Bootstrapping SEM

The validity and acceptability of the structural model can be evaluated in terms of model-fit, that is, GOF indices. In order to determine the model-fit of full SEM, bootstrapping technique is employed. Bootstrapping is a resampling procedure in which the original sample serves as the population (Efron & Tibshirani 1993; Mooney 1997). Through bootstrapping, multiple samples (with the same N as the original sample) are

178 randomly drawn from the original sample with replacement, that is, a given case may be randomly selected more than once in any given bootstrapping data set (Byrne 2009). The CFA model is estimated in each data set, and the results are averaged over the data sets. Unlike Monte Carlo simulation in which multiple samples are randomly generated on the basis of population parameter values and other data aspects (e.g. sample size, amount of non-normality) that are pre-specified by the researcher, bootstrapping allows the population parameters to be generated in advance (Brown 2006). As in bootstrapping, the results of models fitted in the simulated data sets are averaged to examine the behaviour of the estimates (e.g. stability and precision of parameters estimates and test statistics).

Bootstrapping is based on the notion that when the distributional assumptions of normal-theory statistics are violated, an empirical sampling distribution can be relied upon to describe the actual distribution of the population on which the parameter estimates are based (Brown 2006). Since bootstrapping is based on the multiple samples spawned from the original data set, it allows the average estimates and standard errors to be compared against the results from the original sample in order to evaluate the stability of model parameters. Byrne (2009) recommends the use of bootstrapping based on two critically important assumptions associated with SEM that are the requirements of the data to be continuous scale and have a multivariate normal distribution. These underlying assumptions are linked to large-sample theory within which SEM analysis of covariance and mean structures is embedded (Byrne 2009). Likewise, Diaconis and Efron (1983) suggest the appealing feature of bootstrapping as of being free from two constraining statistical assumptions generally associated with the analysis of data (a) that the data are normally distributed; and (b) that the researcher can explore more complicated problems using a wide array of statistical tools not available earlier.

179 Bootstrapping is conducted using SPSS AMOS Statistical Analysis package. The number of bootstrapped samples specified by the researcher should be sufficiently large enough to foster the quality of the averaged estimates. According to Brown (2006), 500 samples are considered common for bootstrapping. Using the CFA measurement models presented in the previous sections, bootstrapping is run by generating 500 random sample from the original data set (N = 297) and then averaging the results of parameter estimates and standard errors across the 500 analyses.

Support for and acceptability of the structural model is evaluated based on the GOF indices cut-off value outlined in Table 6.12. Table 6.43 below illustrates the model fit statistics of the full structural model achieved by bootstrapping. The results are supported and accepted in terms of the selected and most widely reported fit indices in the SEM literature. The model’s p-value (.222) is greater than the threshold value (≥.05) which indicates a strong model-fit. All the incremental fit indices (NFI, TLI and CFI) meet the threshold value ≥.92. The model’s absolute fit index value is also within the recommended range in terms of SRMR and RMSEA (≤.08). Further, the model’s parsimony fit indices (PCFI and PNFI) values are acceptable (≥.5) which show a relatively higher value than the corresponding measurement models. The final structural model is therefore presented in Figure 6.32

Table 6.43. Model-fit Statistics for Structural Model

Chi-square Absolute Fit Indices Incremental Fit Indices Parsimonious Fit Indices

2 (p-value) 2 /DF .222 1.242 RMSEA SRMR .029 .074 NFI TLI CFI .921 .981 .981 PCFI PNFI .935 .868 Model-fit is admissible

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6.7. Summary

Data analysis in this thesis has been preceded by data editing from collected questionnaires and coding the question items. Data screening and preliminary data analysis, including descriptive statistics and sample characteristics were discussed. Data screening was done prior to conducting SEM because the latter is very sensitive to missing data, normality, and sample size. Following this, the number of respondents were analysed and demographic characteristics of this sample have been described.

The second part of data analysis is the use of SEM. Assessment and testing of models using SEM involves two steps: assessment of the measurement model and assessment of the structural model. In order to ensure the validity and reliability of the measurement model, which is the foundation for SEM, the instrument was subjected to very rigorous validation procedures involving measurement purification, content validity and construct validity through both EFA and CFA.

The EFA identified some latent factors and led to some changes in the initial factors proposed for the model. Items that could not be accurately estimated should be dropped since their estimated parameters will not provide any useful insight about the model. As a result, 9 items (CPW3, PRM5, SCC6, MSI6, VM6, RES3, FLP3, FLP6, and INC5) were dropped after the EFA process.

The CFA is used to test the model-fit of each one-factor congeneric and measurement model to make sure the unidimensionality of each interest construct. Accordingly, the initial results indicate the requirements of model re-specification of several models in both one-factor congeneric and higher measurement in order to achieve a more parsimonious model that is required in the next step of the structural model. As a results, nine items (MP1, CPW2, EPR5, PM5, RES7, SID5, FP1, FP3, and OP6) were

182 deleted as a consequence of one-factor congeneric model analysis. In addition, a result of higher-order measurement model, further 4 items (EPR6, CPW1, PM2 and PRM3) were removed. This was done to improve the convergent and discriminant validity. The modified measurement model provides adequate fit to the data, and all indicators are highly loaded on their specified factors. Although this rigorous procedure resulted in the side effect of several items being dropped, the remaining items sufficiently reflect the construct they are measuring. All the constructs contain at least three items.

Once the measurement models are validated and satisfactory fitness achieved, a full structural model was then tested and presented. The validity and acceptability of the structural model was evaluated using bootstrapping technique. Unlike theoretical sampling distribution, the bootstrapped sampling distribution is concrete because it is based on the multiple samples spawned from the original data set. The final GOF indices yield acceptable statistics value in all accounts which suggests the validity of the final structural model. The next chapter (Chapter 7) further conducts the hypothesised structural model in corresponding to the discussion of the research’s findings.

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