Chapter 4 Data analysis and scale purification
4.3 Identifying the factor structure of the M-S-QUAL construct
Item Corrected item-to-total
correlation Ful_p_6 It is truthful about its offerings. 0.80 - Ful_p_7 It makes accurate promises about delivery of products. 0.82 - Re_p_1 It provides me with convenient options for returning items. 0.84 - Re_p_2 This site handles product returns well. 0.85 - Re_p_3 This site offers a meaningful guarantee. 0.88 - Re_p_4 It tells me what to do if my transaction is not processed. 0.75 - Com_p_1 This site compensates me for problems it creates. 0.74 - Com_p_2 It compensates me when what I ordered doesn’t arrive on time. 0.79 - Ful_v_1 It delivers orders when promised. - 0.76 Ful_v_2 This site makes items available for delivery within a suitable
timeframe.
- 0.83 Ful_v_3 It quickly delivers what I order. - 0.80
Ful_v_4 It has in stock the items the company claims to have. - 0.83 Re_v_1 It provides me with convenient options for returning items. - 0.87 Re_v_2 This site handles product returns well. - 0.89 Re_v_3 This site offers a meaningful guarantee. - 0.89 Com_v_1 This site compensates me for problems it creates. - 0.87 Com_v_2 It compensates me when what I ordered doesn’t arrive on time. - 0.87 Com_v_3 It picks up items I want to return from my home or business. - 0.76
4.3 Identifying the factor structure of the M-S-QUAL construct
An exploratory factor analysis (EFA) was conducted to examine the factor structure of the 44- and 41-item instruments in more detail. Data on tangible products M-S-QUAL (90valid responses) and intangible products M-S-QUAL (488 responses) were analyzed separately. Before proceeding with our exploratory factor analysis, we measured KMO and conducted Bartlett’s sphericity test to check whether the inter-correlation matrix contained sufficient common variance. As shown in Table 9, a KMO measure of greater than 0.7 and a significant,Bartlett's sphericity test result, indicating exploratory factor analysis should be conducted.
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Table 9. KMO measure and Bartlett’s sphericity test
Tangible products
Intangible products Kaiser-Meyer-Olkin measure of sampling adequacy 0.922 0.885 Bartlett's sphericity test value 9437.043 2280.642
df 171 231.000
Significance level 0.000 0.000
4.3.1 Exploratory factor analysis
We then conducted an EFA to identify the dimensionality of the 44- and 41-item scale using the principle component analysis as the extraction technique, and the varimax orthogonal rotation method. We extracted factors with eigenvalues greater than or equal to 1, yielding four factors for tangible products M-S-QUAL and five factors for intangible products. The employed decision rules applied to identify the factors underlying the M-S-QUAL construct were (1) delete items with a factor loading of less than 0.7 or the loading of greater than 0.3 on two or more factors, (2) mantain a simple factor structure, and (3) exclude single-item factors from the perspective of parsimony (Hinkin, 1998; Straub, 1989).
Three iterative runs based on the aforesaid rules resulted in the deletion of 29 tangible
product M-S-QUAL items. At the end of the factor analysis procedure, we obtained a 4-construct,
15-item instrument. The four constructs were interpreted as efficiency, fulfillment, contact, and recovery, explaining 81.34% of the variance in the dataset. Due to the small sample size (90) for the tangible products shopping experiences, it was not appropriate to conduct CFA in the next stage. For CFA, a minimum sample of 200 has been recommended (Hoelter, 1983), so the factor analysis of tangible products M-S-QUAL ended in this stage. Table 10 summarizes the factor loadings for the condensed 15-item instrument. The significant loading of items on each factor indicates convergent validity, while the discriminant validity of the instrument found supports from the fact that items showed little cross-loadings‧
Table 10. EFA results for tangible products M-S-QUAL
Construct Item code Item description Rotated
factor
Ef_1 It enables me to complete a transaction quickly.
.858
Ef_2 It loads its pages fast. .826
SA_3 Pages at this site do not freeze after I enter my
order information. .804
SA_2 This site does not crash. .704 Fulfillment Ful_p_2 This site makes items available for delivery
within a suitable timeframe. .894
1.85 66.59 0.89 66.52%
Ful_p_4 It sends out the items ordered. .826 Ful_p_1 It delivers orders when promised. .791 Ful_p_6 It is truthful about its offerings. .744 Contact Con_5 It offers the ability to speak to a live person if
there is a problem. .838
1.57 75.92 0.86 66.57%
Con_6 This site provides a telephone number to reach
the company. .820
Con_2 Service agents provide consistent advice. .789 Recovery Re_p_2 This site handles product returns well. .811
1.00 81.34 0.82 61.09%
Re_p_3 This site offers a meaningful guarantee. .767 Re_p_1 It provides me with convenient options for
returning items. .766
The EFA of intangible products M-S-QUAL also followed the rules, and 11 items were deleted. We obtained a 7-factor, 29-item instrument in this stage and used the result to proceed to CFA (see Table 11).
Table 11. EFA results for intangible product M-S-QUAL
Construct Item
code
Item description Rotated
factor loading
Eigenvalue Variance Explained (%) Contact Con_4 Call-center personnel are able to help with problems. .829
9.53 49.15 Con_5 It offers the ability to speak to a live person if there is a
problem.
.791 Con_2 Service agents provide consistent advice. .782 Con_6 This site provides a telephone number to reach the
company.
.758
Con_1 Friendliness when reporting a complaint. .751
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Item description Rotated
factor loading
Eigenvalue Variance Explained (%) Recovery Re_v_3 This site offers a meaningful guarantee. .904
2.33 60.35 Re_v_2 This site handles product returns well. .891
Re_v_1 It provides me with convenient options for returning
items. .873
Com_v_3 It picks up items I want to return from my home or
business. .718
Fulfillment Ful_v_2 This site makes items available for delivery within a
suitable timeframe. .884
2.08 70.36
Ful_v_1 It delivers orders when promised. .837
Ful_v_4 It has in stock the items the company claims to have. .758
Ful_v_3 It quickly delivers what I order. .741
Privacy Pr_2 It does not share my personal information with other sites.
.856
1.17 75.60 Pr_1 It protects information about my web-shopping
behavior.
.779 Pr_3 This site protects information about my credit card. .733
Efficiency Ef_2 It loads its pages fast. .813
1.1 80.39 Ef_1 It enables me to complete a transaction quickly. .780
Ef_4 This site enables me to get on to it quickly. .777
4.3.2 Confirmatory factor analysis
The purpose of the analysis in this stage was to test whether the intangible products M-SQ’s seven dimensions resulted from EFA were appropriate indicators of mobile service quality.
The factor structure extracted by EFA needs to be confirmed by drawing model in AMOS Graphics and linking the valid sample data to the model to calculate path coefficients and model fits. We deleted the items, namely, the observed variables in AMOS, with the low path coefficients (below 0.7) and checked the model fits iteratively.
CFA is a part of structural equation modeling (SEM) which is permitting existence of measurement errors or residuals between exogenous variables and endogenous variables.
Modification indices suggested remedies to discrepancies between the proposed and estimated model. However, there was not much we can do by way of adding regression lines to fix model
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fit, as all regression lines between latent and observed variables are already in place. We looked the modification indices for the covariances in CFA. We could not covary error terms with observed or latent variables, or with other error terms that are not part of the same factor. The modification available to us is to covary error terms that are part of the same factor.
The other model adjustment method depends on the standardized residual covariances among observed variables. If the values of the standardized residual covariances were too high (greater than 2), the items could be considered for deletion. The above three methods were executed until the model fits were good. The final model after CFA is shown in Figure 4, and all paths in the model were confirmed, indicating a good fit between the model and the data. We obtained a 4-construct, 16-item instrument, and used the standardized factor loading to calculate composite reliability and average variance extracted (AVEs) of each construct to verify the convergent validity (see Table 12).
Table 12. CFA and reliability results (intangible products)
Construct Item code Item Factor
loading Efficiency Ef_4 This site enables me to get on to it quickly. 0.90
0.939 83.79%
Ef_1 It enables me to complete a transaction quickly. 0.91 Ef_2 It loads its pages fast 0.93 Fulfillment Ful_v_3 It quickly delivers what I order. 0.92
0.924 80.26%
Ful_v_1 It delivers orders when promised. 0.88 Ful_v_2 This site makes items available for delivery within a
suitable timeframe.
0.88 Privacy Pr_3 This site protects information about my credit card. 0.88
0.930 81.59%
Pr_1 It protects information about my web-shopping behavior. 0.91 Pr_2 It does not share my personal information with other sites. 0.93 Contact Con_1 Friendliness when reporting a complaint. 0.92
0.916 78.36%
Con_2 Service agents provide consistent advice. 0.92 Con_5 It offers the ability to speak to a live person if there is a
problem.
0.82 Con_6 This site provides a telephone number to reach the
company.
0.80 Recovery Re_v_1 It provides me with convenient options for returning items. 0.92
0.956 87.81%
Re_v_2 This site handles product returns well. 0.94 Re_v_3 This site offers a meaningful guarantee. 0.94
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Model fit measures can be obtained to assess how well the proposed model captures the covariance between all items or measures in the model. If the constraints the researcher has imposed on the model are inconsistent with the sample data, then the results of statistical tests of model fit will indicate a poor fit and the model will be rejected. Poor fit may be due to some items measuring multiple factors, or may be attributable to some items under a factor being more related to others (wiki). The Chi-square (x statistic is used most often as a descriptive index of fit, rather than as a statistical test. A smaller x value indicates s better fitting models with an insignificant x being desirable. In larger sample sizes, power is so high that even models with only trivial misspecifications are likely to be rejected. The recommended values for goodness-of-fit and the CFA results are summarized in Table 13. The overall structural goodness-of-fit results of these analyses showed the model provided a reasonable degree of fit.
Table 13. Comparisons of goodness-of-fit indices for the model
Model Fit Indices Criterion Guidelines CFA Results (Intangible)
Chi-square ( ) 232.675
Degree of freedom 92
Absolute fit measures
GFI ＞.80 (MacCallum & Hong, 1997) 0.945 RMSEA ＜.10 (Steiger, 1990) 0.056 SRMR ＜.05 (Jöreskog & Sörbom, 1992)
Normed chi-square ( / ＜3 (Hair et al., 2010) 2.529 Incremental fit measures
NFI ＞.90 (Bentler, 1992) 0.97 CFI ＞.90 (Gerbing & Anderson, 1992) 0.982 Parsimony fit measurement
AGFI ＞.80 (MacCallum & Hong, 1997) 0.918