4.4.1 Reliability and validity
Results from the factor analysis (CFA) are summarised in Table 4-4. Convergent validity was assessed via factor loadings of each observed variable and average variance extracted (AVE), and reliability was examined via composite reliability (CR, otherwise known as construct reliability) and Cronbach's alpha. AVE is a summary measure of convergence among a set of items representing a latent variable (Hair et al., 2010). AVE is calculated as the total of all squared standardised factor loadings (𝐿𝑖) divided by the number of items:
AVE =∑𝑛𝑖=1𝐿𝑖2
𝑛 (1)
CR is for assessing reliability and internal consistency of the measured variables representing a latent construct (Hair et al., 2010). It is computed from the squared sum of factor loadings (𝐿𝑖) for each construct and the sum of the error variance terms for a construct (𝑒𝑖): CR = (∑𝑛𝑖=1𝐿𝑖) 2 (∑𝑛𝑖=1𝐿𝑖) 2 +(∑𝑛𝑖=1𝑒𝑖) (2) Factor loadings were statistically significant (p < 0.001) and greater than 0.6. The AVE ranged from 0.518 to 0.751 and the CR ranged from 0.731 to 0.909 and the Cronbach’s alphas ranged from 0.690 to 0.912. All values representing both convergent validity and reliability were found to be in acceptable ranges (Hair et al., 2010). To assess the degree to which a latent variable is distinct from other latent variables, discriminant validity was also examined. If the AVE for each construct is greater than its shared variance with any other construct, discriminant validity is supported (Fornell and Larcker, 1981; Farrell, 2010; Götz et al., 2010). Average shared variance (ASV) can be computed as the total of squared shared variances divided by the number shared variances. As Table 4-4 presents, ASV of each construct was lower than its AVE value and thus, a good discriminant validity was proven (Fornell and Larcker, 1981). Therefore, the CFA results confirmed that internal consistency exists and the variables are reliable and have good construct validity.
Table 4-4. Results of confirmatory factor analysis
4.4.2 Results from the path analysis
The structural model was tested using maximum likelihood estimation. In order to measure validity of the path model itself, some significant fit indices require to be noticed. As researchers have argued different cut-off values for each fit index, some of the values are listed in Appendix 5. First, goodness-of-fit index (GFI) is widely used fit index to measure the model fit and the higher value which is close to 1 indicates the better fit. GFI of the path model estimated in this study was 0.932 indicating a good fitting model. However, GFI is known as an early attempt to produce a fit statistic which is less sensitive to sample size so that is suggested to be used as only guidance (Marsh and Jackson, 1999; Hair et al., 2010). Alternatively, adjusted root mean square error of approximation (RMSEA) also represents how well a model fits a population. Lower RMSEA values indicate better fit and it was suggested to be lower than 0.07 or 0.08 to be referred to as a good RMSEA (Hair et al., 2010; Arbuckle, 2013). RMSEA of the tested model was 0.055 which was lower
RMSEA = 0.050; GFI = 0.942; CFI = 0.976; χ2/df = 2.221
Observed variable Factor loading p < 0.001 AVE CR Cronbach’s alpha ASV AN1 AN2 0.960 0.762 0.751 0.856 0.843 0.315 D1 D2 D3 D4 D5 0.794 0.830 0.741 0.852 0.859 0.666 0.909 0.912 0.447 H1 H2 H3 0.840 0.790 0.926 0.729 0.889 0.904 0.443 C1 C2 C3 0.686 0.790 0.677 0.518 0.762 0.756 0.433 AT1 AT2 0.919 0.576 0.588 0.731 0.690 0.120 R1 R2 R3 0.689 0.959 0.799 0.678 0.861 0.839 0.005
than the cut-off value indicating the model fit well. Next, normed Chi-square (χ2/df) is a ratio of Chi-square to the degrees of freedom for the model which also shows how well the model fits. There have been some debates over the acceptable range of this measure but the estimated χ2/df value of the tested path model was 2.479, which was within the acceptable range that has been proposed (Carmines and McIver, 1981; Marsh and Hocevar, 1985; Hair et al., 2010). The last fit index is comparative fit index (CFI) which compares the fit of a tested model to that of an independent model (otherwise, known as a null model) which is a model in which observed variables are uncorrelated. CFI above 0.9 are generally associated with a model that fits well (Hair et al., 2010; Arbuckle, 2013). CFI of the model estimated in this study was 0.967. On the whole, the fit indices suggested that the path model was a good fitting model.
The standardised estimates of the path analysis were plotted in Figure 4-5 and some indirect effects were listed in Table 4-5. It was found that noise sensitivity had a positive direct impact on disturbance (β = 0.518, p < 0.001) indicating those who were sensitive to noise were more easily disturbed by floor impact sounds. Noise sensitivity also influenced annoyance indirectly via disturbance (β = 0.496, p < 0.001). In addition, noise sensitivity had indirect effects on health complaints (β = 0.460, p < 0.001) and coping (β = 0.468, p < 0.001) via disturbance and annoyance. Disturbance had a positive direct effect on noise annoyance (β = 0.959, p < 0.001) and it had indirect effects on health complaints and coping, 0.888 and 0.905 respectively (p < 0.001). These findings suggest that more frequent disturbance increases not only noise annoyance but also subjective health complaints and coping. Noise annoyance positively affected coping (β = 0.944, p < 0.001) and health complaints (β = 0.927, p < 0.001). Therefore, the findings suggest that increased noise annoyance may lead people to employ avoidant coping behaviours more frequently and to report more health complaints. In addition, mean differences compared between those who reported low noise annoyance and high noise annoyance also confirmed the findings. People who responded that they were highly annoyed with floor impact sounds reported more coping behaviours and health complaints than those who reported low noise annoyance (Table A-2 and A-3 in Appendix 6). On the other hand, the path analysis found no significant impact of the two attitudinal variables (negative attitude to authorities, closeness with neighbours) on coping.
Table 4-5. Indirect effects of noise sensitivity and disturbance on annoyance, health complaints, and coping
**p < 0.001, *p < 0.05
Noise sensitivity Disturbance
Annoyance 0.50**
Health complaints 0.46** 0.89**
Coping 0.47** 0.91**