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


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


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


10.77 8.61

Age (years) 41.25 9.16









High School

Associates Degree



Post-Graduate Degree











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


(4) Opportunity to

Gain New Skills

(1) Recognition of Tech.

& Bus. Role Change

(7) Challenging Work (Internal


(8) Autonomy of Work

(9) Job Satisfaction

(6) Feedback from


(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


Table 4. Variables, symbols and respective sources of evidence


(from RCM)

Symbol Possible Values Evidence Source

(Survey Data)

Recognition of

Role Change

RR {yesRR, noRR}


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}



Actual layoffs reported in the firm,

industry, media

Job security.

Sign Up For



{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


Feedback from


FS {yesFS, noFS}


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




CW {yesCW, noCW} E7 Stimulating and challenging work.

Autonomy of


AW {yesAW, noAW}


I have a lot of autonomy in my job. That,

is, I decide how to go about doing my


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.