Chapter 4: DATA ANALYSIS AND FINDINGS
4.4. Confirmatory Factor Analysis (CFA)
Hair et al, (2010) state “CFA is a way of testing how well measured variables represent a smaller number of constructs. CFA is applied to test the extent to which a researcher’s a – priori, theoretical pattern of factor loadings on pre-specified construct represents the actual data; CFA statistics tell us how well our theoretical specification of the factors matches reality (the actual data). In a sense, CFA is a tool that enables us to either “confirm” or
“reject” our preconceived theory”.
According to Hair, measurement model validity depends on establishing acceptable levels of goodness – of – fit for the measurement model and finding specific evidence of construct validity. In model fit testing, some researchers use indices such as Chi – square ( 2 ) index (CMIN), df (degree of freedom), statistical significance of chi – square(p). A p – value for the chi – square test (< 0.05) indicates that the two covariance matrices are statistically different and indicates a problem with the fit. Thus, to support the idea that a proposed theory fits reality, some researchers look for a small chi – square values and corresponding large p – value (p > 0.05) (Hair et al 2010).
However, there are some problems with the chi – square test. The 2 value increases as sample size increases. Hair et al (2010) state “typical models today are more complex and have a sample size that make the chi – square significance test less useful as a Good – of – fit measure that always separates good from poor models” and they advice that no matter what the chi – square result, the researcher should always complement it with other GOF indices. Consequently, this study use Chi – square/df index (CMIN/df), GFI – Goodness of Fit index; CFI – Comparative Fit Index, TLI – Tucker &
Lewis Index and RMSEA – Root Mean Square Error Approximation. If a model gets GFI, TLI, CFI >= 0.9 (Bentler and Bonett, 1980); CMIN/df <= 2 (Nguyen and Nguyen 2008); in some cases - CMIN/df <=3 (Carmines and
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McIver 1981 cited from Netemeyer et al 1991); RMSEA <=0.08 (Steiger 1990, Nguyen and Nguyen 2008) then model can be considered as a good – fit – model.
In construct validity testing, researchers usually use some evaluations such as (1a) Composite Reliability; (1b) Extracted Variance; (1c) Cronbach’s Alpha coefficient; (2) Unidimensionality; (3) Convergent Validity; (4) Discriminant Validity and (5) Nomological Validity. Joreskog 1971’s and Fornell and Larcker 1981’s formula calculate Composite Reliability (ρ c ) and Extracted Variance (ρ vc ) (quoted in Nguyen and Nguyen 2008):
Where:
i : standardized regression weights of “i” variable.
ρ c ; ρ vc should be greater than 0.5 (Hair et al 2010; Nguyen and Nguyen 2008).
For assessing the Unidimensionality, Steenkamp and Van Trijp (1991) advised that as the goodness of fit is good then the constructs are uni - dimensional except the cases of correlation between errors (Nguyen and Nguyen 2008, p 125). The scales get the Convergent Validity if it has the standardized loading estimate greater than 0.5 (p<5%) (Gerbing and Anderson 1988 cited from Nguyen and Nguyen 2008). According to Hair, Discriminant Validity is the extent to which a construct is truly distinct from other constructs. The correlation between any two constructs can be specified (fixed) as equal to one. If the fit of the two construct model is significantly different from that of one-construct model, then discriminant validity is supported. Nomological Validity is then tested by examining whether the correlation among the constructs in a measurement theory make
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sense (Hair et al 2010). It will be assessed in the theoretical model (Anderson and Gerbing 1988 cited from Nguyen and Nguyen 2008, p 42).
Figure 4.4 presents the CFA’s result of Saturated Model 3 . This model got chi-square value = 538.437; df = 199; p = 0.000 (less than 0.05); Chi – square/df = 2.706 (<3); TLI and CFI > 0.9; RMSEA = 0.06 < 0.08; GFI = 0.891 < 0.9. These results show that the saturated model achieved an acceptable fit to the data. Based on Modification Index 4 , the analysis was repeated with some adjustment in order to have a better model.
3 The saturated model is the model in which all constructs were freely related with each other (Nguyen et al 2008).
4 Each parameter that has a modification index greater than a specified threshold appears here, together with two numbers in columns labeled:
M.I.: modification index
Par Change: estimated parameter change
If no modification indices are displayed, this means that none exceed the specified threshold
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Figure 4.4: Saturated Model
Figure 4.5 shows CFA’s result in the Refined Saturated Model. It had chi – square value of 403.663; df = 194; p = 0.000; chi –square/df = 2.081; GFI, TLI and CFI > 0.9 and RMSEA < 0.08 (= 0.052). These results show the Refined Saturated Model was a good model fit. Table 4.5 presents the comparison of indices between Saturated Model and Refined Saturated Model.
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Figure 4.5: Refined Saturated Model
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Table 4.5: Model Fit Summary - Comparison
Saturated model Refined Saturated Model
CMIN 538.437 403.663
DF 199 194
P 0.000 ( < 0.05) 0.000 ( < 0.05) CMIN/DF 2.706 ( < 3) 2.081 ( < 3) GFI 0.891 ( < 0.9) 0.917 ( > 0.9) TLI 0.914 ( > 0.9) 0.945 ( > 0.9) CFI 0.926 ( > 0.9) 0.954 ( > 0.9) RMSEA 0.066 ( < 0.08) 0.052 ( < 0.08)
As shown above, for assessment construct validity, researchers evaluate (1) the composite reliability, (2) variance extracted, unidimensionality, (3) convergent validity and (4) discriminant validity. Table 4.6 shows the reliability (Cronbach’s Alpha and Composite) results and Extracted Variance results. Most of constructs had the reliability values greater than 0.8 and extracted variance values greater than 50% except for the CET construct (46%). To improve the extracted variance, some researchers reduce several items in each construct. This job needs to be considered carefully because it may be influenced to the content validity. In this study, two – items (CET 1 and CET 3) were deleted from the CET scale due to its lowest standardized regression weights. Figure 4.6 presents the Final Saturated Model after it was deleted two items.
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Table 4.6: Assessment Construct Validity Result
Constructs Items N o
Reliability Extracted Variance
(%) Cronbach’s
Alpha Composite
CET 5 0.805 0.807 46 < 50%
IPQP 4 0.859 0.846 58
PAT 5 0.925 0.922 70
COS 4 0.825 0.824 55
DC 4 0.846 0.854 60
Figure 4.6: Final Saturated Model
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As shown in Table 4.7, the Final Saturated Model had chi- square value of 280.219, df = 155; p = 0.000 (< 0.05); Chi – square/ df = 1.808 (<2); GLI, TLI,CFI > 0.92; RMSEA = 0.045 ( <0.05). The results indicate that the final saturated model received a good fit to the data and supporting for the unidimensionality of the scales such as CET and DC. Three scales (IPQP, PAT, COS) had a correlation between errors (e6 <-> e7, e10<-> e11, e11<-
>e13, e13<->e14, e17<->e18). Thus, they did not get the condition for the unidimensionality.
Table 4.7: Model Fit Summary - Final Saturated Model
Indices Value
CMIN 280.219
DF 155
P 0.000 ( < 0.05)
CMIN/DF 1.808 ( < 2)
GFI 0.934 ( > 0.92)
TLI 0.964 ( > 0.95)
CFI 0.97 ( > 0.95)
RMSEA 0.045 (< 0.05)
The extracted variance of CET construct improved from 46% to 53%.
Table 4.8 shows the new results for Cronbach’s Alpha Reliability, Composite Reliability and Extracted Variance.
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Table 4.8: Assessment Construct Validity Result
Constructs Items N o
Reliability Extracted Variance
(%) Cronbach’s
Alpha Composite
CET 3 0.765 0.769 53 >50%
IPQP 4 0.859 0.846 58 >50%
PAT 5 0.925 0.922 70 >50%
COS 4 0.825 0.824 55 >50%
DC 4 0.846 0.854 60 >50%
Table 4.9 presents the standardized and unstandardized factor loadings. All factor loadings were high (>0.5) and significant supporting the convergent validity of the scales. Moreover, as the Table 4.10 show, the correlations between constructs were significantly different from unity, indicating that the discriminant validity across constructs was achieved.
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Table 4.9: Regression weights and standardized regression weights summary
Regression weights Standardized regression weights
Estimate S.E. C.R. P Estimate
CET5 <--- CET 1 CET5 <--- CET 0.787
CET4 <--- CET 1.022 0.09 11.309 *** CET4 <--- CET 0.731 CET2 <--- CET 0.945 0.087 10.814 *** CET2 <--- CET 0.656
IPQP4 <--- IPQP 1 IPQP4 <--- IPQP 0.696
IPQP3 <--- IPQP 1.351 0.097 13.928 *** IPQP3 <--- IPQP 0.911 IPQP2 <--- IPQP 1.087 0.086 12.678 *** IPQP2 <--- IPQP 0.709 IPQP1 <--- IPQP 1.164 0.091 12.789 *** IPQP1 <--- IPQP 0.716
PAT5 <--- PAT 1 PAT5 <--- PAT 0.838
PAT4 <--- PAT 1.117 0.042 26.55 *** PAT4 <--- PAT 0.869 PAT3 <--- PAT 0.95 0.051 18.649 *** PAT3 <--- PAT 0.811 PAT2 <--- PAT 1.175 0.058 20.122 *** PAT2 <--- PAT 0.892 PAT1 <--- PAT 1.073 0.065 16.607 *** PAT1 <--- PAT 0.774
COS4 <--- COS 1 COS4 <--- COS 0.61
COS3 <--- COS 0.883 0.081 10.929 *** COS3 <--- COS 0.613 COS2 <--- COS 1.296 0.107 12.11 *** COS2 <--- COS 0.882 COS1 <--- COS 1.264 0.105 12.022 *** COS1 <--- COS 0.813
DC4 <--- DC 1 DC4 <--- DC 0.903
DC3 <--- DC 0.969 0.043 22.316 *** DC3 <--- DC 0.89 DC2 <--- DC 0.798 0.053 15.053 *** DC2 <--- DC 0.667 DC1 <--- DC 0.653 0.051 12.822 *** DC1 <--- DC 0.593
Table 4.10: Testing the discriminant validity Correlation between
variables R S.E 1-R C.R. p
IPQP <--> PAT 0.14 0.050 0.86 17.258 0.000 PAT <--> COS 0.30 0.048 0.71 14.646 0.000 COS <--> DC 0.11 0.050 0.89 17.810 0.000 CET <--> IPQP 0.10 0.050 0.90 17.918 0.000 CET <--> PAT 0.19 0.049 0.81 16.376 0.000 CET <--> DC 0.36 0.047 0.64 13.601 0.000 IPQP <--> COS -0.10 0.050 1.10 21.878 0.000 PAT <--> DC 0.30 0.048 0.70 14.518 0.000 IPQP <--> DC -0.14 0.050 1.14 22.877 0.000 CET <--> COS 0.06 0.050 0.94 18.636 0.000
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