DATA ANALYSIS METHODOLOGY

The data from the survey is analysed using descriptive analysis, confirmatory factor analysis (CFA) and structural equation modelling (SEM). Descriptive analysis is used to give the overall picture of the respondents’ demographic profiles. Confirmatory factor analysis (CFA) is conducted to evaluate whether the sub scales actually fall into the right group.

This is to address the issue of scale measurement construct validity. A Cronbach alpha test will also be conducted to address the issue of the reliability of the scale measurement. The final analysis involves Structural Equation Modelling that aims to identify the interrelations between the latent variables.

5.6.1 The Basic Concept of Structural Equation Modelling (SEM)

Structural equation modelling (SEM) grows out of, and serves purposes similar to, multiple regression, but in a more powerful way which takes into account the modelling of interactions, nonlinearities, correlated independents, measurement errors, correlated error terms, multiple latent independents each measured by multiple indicators, and one or more latent dependents also each with multiple indicators.

Hair et al. (2006, p. 703) also argued that, “SEM is the best multivariate procedure for testing both the construct validity and theoretical relationships.” SEM is used as a more powerful alternative to multiple regressions, path analysis, factor analysis, time series analysis, and analysis of covariance.

Hair et al. (2006) added that by using SEM, the strength of relationships between constructs could be identified more accurately because it will consider measurement errors. The advantages of SEM compared to multiple regression include:

i) More flexible assumptions (particularly allowing interpretation even in the face of multi-collinearity);

ii) The use of confirmatory factor analysis to reduce measurement error by having multiple indicators per latent variable;

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iv) The desirability of testing models overall rather than coefficients individually, v) The ability to test models with multiple dependents;

vi) The ability to model mediating variables rather than be restricted to an additive model;

vii) The ability to model error terms;

viii) The ability to test coefficients across multiple between-subject groups; ix) In addition, the ability to handle difficult data (time series with auto-correlated

error, non-normal data, incomplete data).

Moreover, where a regression is highly susceptible to errors of interpretation by misspecification, the SEM strategy of comparing alternative models to assess relative model fit makes it a more robust method. Nevertheless, SEM requires several procedural steps to be taken. Therefore, in the next section, a brief discussion of the six stages of the procedural steps in structural equation modelling will be provided.

5.6.2 The Procedural Steps in SEM

Figure 5-8: Six-Stage Process for Structural Equation Modelling Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

Source: Adopted from Hair et al. (2006, p. 759) Defining the Individual Constructs What items are to be used as measured variables

Develop and Specify the Measurement Model Make measured variables with constructs. Draw a path diagram for the measurement

model

What items are to be used as measured variables Designing a Study to Produce empirical Results Asses the adequacy of the sample size. Select

the estimation method and missing data approach.

Assessing Measurement Model Validity Asses line of GOF and construct validity of

measurement model

Specify Structural Model Convert measurement model to structural

model. Measurement Model Valid?

Assess Structural Model Validity Assess the GOF and significance, direction and

size of structural parameter estimates.

Structural Model Valid? Refine model and test new data Draw substantive conclusion and recommendation s Refine measures and design a new study Proceed to test structural model with stage 5 & 6 No Yes

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5.6.3 Guidelines for Establishing Acceptable and Unacceptable Fit

Guidelines in assessing the measurement and structural model are based on the several Goodness of Fit indices (GOF). The SEM has three categories of goodness-of-fit: absolute fit measures, incremental fit measures, and parsimonious fit measures. The absolute fit measure determines the overall model fit. The tests used in the absolute fit measures are likelihood ratio χ2 _{statistics, the goodness-of-fit index (GFI), and the root mean square error}

of approximation (RMSEA). The second category, called the Incremental Fit measure, evaluates the proposed model compared to the baseline model (also known as the independent model).

Examples of this measure are the adjusted goodness-of-fit index (AGFI), the normed fit index (NFI), the incremental fit index (IFI), and the comparative fit index (CFI). The third category is the Parsimonious Fit measure, which includes the parsimonious normed fit index (PNFI), the parsimonious comparative index (PCFI), and the Akaike information criterion (AIC). The magic 0.90 cut off is normally used for several indices such as CFI, and TLI. However, Hair et al. (2006) differentiated the cut off for the indices based on the sample size and the number of variables (m). The following table shows the respective indicators of acceptable GOF indices across different model situations.

Table 5-9: Characteristics of Different Fit Indices Demonstrating Goodness of Fit across Different Model Situations

N < 250 N > 250 No of vars (m) m ≤ 12 12 < m < 30 m ≥ 30 m ≤ 12 12 < m < 30 m ≥ 30 2 Insignificant p- values expected Significant p-values can result even with good fit Significant p-values can be expected Insignificant p-values can result with good fit Significant p-values can be expected Significant p-values can be expected 2_{/DF < 3 < 3 < 3 < 3 < 3 < 3} CFI or TLI ≥ 0.97 ≥ 0.95 > 0.92 ≥ 0.95 ≥ 0.92 ≥ 0.90

RNI May Not diagnose misspecification as well ≥ 0.95 > 0.92 > 0.90 SRMR Could be biased upward ≤ 0.08 CFI ≥ 0.95 ≤ 0.09 CFI ≥ 0.92 Could be biased upward ≤ 0.08 CFI ≥ 0.92 ≤ 0.08 CFI ≥ 0.92 RMSEA < 0.08 CFI ≥ 0.97 < 0.08 CFI ≥ 0.95 < 0.08 CFI ≥ 0.92 < 0.07 CFI ≥ 0.97 < 0.07 CFI ≥ 0.92 < 0.07 CFI ≥ 0.90 Source adopted from Hair et al. (2006, p. 753).

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In the current study, the number of samples is 560 and m is greater than 30. Therefore, the current study will use items in the far right column in the table above. However, some argue that values above 0.9 are acceptable cut offs (Bentler and Bonnett 1980; Hoyle and Panter 1995). Thus, this rule is often disputed and disregarded (Bollen 1989; Hoyle and Panter 1995).

Cohen (1988), for example, has a lower cut-off, of 0.8 (Wong and Jeffery 2002). Bollen (1989) suggested that a significant criterion “may be simply to compare the fit of one's model to the fit of other, prior models of the same phenomenon” (Wong and Jeffery 2002, p. 9). For example, quoted from Moss (2009), a CFI of .85 may represent progress in the context of a study where the best prior model had a fit of .70 (Bollen 1989). Therefore, since this is an initial study in the context of ICCs, any results obtained presently can then become the cut off for future studies.

5.7 CHAPTER SUMMARY

The proposed research design is a sequential mixed model design. The research will have a theoretical lens (the research framework) which overlays the three phases. The phases are a combination of interviews followed by an online survey. In the first phase, several semi- structured interviews were conducted with ICC users in order to capture the potential antecedents of customer satisfaction as well as to ensure that the survey questions are understood. In the second phase, religiosity scale was developed taking the experts opinion and culling and sorting processes from 27 religiosity scales found from the literature. In the third phase, online surveys were administered to credit-card users. Emails were sent to potential respondents redirecting them to answer the questionnaire at a web-based online survey. The respondents need to answer a screening question as to whether or not they own a credit card before completing the entire survey. An analysis of the survey data will then take place after the third phase of the research design.

This study employs confirmatory factor analysis and structural equation modelling. The major limitation of the proposed research design is time, because the transitions from phase one to phase three are sequential.

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