Structural Path Modelling Analysis
This chapter explains the use of a structural equation modelling (SEM) and path analysis method for hypotheses testing. It is divided in 4 parts. Section 7.1 – 7.2 present a five-step process (Schumacker and Lomax, 2004) to specify and estimate two SEM path models. Section 7.elaborates a bootstrapping procedure to validate the reliability of the model fit indices and the accuracy of the path estimates. At last, Section 7.4 presents the results and explains the use of the path models for hypotheses testing.
Hypothesised Model (a) for Testing H1
Two structural path models were developed to test the cause and effect relationships. Model (a) (Figure 7.1) was developed to test H1 as defined in Section 4.3.2 (Figure 4.9).
Figure 7.1 Hypothesised model (a) for H1
H1 was expanded to take into account the relationship between the four building block shop floor management tools and the two improvement practices. This yielded the following eight sub-hypotheses (Table 7.1).
H1. The building block shop floor management tools have positive effects on the improvement practices
H1a Implementation of standard operations has positive effects on QCCs
H1b Implementation of waste removal has positive effects on QCCs
H1c Implementation of 5S practice has positive effects on QCCs
H1d Implementation of visual management has positive effects on QCCs
H1e Implementation of standard operations has positive effects on Teians
H1f Implementation of waste removal has positive effects on Teians
H1g Implementation of 5S practice has positive effects on Teians
H1h Implementation of visual management has positive effects on Teians
Table 7.1 the sub-hypotheses for H1
The paths in this model were then specified, identified, estimated, tested and modified by using a five-step PA process (Figure 5.12 in Section 5.3.3).
Model specification for model (a)
A full PA model was created by using the AMOS Graphics which used SEM’s path symbol notation (see Figure 5.9 in Section 5.3.1). The hypothesised path model (a) consisted of 6 latent variables and 9 inferred observed variables. Figure 7.2 depicts the hypothesised path model (a).
Figure 7.2 The hypothesised path model (a) based on the theoretical model (AMOS Graphics)
The variables in hypothesised path model (a) were developed and tested in the previous chapter and they are listed in the following Table 7.2.
Associated measurement scales Latent variables in the PA model Observed variables in the PA Model Total
1 Standard operations SDO_1 StandardOp (the sum of SDO1- SDO4) 1
2 Waste removal WSR_2 WasteRe (the sum of WSR1- WSR3) 1
3 5S practice I5S _3 FiveS (the sum of I5S1- I5S15) 1
4 Visual management VSI _4 VisualMa (the sum of VSI1- VSI4) 1
5 QCCs QCC_5 QC_Met (the product of QC_Meet_Times ;
QC_Met_Length), QC_Comp and QC_Pres 3
6 Teians Teian_6 Tn_Sub and Tn_Acc 2
Total Latent Variables 6 Total Observed Variables 9
Table 7.2 The latent and observed variables in the hypothesised path model (a)
The model included four latent variables that represent shop floor management tools (SDO_1, WSR_2, I5S_3 and VSI_4) and two latent variables that represent improvement implementation (QCC_5 and Teian_6). Each of the latent variables was measured by their associated observed variable(s). In addition, the four shop floor management latent variables (SDO_1, WSR_2, I5S_3 and VSI_4) were hypothesised independent variables. They were regressed onto their respective dependent variables (QCC_5 and Teian_6). Each of the dependent variables was assigned a residual error term (r1 and r2) and each of the observed variables was assigned a measurement error (e1 to e9) respectively. Finally, the four shop floor latent variables (SDO_1, WSR_2, I5S_3 and VSI_4) were depicted to have inter-correlation.
Model identification for model (a)
Once the model was specified, it was vital to identify the degrees of freedom before the the model estimation (see Table 5.12 in Section 5.3.3). As per the opinion of Rigdon ( 1994, p276), the model (a) was over-identified. As depicted in Table 7.2, the model contained 9 observed variables, hence it had 45 (calculated by 9×10/2) observations or distinct sample moments. Taking in to account the AMOS Parameter Summary, the hypothesised model (a) had 28 unfixed parameters (distinct parameters to be estimated). Thus, the hypothesised path model had 17 (calculated by 45-28) degrees of freedom (D.f) (Table 7.3).
Number of distinct sample moments: 45
Number of distinct parameters to be estimated: 28
Degrees of freedom (45 – 28): 17
Table 7.3 Computation of degrees of freedom (Hypothesised path model (a), AMOS Output)
In the next step statistical power (?) was obtained. As per recommendation of McQuitty (2004) (Ref. Table 5.14 in Section 5.3.3) the sample size achieved was adequate and the statistical power of the hypothesised path model (a) was ?;0.70 (high), as D.f. of the model was 17 and the sample size was 502
Model estimation for model (a)
After completing the model identification, the model estimation procedure was selected.). Tthe ULS, WLS and ADF were discarded as the sample size was less than 1000 (Ref. Section 5.3, Table 5.15). Since the variables violated the normality assumption, as identified in Section 6.2, the ML method, rather than the GLS method, was adopted for the estimation of parameters.
Model testing for model (a)
As discussed above the ML method was implemented to the model. Following Section 5.3.3, the three common testing indices: i) the parameter estimates with statistical significance level and standard errors; ii) the residuals; and iii) the model fit indices; were included to indicate the model fit.
Firstly, as presented below in the Table 7.4, only 5 paths had significant estimates (P15, P26, P35, P36 and P46, p?0.05, or ‘***’ which indicates p0.05). They indicated poor model fit (Wu, 2009).
Label Standardised Path Estimate Path Estimate S.E. C.R. P (Sign.)