CHAPTER 3 RESEARCH METHODOLOGY - …shodhganga.inflibnet.ac.in › bitstream › 10603 › 41930 › 8 › 08...39 CHAPTER 3 RESEARCH METHODOLOGY 3.1 GENERAL This chapter addresses

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CHAPTER 3

RESEARCH METHODOLOGY

3.1 GENERAL

This chapter addresses the methodology adopted for capturing the

data, needed to achieve the aim and objectives of the research. It is organised

in sections covering: the formulation of the objectives of the study,

identification of the resource constraint factors and questionnaire design, data

collection using the questionnaire survey, data analysis by the descriptive

statistical analysis, identification of critical factors using Relative Importance

Index Method (RII), grouping of factors (factor reduction) using the factor

analysis test, selection of the final critical factors, development of the time

overrun model and its validation, scenario analysis, and findings and

conclusion.

3.2 STUDY METHODOLOGY

The objective of the present research is to study the influences of the resource constraints on the time overrun of construction projects. An extensive literature review has been carried out, to identify the factors influencing the time overrun of construction projects. A questionnaire was developed considering the factors influencing the time overrun of construction projects in India. Before distributing the questionnaire, a pilot study was conducted. The basic purpose of the pilot study was to verify the completeness of the questionnaire in capturing the factors relevant for India. The questionnaire was distributed among construction professionals, and the

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data was collected. The data collected was analysed, using statistical methods, such as the descriptive statistics analysis, relative importance index analysis, Spearman rank order correlation test and factor analysis. Using the factor reduction technique, five factors were extracted out of the thirty three resource constraint factors originally considered. After the factor reduction, an equation for estimating the time overrun of construction projects was developed using structural equation modeling method. A scenario analysis was conducted, and finally the findings and conclusions are presented.

The flow chart of the research methodology is presented in

Figure 3.1.

Figure 3.1 Research methodology

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3.2.1 Concerning Objective One: (To Identify the Factors Affecting

the Time Overrun of Construction Projects)

The literature about time overrun was reviewed (Frimpong et al

2003; Koushki et al 2005; Ogunsemi & Jagboro 2006; Fong et al 2006; Lo et al

2006; Assaf & AL-Hejji 2006; Sambasivan & Soon 2007; Alghbari et al 2007) to

identify the factors influencing the time overrun of construction projects. In

addition, there are other local factors that have been added, as recommended

by local experts.

33 factors influencing the time overrun of construction projects are

selected. These factors are grouped under four heads, namely, man power,

material, equipment and finance. Each factor is given a label. Manpower is

represented by MP, material by MA, equipment by EQ and finance by FI. Out

of the thirty three factors considered, 11 factors are man power related, 10

factors are material related, 7 factors are equipment related and 5 factors are

finance related. The factors which are considered in the questionnaire are

summarized and presented in Table 3.1.

Table 3.1 List of factors identified, grouped under four heads

Group Label of

each factor

Factors

Man Power

MP 01 Shortage of labour MP 02 Lack of skilled labour MP 03 Migrant labour MP 04 Labour injuries, disputes and strikes MP 05 Unqualified work force team MP 06 Personal conflicts among labour MP 07 Obtaining permits for migrant labour MP 08 Motivation MP 09 Communication MP 10 Mobilization MP 11 Absenteeism of labour

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Table 3.1 (Continued)

Group Label of

each factor

Factors

Equipment

EQ 01 Availability of equipment EQ 02 Complication of advanced technology equipment EQ 03 Transportation of equipment EQ 04 Idle time of equipment EQ 05 Complication of hire EQ 06 Disruption of accessories EQ 07 Poor maintenance of equipment

Materials

MA 01 Shortage in construction materials MA 02 Materials selection and changes in types and

specifications during construction MA 03 Slow delivery of materials MA 04 Poor quality of materials MA 05 Damage of materials in storage MA 06 Damage of sorted materials while they are needed

urgently MA 07 Poor procurement of materials MA 08 Proportion of offsite prefabrication MA 09 Imported, Ordered materials and plant items MA 10 Manufacturing difficulties of special materials

Finance

FI 01 Cash Flow (Inflow & Outflow) FI 02 Slab of payment during construction FI 03 Financing by contractor during construction FI 04 Financing between the owner and contractor FI 05 Unavailability of financial incentive

3.2.2 Concerning Objective Two (To , Consultants and erceptions of the Relative Importance of the Time Overrun in Construction Projects)

A structured questionnaire survey approach is considered to study the impact of various attributes and factors influencing time overrun. In addition, the questionnaire can assist to study the attitude of owners , consultants and contractors towards the factors that affect the time overrun in the construction industry.

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The relative importance index method (RII) is used here to

determine the owners , consultants and contractors perceptions of the

relative importance of the factors influencing time overrun in Indian

construction projects. The relative importance index is computed, as

presented in Section 3.4.1.

3.2.3 Concerning objective three (To identify the most significant

factors causing time overrun of construction projects)

The relative importance index method (RII) is also used to

determine the most significant factors influencing the time overrun of

construction projects in India.

The factor analysis is employed to establish which of the variables

could be the measuring aspects of the same underlying dimensions. Based on

the factor analysis, the thirty three factors identified as the most significant

factors influencing the time overrun of construction projects in India are

clustered under five components, and the details regarding the factor analysis

are presented in Section 3.5.

3.2.4 Concerning Objective Four (To Evaluate the Degree of

Agreement/Disagreement between , and

the Ranking of the Factors causing

Time Overrun of Construction Projects)

The degree of agreement between parties regarding the ranking of

factors is determined, according to the Spearman rank correlation

Coefficient. The degree of agreement is determined, as presented in Section

3.4.3.

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3.2.5 Concerning Objective Five (To Test the Hypothesis to Verify

the Association between the Ranking of the ,

and

Overrun)

To test the hypothesis that there is no significant difference of

opinion between the three parties, regarding factors influencing time overrun.

The Spearman rank correlation coefficient is used according to two

hypotheses. This hypotheses are (Sambasivan & Soon 2007):

Null Hypothesis: H0: There is insignificant degree of agreement

among the owners, contractors and consultants.

Alternative Hypothesis: H1: There is significant degree of

agreement among the owners, contractors and consultants.

3.2.6 Concerning Objective Six (To Develop a Model to Depict the

Relationship between Resource Constraints and Time Overrun)

Structural Equation modeling (SEM) is adopted to analyse the

factors influencing the time overrun of construction projects. The SEM

method is suitable for exploring relationships among the variables. In this

study, a component based analysis is used, as it is more advisable when the

causal relation (Hair et al 2011) is studied. A model is developed to depict the

relationship between the influential resource constraint factors and the time

overrun. A case study for the validation of the proposed model is presented in

Section 6.9.

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3.2.7 Concerning Objective Seven (To Formulate the

Recommendations to Reduce the Time Overrun of

Construction Projects so as to Improve the Performance of

Construction Projects)

The practices concerning the time overrun such as time, cost,

project owner satisfaction and the safety checklists are analyzed, in order to

know the main practical problems of projects time overrun in India and, then

to formulate the recommendations to reduce the time overrun of construction

projects in India.

3.3 DATA COLLECTION

3.3.1 Questionnaire Design

A questionnaire was developed to assess the perception of clients,

consultants, and contractors on the relative importance of factors influencing

the time overrun of construction projects in India. The questionnaire was

divided into two parts. The first part consisted of general information about

the respondent. The second part of the questionnaire focused on the resource

constraint factors, causing the time overrun of construction projects in India.

3.3.2 Data Measurement

In order to be able to select the appropriate method of analysis, the

level of measurement must be understood. For each type of measurement,

there is/are an appropriate method/s that can be applied, and not others. In this

research, ordinal scales were used. The ordinal scale, as shown in Table 3.5, is

a ranking or a rating scale, that normally uses integers in the ascending or

descending order. The numbers assigned as important (1, 2, 3, 4, 5) do not

indicate that the interval between scales are equal, nor do they indicate

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absolute quantities. They are merely numerical labels. Based on the Likert

scale, we have the following Table 3.2 (Iyer and Jha 2005)

Table 3.2 Ordinal scale used for data measurement

Item Very low low Moderate High Very high

Scale 1 2 3 4 5

3.3.3 Pilot Study

. The objective of the pilot study is to verify the completeness of

the questionnaire. Before distributing the questionnaire, a pilot study was

conducted on a limited scale. All the respondents agreed, that the

questionnaire was sufficient to capture the causes of time overrun of

construction projects. Based on this, the questionnaire was finalized

3.3.4 Sample Size and Sampling Technique

The sampling method used in this study was convenience and

snowball sampling. This sampling comes under the class of non-probability

sampling techniques. The sample elements are identified by friends and

through referral networks. This method of sampling is preferred, when it is

difficult to get response from sample population selected at random (Sekaran

2000).

Commonly, the calculated sample size is increased by 30%-40% to

compensate for no response, therefore, the total numbers of questionnaires

were randomly distributed in Indian construction firms.

The survey was self administered, and the questionnaire was

distributed to 463 construction professionals from various construction

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organizations in India. Before handing over the questionnaires, all the

questions were explained to the respondents, so that they could fill the

questionnaire easily and properly. The responses were collected and analyzed.

Out of 463 copies of the questionnaire distributed to respondents 155 were

retrieved and analyzed.

3.3.5 Descriptive Statistics

The questionnaire was distributed to 463 construction

professionals, out of which 155 responses were received and thus, the

response rate of 33 details of the samples,

like gender, designation, working experience, types of organization, project

annual turnover and types of projects are explained using descriptive statistics

in Chapter 4.

3.4 STATISTICAL METHODS OF ANALYSIS

The statistical methods of analysis employed in this study other

than descriptive statistics, are the relative importance index analysis,

Spearman rank order correlation test, factor analysis, and multi - variate

analysis.

3.4.1 Relative Importance Index (RII) Method

The relative importance index method is used to determine the

relative importance of the various causes of time overrun. The same method

was adopted in this study within various groups (i.e. clients , consultants or

contractors ). The five-point scale ranging from 1 (not important) to 5

(extremely important) was adopted, and transformed to relative importance

indices (RII) for each factor as follows:

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1<Index <0

NA

WRII

N

1ii

(3.1)

where Wi is the weight given to each factor by the respondents and ranges

from 1 to 5, A is the highest weight equal to 5, and N is the total number of

respondents.

The RII was used to rank (R) the different causes. These rankings

made it possible to cross-compare the relative importance of the factors as

perceived by the three groups of respondents (i.e. clients, consultants and

RII perceived by all the respondents was

used to assess the general and overall rankings in order to give an overall

picture of the causes of time overrun in the Indian construction industry.

These rankings made it possible to cross compare the relative importance of

the items as perceived by the three groups of respondents. The weighted

average for each item for the three groups of respondents was determined and

ranks (R) were assigned to each item representing the perception of the three

groups (Iyer and Jha, 2005).

3.4.2 Reliability

In addition, the internal consistency of the data is required.

reliability.

3.4.3 Validity Test

To ensure the validity of the questionnaire, two statistical tests were

applied. The first test is the Criterion-related validity test (Spearman test),

which measures the correlation coefficient between each item in one Group

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and the whole Group. To test the criterion related validity test, the correlation

coefficient for each item of the group factors and the total of the field, is

achieved. The significance (p-values) are less than 0.01, and the correlation

; therefore, it can be said

that the paragraphs of each field are consistent and valid to measure what it

was set for. The second test is the structure validity test (Spearman test) that

was used to test the validity of the questionnaire structure, by testing the

validity of each field and the validity of the whole questionnaire. It measures

the correlation coefficient between one field and all the fields of the

questionnaire that have the same level of a similar scale.

3.5 FACTOR ANALYSIS

In the absence of any standard lists of selection factors, there was a

considerable risk of the analysis of the responses yielding diverse results.

Thus, in establishing the list of factors, it was considered important to ensure

that the factors are of adequate relevance, and were also independent. The

response were therefore further analysed, by grouping them using the factor

analysis.

The appropriateness of employing the factor analysis was first

confirmed by a number of tests including Kaiser-Meyer-Olkin (KMO), the

measure of sampling adequacy and Bartlett test of sphericity. The principal

component analysis was then employed to extract the group factors with

eigenvalues greater than 1, suppressing all other factors with eigenvalues less

than 1,

clarify the factor pattern so as to ensure that each variable loads high on one

group factor, and very minimal on all other group factors, the variables were

the varimax orthogonal rotation method.

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3.5.1 Kaiser Meyer Olkin (KMO) Test and Bartlett's Test of

Sphericity

The KMO statistic varies between 0 and 1. A value of 0 indicates

that the sum of partial correlations is large, relative to the sum of correlations,

indicating diffusion in the pattern of correlations (hence, the factor analysis is

likely to be inappropriate). A value close to 1 indicates that patterns of

correlations are relatively compact, and so, the factor analysis should yield

distinct and reliable factors. Kaiser (1974) recommended values greater than

0.5 as acceptable. Furthermore, values between 0.5 and 0.7 are medium,

values between 0.7 and 0.8 are good, values between 0.8 and 0.9 are very

good, and values greater than 0.9 are excellent. For these data, the values are

greater than 0.9, which falls in the range of being excellent; so it should be

clear that the factor analysis is appropriate for these data.

correlation matrix is an identity matrix. For the factor analysis to work, it

needs some relationship between the variables and if the R- matrix, were an

identity matrix then all correlation coefficients would be zero. So this test has

to be significant (Significance value less than 0.05). A significant test

identifies that the R-matrix is not an identity matrix; therefore, there are some

relations <

0.001), and the factor analysis is appropriate.

3.5.2 Communalities

Communalities indicate the amount of variance in each variable

that is accounted for. The initial communalities are estimates of the variance

in each variable accounted for by all the components or factors. Extraction

communalities are estimates of the variance in each variable, accounted for by

the factors (or components) in the factor solution. Small values (< 0.4)

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indicate variables that do not fit well with the factor solution, and should

possibly be dropped from the analysis.

3.5.3 Extraction of Factors

The total number of common factors that can be extracted from any

factor analysis is equal to or less than the number of variables involved. The

important factors are those whose Eigen values are greater than or equal to 1,

because an Eigen value is a measure of how a standard variable contributes to

the principal components. A component with an Eigen value of less than 1 is

considered less important than such an observed variable, and can be ignored

(Kim and Mueller 1994).

3.5.4 Rotated Component Matrix

Rotation is a method used to simplify the interpretation of a factor

analysis. The rotated component matrix is a matrix of the loading for each

variable onto each factor.

3.6 DEVELOPMENT OF MODEL FOR TIME OVERRUN

After the factor analysis is carried out the structural equation

modelling is done for time overrun. Hence, the SEM model is the prediction

of the complicated process that has been attempted to be modelled. SEM is a

collection of statistical techniques that allows a set of relations between one or

more Independent Variables (IVs), either continuous or discrete, and one or

more Dependent Variables (DVs), either continuous or discrete, to be

examined. Both IVs and DVs can be either measured variables (directly

observed), or latent variables (unobserved, not directly observed). SEM is

also referred to as causal modeling, causal analysis, simultaneous equation

modeling, and analysis of covariance structures, path analysis, or

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confirmatory factor analysis (Kline 1998; Mueller 1996). Structural Equation

Modeling (SEM) is superior to other methods, since it combines a

measurement model (confirmatory factor analysis), and a structural model

(regression or path analysis) in a single statistical test. It recognizes the

measurement error, and also offers an alternative method for measuring the

prime variables of interest through the inclusions of the latent variables and

surrogate variables. The major aim of these models was to fit and cover the

relevant research characteristics such as time overrun, in the resource

schedule performance measures and indicators in this research.

3.6.1 Limitations of the Structural Equation Model

The models are constructed for fitting the sample covariance

instead of the sample values themselves. This leads to the elimination of

much valuable information about the data, such as the means, skewness and

kurtosis. Yet, sample covariance is only one of the many characteristics of the

data, and is not sufficient enough to understand the total structure of the data.

Since the results of SEM are subject to sampling or selection

effects, with respect to at least three aspects of a study, viz, individuals,

measures, and occasions, the generalizability of the findings is also a

limitation of SEM. Researchers should specify the population of interest in

their hypothesis, and acknowledge that the conclusions derived from the

model cannot be generalized, except for that population. The indicators which

represent the latent variables should be chosen very carefully, because the

nature of the construct can shift with the choice of indicators, which in turn,

can influence the results and their interpretation. The findings can show

changes over time; therefore, the effect of one variable on another cannot be

identified as a single true effect, unless the variables do not change over any

time period of interest.

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Another important limitation is the necessity of large sample sizes,

in order to maintain power and obtain stable parameter estimates and standard

errors. Some methods are developed for parameter estimation of small sample

size, after all estimates settle down at the smallest sample sizes, whereas

standard errors are determined still according to a larger number of samples

(Bentler 2006). A chi-square test which is the most common fit measure is

only recommended with moderate samples; in addition, coefficient alpha, the

most common measure of reliability, has several limitations; for instance,

coefficient alpha wrongly assumes that all items contribute equally to

reliability.

3.6.2 Model Specification

Model specification involves using all of the available relevant

theory, research, and information, and developing a theoretical model. Thus,

prior to any data collection or analysis, the researcher specifies a specific

model that should be confirmed with the variance and covariance data. In

other words, the available information is used to decide which variables to

include in the theoretical model, and how these variables are related

(Schumacker & Lomax 2004).

3.6.3 Model Identification

Identification refers to the amount of information available in the

covariance matrix, relative to the number of parameters that a researcher

extracts from these data.

The parameters in a model can be specified either as free, fixed, or

constraint. A free parameter is one that is unknown, and therefore needs to be

estimated. A fixed parameter is one that is not free, but is fixed to a specified

value, typically 0 or 1. A constraint parameter is one that is unknown, but is

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constrained to equal one or other parameters (Schumacker & Lomax 2004). In

addition, model identification depends on the designation of parameters as

fixed, free, or constraint, due to its effect on the number of parameters that

require to be identified.

The aim of SEM is to specify a model as over identified; therefore,

the model has positive degrees of freedom that allow the testing/confirming

the validity of the model.

3.6.4 Model Estimation

observed population covariance matrix, sample covariance matrix (S), with

the residual matrix (the difference between

equal zero, 2 = 0; it means that it is a perfect model fit to the data. There

are different methods available for the estimation of the model; however, the

widely used models are the maximum likelihood (ML), generalized least

squares (GLS), least squares (LS), asymptotic distribution free (ADF), and

robust.

Maximum Likelihood (ML): is the most popular method among all

estimation methods, because it provides unbiased, consistent estimates of

population parameters; in addition, admissible model solutions and stable

parameter estimates can be obtained, in the case of small sample sizes. ML

methods are scale free, which means that the output of this method obtained

by the transformation of the scale of one or more of the observed variables,

and the output of the untransformed output are related (Schumacker & Lomax

2004). However, ML assumes multivariate normality, and non-normality in

the data can potentially lead to seriously misleading results. Nonetheless, ML

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is also determined as quite robust against the mild violation of the normality

assumption (Bentler 1995).

Generalized Least Squares (GLS): GLS is an adaptation of least squares to

minimize the sum of the differences between the observed and predicted

covariance. It is probably the second-most common estimation method after

ML. GLS assumes multivariate normality like ML. The GLS estimation

process requires much less computation than ML; however, this should not be

accepted as an advantage, due to the powerful desktop computers with well-

constructed SEM programs. Olsson et al (2000) evaluated the parameter

estimates and overall fit of ML and GLS under different model conditions,

including non-normality, and concluded that ML could provide more realistic

indices of the overall fit and less biased parameter estimates for paths, than

the GLS under different misspecifications. In addition, ML performs better

for small samples; therefore, ML should generally be preferred for small

samples.

Asymptotic Distribution Free (ADF): Unlike the other methods, this

method does not require the multivariate normality assumption.

Unfortunately, this method is data-intensive; in other words, this methodology

requires really large sample sizes, to obtain model convergence and stable

parameter estimates. However, Yuan & Bentler (1997) found out that ML is

much less biased than ADF estimators for all distributions and sample sizes,

but when the sample size is large, ADF can compete with ML.

Robust: The strength of this method is that normality is not a requirement. In

this method, the estimates provided from the methods are accepted, but the

chi-square and standard errors are corrected to the non-normality situation.

The chi-square test is corrected in the conceptual way described by

Bentler (1996). Also, robust standard errors developed by Bentler (1996) are

provided as an output of the robust analysis, and they are correct in large

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samples, even if the distributional assumption regarding the variables is

wrong (Bentler 2006). Although these robust statistics are computationally

demanding, they have been shown to perform better than the uncorrected

statistics, where the assumption of normality fails to hold and performs better

than the ADF. One important caveat regarding the use of robust statistics is

that, they can be computed only from raw data (Byrne 2006).

3.6.5 Model Testing

After the determination of the parameter estimates for a specified

SEM model, the model should be examined to see how well the data fit the

data; in other words, how well the theoretical model is supported by the

obtained sample data should be determined. Different fit indices are

developed for that purpose, namely, the chi-square, Normed Fit Indices

(NFI), Non-Normed Fit Indices (NNFI), Comparative Fit Indices (CFI),

Bollen Fit Indices (IFI), McDonald fit indices (MFI), Goodness of fit indices

(GFI) and Root Mean-Square Error of Approximation (RMSEA).

3.6.6 Model Fit Indices

In order to evaluate the model fit, model fit indices are used. There

are dozens of model fit indices described in the SEM literature, and new

indices are being developed all the time. It is up to the properties of the data

to decide, as to which particular indices and which values to report (Kenny &

McCoach 2003; Marsh et al 2004). Described next is a minimal set of fit

indices that is going to be reported and interpreted, when reporting the results

of SEM analysis of this research. The fit indices that are least affected by the

sample size were selected. These statistics include (1) Chi-square; (2) the root

mean square error of approximation (RMSEA; Steiger 1990) with its 90%

confidence level; (3) Comparative fit index (CFI; Bentler 1990); (4) Non-

Normed Fit Index (NNFI); and (5) Bollen Fit Indices (IFI).

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3.6.7 2)

The value of 2 for a just identified model generally equals zero and

has no degrees of freedom. If 2= 0, the model perfectly fits the data. As the

value of 2 increases, the fit of an over identified model becomes increasingly

worse. The only parameter of a central Chi-square distribution is its degrees

of freedom (Kline 2005).

3.6.8 Normed Fit Indices

The NFI indicate the proportion in the improvement of the overall

fit of the developed model to a null model. The NFI range from zero to one

with higher values indicating a better fit; however, in small samples, it may

not reach 1.0 when the model is correct (Bentler 2006). A rule of thumb for

this index is that, 0.95 is indicative of a good fit relative to the baseline model,

while values greater than 0.90 may be interpreted as an acceptable fit

(Schermelleh-Engel et al 2003). The most important disadvantage of this

index is that, it is affected by sample size.

3.6.9 Non-Normed Fit Indices

NNFI is also known as Tucker-Lewis index (Bentler 2006). NNFI

generally ranges from zero to one, with higher values indicating a better fit;

but, since this index is not normed, values can fall outside the range 0-1. This

index is also affected by the complexity of the model; in other words, by

increasing the complexity of the model, the values of this index decrease. The

most important advantage of this index is that, it is one of the fit indices less

affected by the sample size (Bentler 1990).

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3.6.10 Comparative Fit Indices

The CFI is one of a class of fit statistics, known as incremental or

comparative fit indices, which are among the most widely used in SEM. All

these indices assess the relative improvement in the

model compared with a baseline model. It is developed by Bentler (1990) for

avoiding the underestimation of fit in small samples. CFI is derived from the

comparison between the hypothesized and the independent models. The CFI

ranges from zero to one, with higher values indicating a better fit. A rule of

thumb for this index is that 0.95 is indicative of a good fit, relative to the

independence model, while values greater than 0.90 may be interpreted as an

acceptable fit (Byrne 2006).

3.6.11 Bollen Fit Indices

It is developed to address the issues related to parsimony and

sample size. IFI is computed basically by using the same procedure as that of

NFI, except that degrees of freedom are considered (Byrne 2006). A rule of

thumb for this index is that 0.95 is indicative of a good fit relative to the

independence model, while values greater than 0.90 may be interpreted as an

acceptable fit (Meehan and Stuart 2007).

3.6.12 Goodness of Fit Indices (GFI):

GFI is the measure of how much better the model fits, as compared

to the null model (Schermelleh-Engel et al 2003). The GFI ranges from zero

to one with higher values indicating a better fit, but in some cases the values

of GFI can fall outside the range 0-1. A rule of thumb for this index is that

0.95 is indicative of a good fit relative to baseline model, while values greater

59

than 0.90 may be interpreted as an acceptable fit (Schermelleh- Engel et al

2003).

3.6.13 Root Mean-Square Error of Approximation

The RMSEA is a parsimony-adjusted index, in that its formula

includes a built-in correction for model complexity. The RMSEA measures

the error of approximation. The value of zero indicates the best fit, and higher

values indicate a worse fit. The RMSEA estimates the amount of error of

approximation per model degree of freedom, and takes the sample size into

a close approximate

fit, values between 0.05 and 0.08 suggest reasonable error of approximation,

a poor fit (Browne & Cudeck 1993); this can be

provided by utilizing interpretative guidelines (Hu & Bentler 1999; Hu &

Bentler 1998); finally and most importantly, a confidence level is obtained as

an output. RMSEA values smaller than 0.05 indicate a good fit, values

between 0.05 and 0.08 indicate an adequate fit, and values between 0.08 and

0.10 indicate a mediocre fit, whereas values larger than 0.10 indicate that the

model should not be accepted (Schermelleh-Engel et al 2003). However,

when the sample size is small, this index tends to over-reject the true

population models (Hu & Bentler 1999).

3.6.14 Normality

Most of the estimation methods assume normal distributions for

continuous variables. Non-normal data can occur because of the scaling of

variables or limited sampling of subjects, and the normality can be on two

levels; univariate and multivariate normality. Univariate normality concerns

the distribution of the individual variables. The normality of a variable can be

evaluated according to the standard error of skewness and kurtosis. The

standard error of skewness is calculated by the ratio of skewness to its

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standard error; values of standard error of skewness between -2 and 2 indicate

the normality of the variable. A large positive value of skewness indicates a

long right tail; an extreme negative.

3.7 SCENARIO ANALYSIS

The s

is to changes in the value of the parameters of the model and to changes in the

structure of the model. Scenario analyses focus on the variation impact between

two parameters. Parameter sensitivity is usually performed as a series of tests in

which the modeler sets different parameter values, to see how a change in the

parameter causes a change in the dynamic behavior of the time overrun. By

showing how the model behavior responds to changes in parameter values, the

scenario analysis is a useful tool in model building as well as in model

evaluation.

3.8 SUMMARY

An outline of the research methodology adopted for carrying out this

research is presented in this chapter.