that X is true with belief 0.6 and Y is true with belief 0.7. Similarly,
we know that Z is not true with belief 0.20, i.e., Bel(~z) = 0.20, given the knowledge about
X and Y expressed in terms of the following m-values: mX(x) = 0.6, mX(~x) = 0.2, mX({x,~x})
= 0.2, and mY(y) = 0.7, mY(~y) = 0, mY({y,~y}) = 0.3.