EFA test, the next step is the model testing process. This step
involves running a confirmatory analysis (EFA) test followed by a structural path testing.
7.5 Model Testing Procedures
Anderson & Gerbing (1988) classified the model testing
process into two steps: confirmatory factor analysis and
structural path model. In structural equation modeling
(SEM), the CFA tests are considered as the critical starting
(Hair et al., 2010). In this two-step method, a measurement
model is estimated and then tested for the full structure
model, as suggested by Townsend, Yeniyurt, Deligonul and
Cavusgil (2004), Zou and Cavusgil (2002).
7.5.1 Confirmatory Factor Analysis (CFA)
This section provides the key findings regarding the initial
measurement model fit. Using the results of the EFA stage,
the confirmatory factor analysis (CFA) measurement model
was developed and tested. The evaluation of the measurement model of CFA helps for a better understanding of how
good the measurement items reflect the latent variables. In
this study, the item loadings and fit-indices of all constructs
are measured and are summarized in the following paragraphs: The fit statistics of the constructs of a model indicate
a good fit to the data (Fındık & Özkan, 2010). Table 7.4
contains a summary of achieved fit indices for the overall
model.
Many researchers agree on the following indices that
should be reported for a good fit model (Fındık & Özkan,
2010):
• The primary fit indicator is the v
2 /df (chi-square/degrees
of freedom ratio). The fit statistics of all constructs show
a good fit to the data, where v
2 /df = 1.329, which does not
exceed the recommended threshold. The lesser value is
better, however, between 2 and 5. Therefore, the
researcher considered other important indexes (Blunch,
2013). These indices include the root-mean-square
residual (RMR) (Jöreskog & Sörbom, 1981), the
root-mean-square error of approximation (RMSEA)
(Steiger, 1990), the normed fit index (NFI) (Bentler and
Bonnett, 1980), and the comparative fit index
(CFI) (Bentler, 1990).
• Root mean square error of approximation (RMSEA)
indexes for the overall model are equal to 0.033.
The RMSEA value (0.33) meets the standards of <0.05.
The RMSEA value <0.05 indicates good fit; a value
<0.10 shows an acceptable fit and RMSEA >0.10 indicates a poor fit.
• CFI equals 0.979, which is above the recommended 0.90.
• Normed fit index (NFI) is 0.921, which is appropriate.
• The NFI value close to 0.95 reflects a good fit. NFI varies
from 0 (no fit) to 1 (perfect fit).
• Root mean square residual (RMR) of 0.035 is a good
fit because the lesser the RMR, the better the model, and
RMR of zero shows a perfect fit.
The summary of path coefficients, regression weights,
critical ratio (CR), and significance (P-values) for the constructs of the overall CFA model is shown in Table 7.5.
Reliability and validity of CFA model: One of the
advantages of CFA is that while performing CFA testing, the
reliability and validity of the variable can also be tested
(Byrne, 2010). The higher is the reliability, the lower will be
the measurement errors (Hair et al., 2010). The convergent
validity is the extent to which the items within a construct
are correlated. It indicates how well the items explain the
factor. The convergent validity is evaluated by testing the
modification coefficients, factor loadings, and variances. The
discriminant validity is the extent to which the factors or
constructs of a model are unique (Bagozzi &Yi, 1991;
Hussain, Khan, & Al-Aomar, 2016). Using standardized
regression weights and SPSS/AMOS’s correlations into
validity testing tools within the ‘Stats Tools Package’
(Gaskin, 2012), the validity and reliability testing results
were calculated.
• Average variance extracted (AVE): This is a measure
of convergent validity and should be above 0.5 (Hair
et al., 2010). All AVE is above 0.5 except H-construct
value, which is 0.305. The items belonging to the factor
itself should better explain it than the items belonging to
other factors (Straub, Boudreau & Gefen, 2004). It should
be higher than MSV and ASV.
• Composite reliability (CR): It measures the reliability of
the factors and should ideally be above 0.75. All CR
values are above 0.75 except H-construct value.
• Average shared squared variance (ASV): ASV is
similar to MSV, but takes the average of the squared
Table 7.4 Achieved fit indices
for all constructs
Achieved fit indices for the overall model
X2/df
GFI
AGFI
NFI
CFI
TLI
PCLOSE
RMSEA
RMR
1.329
0.905
0.883
0.921
0.979
0.975
1.000
0.033
0.035
7.4 Overall Exploratory Factor Analysis
65
involves running a confirmatory analysis (EFA) test followed by a structural path testing.
7.5 Model Testing Procedures
Anderson & Gerbing (1988) classified the model testing
process into two steps: confirmatory factor analysis and
structural path model. In structural equation modeling
(SEM), the CFA tests are considered as the critical starting
(Hair et al., 2010). In this two-step method, a measurement
model is estimated and then tested for the full structure
model, as suggested by Townsend, Yeniyurt, Deligonul and
Cavusgil (2004), Zou and Cavusgil (2002).
7.5.1 Confirmatory Factor Analysis (CFA)
This section provides the key findings regarding the initial
measurement model fit. Using the results of the EFA stage,
the confirmatory factor analysis (CFA) measurement model
was developed and tested. The evaluation of the measurement model of CFA helps for a better understanding of how
good the measurement items reflect the latent variables. In
this study, the item loadings and fit-indices of all constructs
are measured and are summarized in the following paragraphs: The fit statistics of the constructs of a model indicate
a good fit to the data (Fındık & Özkan, 2010). Table 7.4
contains a summary of achieved fit indices for the overall
model.
Many researchers agree on the following indices that
should be reported for a good fit model (Fındık & Özkan,
2010):
• The primary fit indicator is the v
2 /df (chi-square/degrees
of freedom ratio). The fit statistics of all constructs show
a good fit to the data, where v
2 /df = 1.329, which does not
exceed the recommended threshold. The lesser value is
better, however, between 2 and 5. Therefore, the
researcher considered other important indexes (Blunch,
2013). These indices include the root-mean-square
residual (RMR) (Jöreskog & Sörbom, 1981), the
root-mean-square error of approximation (RMSEA)
(Steiger, 1990), the normed fit index (NFI) (Bentler and
Bonnett, 1980), and the comparative fit index
(CFI) (Bentler, 1990).
• Root mean square error of approximation (RMSEA)
indexes for the overall model are equal to 0.033.
The RMSEA value (0.33) meets the standards of <0.05.
The RMSEA value <0.05 indicates good fit; a value
<0.10 shows an acceptable fit and RMSEA >0.10 indicates a poor fit.
• CFI equals 0.979, which is above the recommended 0.90.
• Normed fit index (NFI) is 0.921, which is appropriate.
• The NFI value close to 0.95 reflects a good fit. NFI varies
from 0 (no fit) to 1 (perfect fit).
• Root mean square residual (RMR) of 0.035 is a good
fit because the lesser the RMR, the better the model, and
RMR of zero shows a perfect fit.
The summary of path coefficients, regression weights,
critical ratio (CR), and significance (P-values) for the constructs of the overall CFA model is shown in Table 7.5.
Reliability and validity of CFA model: One of the
advantages of CFA is that while performing CFA testing, the
reliability and validity of the variable can also be tested
(Byrne, 2010). The higher is the reliability, the lower will be
the measurement errors (Hair et al., 2010). The convergent
validity is the extent to which the items within a construct
are correlated. It indicates how well the items explain the
factor. The convergent validity is evaluated by testing the
modification coefficients, factor loadings, and variances. The
discriminant validity is the extent to which the factors or
constructs of a model are unique (Bagozzi &Yi, 1991;
Hussain, Khan, & Al-Aomar, 2016). Using standardized
regression weights and SPSS/AMOS’s correlations into
validity testing tools within the ‘Stats Tools Package’
(Gaskin, 2012), the validity and reliability testing results
were calculated.
• Average variance extracted (AVE): This is a measure
of convergent validity and should be above 0.5 (Hair
et al., 2010). All AVE is above 0.5 except H-construct
value, which is 0.305. The items belonging to the factor
itself should better explain it than the items belonging to
other factors (Straub, Boudreau & Gefen, 2004). It should
be higher than MSV and ASV.
• Composite reliability (CR): It measures the reliability of
the factors and should ideally be above 0.75. All CR
values are above 0.75 except H-construct value.
• Average shared squared variance (ASV): ASV is
similar to MSV, but takes the average of the squared
Table 7.4 Achieved fit indices
for all constructs
Achieved fit indices for the overall model
X2/df
GFI
AGFI
NFI
CFI
TLI
PCLOSE
RMSEA
RMR
1.329
0.905
0.883
0.921
0.979
0.975
1.000
0.033
0.035
7.4 Overall Exploratory Factor Analysis
65