Structural Equation Modeling - Data Analysis and Results

Chapter 4: Data Analysis and Results

4.7 Structural Equation Modeling

Figure 8: Suggested structural equation model 4.7.2 Regression Coefficients

The suggested research hypotheses (direct effects) were tested through regression coefficients analysis. Regression coefficients were tested for statistical significance i.e. test the hypothesis that the regression coefficient is equal to 0 i.e. β = 0. Regression coefficients indicate the nature of the relationship between any two categories of variables in the SEM model. Unlike in linear regression, SEM provides the regression coefficients for all relationships, as well as the statistical significance of those relationships. As a result, in the process of analyzing, the researcher had to identify the regression relationships that are relevant to the analysis, and report that based on the output. Further details will be provided in Section 4.8.1 of this study.

4.7.3 Statistical Analysis

Statistical analysis was performed using AMOS v 22. Maximum likelihood was used to estimate the model parameters. The covariance matrix was used for model construction as demonstrated in the following Sections.

4.7.4 The Causal Model

The process of fitting the model in order to test the direct, mediation and moderation effects based on the hypothesis stated in Section 4.6 is outlined hereunder.

The model shows the relationships among the variables as discussed in the literature review chapter of this study. A number of measures have been taken in order to test the relationships. First, error terms were included for two variables, ZOT and ZOID, in order to test for the direct effects. Additional moderation effects that are not included directly in the hypothesis testing processes were added, namely the moderating effects of MCI1 on the relationship between MS (which is represented by the variable ZECSBxMCI1 in the model), and the ECSB on the relationship between MCI2 and MS (which is represented by the variable ZECSBxMCI2 in the model). The output is shown in Figure 9.

Figure 9: Proposed structural model (standardized loadings) 4.7.5 Structural Model Fit

Model fit was assessed using the following measures: CFI, TLI, Cmin, RMSEA, RMSEA upper 90% CI, and SRMR. The cut-off values suggested were used to assess the model fit. These are included in Table 15, which shows the acceptable levels.

The structural model fit is based on six of the eight factors discussed earlier, as shown hereunder. Model fitness is determined by the fact that all values are above the acceptable level. Results in Table 15 hereunder shows that the model is a goodness of fit.

Table 15: Model fitness indices

Measure Value Acceptable value

CFI 0.919 0.906

TLI 0.913 ≥ 0.9

RMSEA 0.061 0.06

RMSEA upper 90% CI 0.066 0.08

SRMR 0.035 <0.05

Cmin (X²/df) 2.06 <5

4.7.6 Variables Summary

A summary of the variables utilized in the moderation (interaction) analysis are as shown in Table 16. A total of 20 variables were used in the models, with 4 error terms included in the analysis.

Table 16: Number of variables used in interaction testing

Type of variables Quantity

Number of variables in your model 20

Number of observed variables 16

Number of unobserved variables 4

Number of exogenous variables 16

Number of endogenous variables 4

4.7.7 ML Discrepancy (Implied vs Sample)

The provided discrepancy function provides the conformity between observed data and the structural equation model as a measure of goodness of fit. The difference with observed mean was at d = 7.83, which is close to the value of 8 argued previously.

The maximum likelihood for the default model, which is part of the bootstrap distributions is shown in Table 17.

Table 17: Maximum likelihood output for the bootstrap distributions Sample Bootstrap distributions

1070.903 |*

1181.175 |*

1291.448 |*

1401.720 |***

1511.993 |********

1622.265 |***************

1732.538 |*******************

N = 10000 1842.810 |********************

Mean = 1807.584 1953.083 |****************

S. e. = 2.006 2063.356 |**********

2173.628 |*****

2283.901 |**

2394.173 |*

2504.446 |*

2614.718 |*

4.7.8 Regression Weights for Mediation and Moderation

The regression weights, shown in Table 18, indicate the effects between the all pairs of variables in the model, as included in SPSS AMOS. The output also indicates the standard errors and the statistical significance of the relationships.

Table 18: Regression weights for all the relationships in the model

Variables Estimate S.E. C.R. P

ZOT <--- ZPOS 0.541 0.041 13.206 ***

ZOID <--- ZEPDM 0.292 0.058 5.073 ***

ZOT <--- ZMCI1x 0.31 0.031 10.084 ***

ZOID <--- ZMCI1x 0.139 0.043 3.222 0.001

ZOT <--- ZMCI2x 0.113 0.031 3.664 ***

ZOID <--- ZMCI2x -0.269 0.043 -6.218 ***

ZOT <--- POSxMCI2 -0.036 0.04 -0.913 0.361

ZOID <--- POSxMCI1 0.034 0.062 0.551 0.582

ZOT <--- EPDMxMCI1 -0.064 0.045 -1.406 0.16

ZOID <--- EPDMxMCI2 0.013 0.056 0.228 0.819

ZOID <--- POSxMCI2 0.05 0.056 0.885 0.376

ZOT <--- EPDMxMCI2 0.032 0.04 0.813 0.416

ZOT <--- ZEPDM 0.048 0.041 1.163 0.245

ZOID <--- ZPOS 0.612 0.058 10.618 ***

ZOT <--- POSxMCI1 0.034 0.044 0.767 0.443

ZOID <--- EPDMxMCI1 -0.104 0.064 -1.624 0.104

ZECSB <--- ZOT 0.183 0.087 2.109 0.035

ZECSB <--- ZOID 0.323 0.061 5.281 ***

ZECSB <--- ZEPDM 0.316 0.054 5.839 ***

ZECSB <--- ZPOS 0.032 0.067 0.476 0.634

ZECSB <--- ZMCI1x 0.157 0.045 3.448 ***

ZECSB <--- ZMCI2x -0.073 0.045 -1.623 0.105

ZECSB <--- OTxMCI1 0.032 0.055 0.588 0.557

ZECSB <--- OTxMCI2 0.118 0.042 2.778 0.005

ZECSB <--- OIDxMCI2 -0.07 0.047 -1.496 0.135

ZECSB <--- OIDxMCI1 -0.02 0.066 -0.306 0.76

ZMS <--- ZECSB 0.2 0.055 3.667 ***

ZMS <--- ZOID -0.094 0.048 -1.943 0.052

ZMS <--- ZOT 0.755 0.056 13.456 ***

ZMS <--- ZECSBxMCI2 0.123 0.042 2.944 0.003

ZMS <--- ZECSBxMCI1 -0.058 0.037 -1.549 0.121

4.7.9 Correlations

The correlation matrix hereunder shows the extent to which the pairs of the variables in the moderation analysis influence one another. Although the statistical significance of the correlation is not tested under AMOS, the correlation output indicates the extent to which the change in one pair of variables influence another pair.

This dimension of the analysis is integral in indicating which pairs of variables change in similar ways. As shown hereunder (Table 19), there is a weak level of correlation between OIDxMCI2 and OIDxMCI1 (R=0.189), but a strong level of correlation between OTxMCI1 and OIDxMCI1 (R=0.858). The rest of the results are included in the Table 19.

Table 19: Correlation matrix for the moderation analysis

Variables Estimate S.E. C.R.

OIDxMCI2 <--> OIDxMCI1 0.201 0.025 7.961

OTxMCI2 <--> OIDxMCI2 0.735 0.071 10.383

OTxMCI1 <--> OIDxMCI1 1.088 0.097 11.242

POSxMCI1 <--> EPDMxMCI1 0.99 0.089 11.093

POSxMCI2 <--> EPDMxMCI2 0.722 0.067 10.703

ZPOS <--> ZEPDM 0.803 0.076 10.595

ZMCI1x <--> ZMCI2x 0.613 0.069 8.848

POSxMCI2 <--> POSxMCI1 0.196 0.025 7.788

POSxMCI2 <--> OTxMCI2 0.224 0.029 7.692

ZECSBxMCI2 <--> ZECSBxMCI1 0.58 0.067 8.67

4.7.10 Covariance

The covariance matrix for the mediation and moderation analysis is as shown in Table 20.

Table 20: Covariances matrix