Dimensional reduction technique analysis using principal component analysis

5.4 Results and Discussion

5.4.1 Dimensional reduction technique analysis using principal component analysis

5.4.1.1 Principal component analysis (PCA) of comfortable riding posture (CRP)

The PCA yielded 3 PCs from the 10 CRP (joint angles) variables. The potential PCs were recognized graphically using the scree plot (see Figure 5.1). This plot implied effective PCs (PC1-PC3) that have Eigenvalues greater than 1. The KMO measure of sampling adequacy was obtained as 0.71 (ranged between 0.70 and 0.79). It can be interpreted as a “middling”

sample size for the research (Cerny and Kaiser, 1977). Bartlett’s test was also found to be significant at p < 0.001, which indicates adequate sample size (Kuo et al., 2019). The intra- correlation coefficients between all the postural (joint angles) variables presented in Appendix L, Table 1.

Following varimax orthogonal rotation, three PCs accounted for 62.97% of the total variance in the original variables (see Table 5.2). PC 1 includes 3 variables (see Table 5.3), and accounts 37.12% of the total variance (Eigenvalue = 3.7). These factors were labeled as “Comfort hip joint angles” because these joints movements take place in the hip joint regions (i.e. Hip flexion/extension, hip adduction/abduction and Lower back joint angle). Since the lower back joint is connected with hip joint (tailbone), we considered it in the “hip joint angle”. PC 2 was comprised of four variables and labeled as the “Comfort joint angles of upper limbs” since its accommodated joint angle related to upper part/limbs of the human body. It accounted for 15.13% of the total variance (Eigenvalue = 1.5). PC 3 consisted of three variables (10.17% of the total variance; Eigenvalue = 1.07) and labeled as “Comfort joint angles of lower limbs” (the joint angles of lower limbs).

Figure 5. 1: Scree plot of CRP

Table 5. 2: Total variance explained for CRP Principal

Component (PC)

Initial Eigenvalues Rotation Sums of Squared Loadings Total

% of Variance

Cumulative

% Total

% of Variance

Cumulative

1 3.713 37.128 37.128 2.212 22.125 22.125

2 1.513 15.130 52.259 2.190 21.897 44.022

3 1.071 10.715 62.973 1.895 18.951 62.973

4 .906 9.059 72.033

5 .808 8.080 80.113

6 .712 7.122 87.234

7 .425 4.252 91.487

8 .400 4.003 95.490

9 .245 2.451 97.941

10 .206 2.059 100.000

Table 5. 3: Results of factor analysis for comfortable riding posture joint angles Principal Component (PC)

1 2 3

θW1 .820

θW2 .750

θW3 .686 .591

θW4 .650 .418

θW5 .790

θW6 .773

θW7 .432

θW8 .444

θW9 .731

θW10 .816

Note. Eigenvectors values < 0.4 suppressed for display in the table.

The PCA results interpret that the CRP could be classified into 3 major principal components, which will effectively represent all the 10 CRP variables (joint angles). The first component represents the joint angles of hip and lower back. The second component represents the joint angles of upper limbs like neck, shoulder, arms and hand/wrist. Whereas, the third component represents the joint angles of lower limbs like knee, foot. Moreover, these three principal components may represent/express 62% of the originals variance.

In line with our results, the study by Vergara and Page (2002) on automotive male drivers also revealed that the hip-related joints expresses most of the joint angles variables. Also, JASO T003:2009 recommend that the hip joint angles can be considered as the key measurements while designing motorcycles.

5.4.1.2 Principal component analysis (PCA) of comfortable riding position (RP)

Four PCs were yielded from the 10 RP variables. The potential PCs (PC1-PC4) were recognized graphically using the scree plot (see Figure 5.2). This plot implied that the effective PCs were having an eigenvalues larger than 1. The KMO measure of sampling adequacy was obtained as 0.64 (ranged between 0.60 and 0.69). It can be interpret as a “mediocre” sample size for the research (Cerny and Kaiser, 1977). Bartlett’s test was also found to be significant at p < 0.001, which indicate that the sample size was adequate (Kuo et al., 2019). The intra- correlation coefficients among the RP variables were presented in Appendix L, Table 2.

Figure 5. 2: Scree plot of RP

Following varimax orthogonal rotation, four PCs of the joint angles accounted for 81.5% of the total variance in the original variables (see Table 5.4). PC 1 includes 4 variables (see Table 5.5) and accounts 32.26% of the total variance (Eigenvalues = 3.2). These factors were labelled as “Vertical dimensions at Sagittal plane” because it accommodates the variables related to Z- axis (i.e. R1, R2, MR1 and H). PC 2 was comprised of two variables and labelled as the

“Dimensions at Transverse plane” since it accommodated variables related to top plane. It accounted for 22.37% of the variance (Eigenvalues = 2.2). PC 3 consisted of three variables (16.59 % of the variance; Eigenvalues = 1.6) and labelled as “Horizontal dimensions at Sagittal plane” because it accommodates variables related to X-axis (i.e. MR2, R3, and R4). PC 4 consisted of one variable (10.12% of the variance; Eigenvalues = 1.01) and labelled as

“Footrest dimensions at Transverse plane” (the footrest dimension in the transverse plane).

The PCA results interpreted that the RP could be classified into 4 major principal components, which will efficiently represent all the 10 riding position variables. The first PC1 represents the vertical dimensions at Sagittal plane like R1, R2, MR1 and H. The second PC2 represents dimensions at Transverse plane like L, T. The PC3 component represents the horizontal dimensions at Sagittal plane like MR2, R3, R4. Whereas, PC4 represents the footrest dimension.

Moreover, these four principal components may represent the 10 originals variables (more than 81% of the variance were explained). In line with our results, the JASO T003:2009 recommend

that the vertical dimensions were key dimensions of motorcycles. Whereas, some of motor vehicle standards (J1100, 2009) were also suggested that the vertical dimensions were key dimensions of vehicle design.

Table 5. 4: Total variance explained for riding positions variables Principal

Component (PC)

Initial Eigenvalues Rotation Sums of Squared Loadings Total

% of Variance

Cumulative

% Total

% of Variance

Cumulative

1 3.226 32.260 32.260 2.736 27.358 27.358

2 2.237 22.374 54.634 2.281 22.811 50.169

3 1.659 16.591 71.225 2.093 20.933 71.103

4 1.012 10.124 81.349 1.025 10.247 81.349