Modeling Uncertain Relationships among Variables
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Srivastava and Lu (2002) have discussed a general approach to modeling various
relationships under belief functions. We will use their approach to model the assumed
relationships among various variables in Figure 4. As given earlier, the ‘AND’ relationship
among X, Y and Z, under belief functions can be expressed in terms of the following
m-value:
mAND({xyz, x~y~z, ~xy~z, ~x~y~z}) = 1.0.
The argument of m-value above determines the possible states of the joint space defining
the ‘AND’ relationship. Similarly, the ‘OR’ relationship can be expressed as:
mOR({xyz, x~yz, ~xyz, ~x~y~z}) = 1.0.
A relationship representing 60% of ‘AND’ and 40% of ‘OR’ can be expressed as:
mR({xyz, x~y~z, ~xy~z, ~x~y~z}) = 0.6, and mR({xyz, x~yz, ~xyz, ~x~y~z}) = 0.4,
where the subscript R stands for the relationship.
Propagation of Beliefs in a Network of Variables
The evidential diagram becomes a network if one item of evidence pertains to two or more
variables in the diagram. Such a diagram is depicted in Figure 2 for a simple case of three
variables. Even though the evidential diagram of IT Job Satisfaction model obtained
through the RCM approach in the current study is not a network (see Figure 4), we
describe the approach of propagating beliefs or m-values through a network of variables
for completeness. The propagation of m-values through a network is much more complex
and thus we will not go into the details of the propagation process in this chapter. Instead,
we will briefly describe the process and advise interested readers to refer to Shenoy and
Shafer (1990) for the details. Also, Srivastava (1995) provides a step-by-step description
of the process by discussing an auditing example.
Basically, the propagation of m-values (i.e., beliefs) through a network of variables
involves the following steps. First, the decision maker draws the evidential diagram with
all the pertinent variables and their interrelationships in the problem along with the
related items of evidence. This step is similar to creating an evidential diagram for the case
of a tree-type diagram. Second, the decision maker identifies the clusters of variables over
which m-values are either obtained from the items of evidence in the evidential diagram
or defined from the assumed relationships among the variables. For example, in Figure
2, the four items of evidence yield the following clusters of variables: {X}, {Y}, {Z},
{X,Y}, and the ‘AND’ relationship defines m-value for the cluster {X,Y,Z}. Thus, in
Figure 2, we have the following clusters of variables over which m-values are defined:
{X}, {Y}, {Z}, {X,Y}, and {X,Y,Z}.
The third step in the propagation process in a network is to draw a Markov8 tree based
on the identified clusters of variables as above. This step is not needed for a tree-type
evidential diagram. One can propagate m-values through a tree-type evidential diagram
without converting the diagram to a Markov tree. The fourth step is to propagate mvalues
through the Markov tree by vacuously extending and marginalizing the m-values
from all the nodes in the Markov tree to the node of interest. The basic approach to
vacuous extension and marginalization remains the same as described earlier through
endnotes 5 and 6.
Since the process of propagating m-values in a network becomes computationally quite
complex, several software packages have been developed to facilitate this process (see,
e.g., Shafer et al., 1988; Zarley & Shafer, 1988; and Saffiotti & Umkehrer, 1991). The
software developed by Zarley and Shafer (1988) and Saffiotti & Umkehrer (1991) require
programming the evidential diagram in LISP. Also, these software programs do not
provide friendly user interfaces. On the other hand the software, “Auditor Assistant,”
developed by Shafer et al. (1988) has a friendly user interface and does not require any
programming language to draw the evidential diagram. In fact, one can draw the evidential
diagram using the graphic capabilities of the software. The evidential diagram drawn by
using “Auditor Assistant” looks very similar to the one drawn by hand. The internal
engine of the program converts this diagram into a Markov tree and propagates m-values
once they are entered in the program. The program can be instructed to evaluate the
Figure 2: Evidential diagram as a network
X: (x, ~x)
Y: (y, ~y)
Z: (z, ~z)
Evidence for Z
Evidence for Y
Evidence for X
A ND
Evidence for X
and Y, both
network which then provides the aggregated m-values at each cluster of variables in the
network. One can then analyze how one variable impacts another variable by making
changes in the input m-values in the network.
Since the evidential diagram in our case is a simple tree, it is pretty straight forward to
propagate m-values through such a tree as described Appendix C. In order to analyze the
model in Figure 4, we develop a spreadsheet program that combines different m-values
at each variable and then propagates them through the tree to the desired variable. This
process is elaborated in Section VI.
Illustration of Evidential Reasoning:
Causal Map of IT Job Satisfaction
Job satisfaction of information technology (IT) workers has been the focus of several
information systems studies (e.g., Igbaria & Guimaraes, 1993; Gupta et al., 1992; Thatcher
et al., 2003). Organizations want to retain their best IT workers as long as they possess
the skills necessary to accomplish the job. However, there is growing concern that many
long term IT employees no longer fit the needs of their employers.
The general consensus from the research is that job satisfaction is negatively related to
turnover intention (e.g., Thatcher et al., 2003). In other words, workers who are highly
satisfied with their jobs are less likely to contemplate seeking other employment and
many unsatisfied workers enter the job market. In the current environment of radical role
changes (Darais et al., 2003) and selectivity in hiring, IT workers within firms are
experiencing anxiety and frustration, wondering what skills they will need to remain
marketable in the future. The current trend with offshoring many IT jobs has exacerbated
this problem for many workers. IT workers with traditionally secure positions are not
immune to the pressures of this dynamic job environment.
In the present study, the IT Professional Job Satisfaction Model was developed based
on 83 discovery interviews with IT workers in various job positions including systems
analysts, programmers, technical specialists, and systems project managers. Table 3
shows the demographics for the interview sample.
These workers were from eight different corporations in a variety of industries (e.g.,
banking and insurance, manufacturing, education, state and local government). They
voluntarily discussed their opinions on a number of job-related issues, generally
focusing on their feelings of uncertainty regarding their personal contributions and job
security (see the Interview Protocol in Appendix B). Interviews were generally 30 – 45
minutes in length and tape recorded, with the consent of the participant. Then, the
interviews were transcribed and the causal statements were highlighted and analyzed
according to the RCM technique described in Section II of this chapter. The causal map
(Figure 3) was created based on the concepts represented in the transcripts.
In analyzing the data, one clear finding is that most of the IT personnel interviewed had
difficulty describing how they fit within the corporate structure. They acknowledged that
their contributions were important, but they felt they were personally expendable.
Several persons similarly stated, “I’m just a cog in the wheel.” As many researchers and
practitioners have noted (e.g., Darais et al., 2003), in order to survive in the IT field,
workers must continue to retrain and learn new skills. Therefore, acknowledgement of the
need to change is depicted as the first node in the IT Professional Job Satisfaction Model
(see Figure 3, Item 1). The interviewees indicated that skills stagnation often threatened
job security. This realistic fear of job loss (Figure 3, Item 2) is a powerful motivator in
pursuing necessary training.
IT workers in the interviews discussed the importance of seeking out training opportunities
(Figure 3, Item 3), whether offered by the corporation as in-house training,
enrollment in formal college courses, or on-line, computer-aided learning. These courses
might entail attaining certification credentials, college credit, or practical experience.
According to a majority of interviewees, if training is available at the place of work, and
offered during work hours, employees are more likely to take advantage of the instruction.
In contrast, off-hours training, to be completed outside of work on one’s personal time,
was less attractive to these employees. However, there is no guarantee that participation
in training courses produces adequate knowledge for accomplishing new tasks.
Beyond merely gaining new knowledge and skills (Figure 3, Item 4), interviewees stressed
that they must also be able to practice and apply the new skills in a meaningful way (Figure
3, Item 5). In other words, they believe that their training must be utilized on work projects
in order for the new skills to become part of workers’ permanent skill sets. Unfortunately,
technical skills are often lost if they are not used soon after the course is completed
(Radding, 1997).
Some of the relevant elements of job satisfaction (Figure 3, Item 9) that emerged from this
study were perceived feedback from supervisors and co-workers (Figure 3, Item 6),
Table 3. Interview sample demographics
Demographic Mean (n=83) SD or Percent
Number of years experience
with current project
5.80 6.10
Tenure (# of years with the
organization)
10.77 8.61
Age (years) 41.25 9.16
Gender
Female
Male
35
48
42%
58%
Education:
High School
Associates Degree
BA/BS
MA/MS/MBA
Post-Graduate Degree
13
14
40
14
2
15.7%
16.9%
48.2%
16.8%
2.4%
participation in challenging projects (Figure 3, Item 7), and autonomy within the work
setting (Figure 3, Item 8). Many IT projects involve teams working together to accomplish
defined objectives. Direct feedback obtained from supervisors and co-workers (Figure
3, Item 6) increases job satisfaction because there is less ambiguity about perceived
performance. For instance, the interviewees stated that they like to receive continuous
feedback in order to determine whether they have adequately satisfied the user requirements
and specifications during systems development.
Next, challenging projects (Figure 3, Item 7) provide intrinsic motivation for IT workers.
Interviewees remarked that they were anxious to tackle difficult problems for the basic
joy of simply discovering new solutions. But, beyond the initial pleasure of design
development is the pride of successful implementation and user adoption of their creative
solutions. These accomplishments instill job satisfaction at a deep level for IT problemsolvers.
Figure 3. Information technology professional job satisfaction model
(2) Fear of Job Loss
(Job Security)
(3) Sign Up For
Training to Gain New
Skills
(4) Opportunity to
Gain New Skills
(1) Recognition of Tech.
& Bus. Role Change
(7) Challenging Work (Internal
Motivation)
(8) Autonomy of Work
(9) Job Satisfaction
(6) Feedback from
Superiors/Co-Workers
(5) Opportunity to
Use New Skills
Finally, the level of autonomy (Figure 3, Item 8) positively affects job satisfaction
because most IT employees prefer freedom and independence in determining relevant
job-related decisions (Ang & Slaughter, 2001; Hackman & Oldham, 1976). According to
the interviewees, they derive positive affect from exercising autonomy in project
completion, resulting in increased job satisfaction.
Table 4 shows evidence used to support the construct measures. For this study, evidence
was obtained from survey data. The survey was developed as an extension of a study
in which the RCM technique was used to develop a model of work identity for IT
professionals (Buche, 2003). Other possible examples of evidence would be additional
interviews, observation, evaluation of documentation, and reviewing physical artifacts.
Some of the elements could be gathered from supervisors and secondary sources,
triangulating the evidence to analyze the model and to predict job satisfaction of IT
professionals.
Table 4. Variables, symbols and respective sources of evidence
Variable
(from RCM)
Symbol Possible Values Evidence Source
(Survey Data)
Recognition of
Role Change
RR {yesRR, noRR}
E1
In my role I am most valued for my
technical abilities.
My business knowledge is my most
important contribution to the organization.
In my organization, I am perceived to be a
technical expert.
I could not be successful this job without
broad knowledge of the business domain.
Fear of Job Loss
(Job Security)
JT {yesJT, noJT}
E2.1
E2.2
Actual layoffs reported in the firm,
industry, media
Job security.
Sign Up For
Training
ST
{yesST, noST} E3 Availability of training to learn new skills.
Opportunity to
Gain New Skills
GS {yesGS, noGS} E4 Opportunities to learn new things from
my work.
Opportunity to
Use New Skills
US {yesUS, noUS} E5 Opportunities to apply new skills in my
work.
Feedback from
Superiors/Coworkers
FS {yesFS, noFS}
E6
My managers or co-workers often let me
know how well I’m doing on my job.
I’m frustrated by the fact that my
supervisor and co-workers almost never
give me any feedback about how well I
am doing my work.
My supervisor gives me specific inputs on
how well I am performing my
responsibilities.
Challenging
Work
CW {yesCW, noCW} E7 Stimulating and challenging work.
Autonomy of
Work
AW {yesAW, noAW}
E8
I have a lot of autonomy in my job. That,
is, I decide how to go about doing my
projects.
The job denies me any chance to use my
personal initiative or judgment in carrying
out the work.
My job gives me considerable opportunity
for independence and freedom in how I do
my work.