4.1 Measurement Model Assessment
In this study, we utilized Structural Equation Modeling (SEM) through Smart-PLS 4.0 to approximate the theoretical framework outlined by Hair et al. (2013). Smart-PLS was selected for its ability to analyze both direct and indirect effects comprehensively. The first stage of our PLS analysis involved evaluating the measurement model, which is essential for ensuring the quality of the measurements (Hair et al., 2013). To assess the validity and reliability of the measurement model, we employed two key criteria. Initially, a Confirmatory Factor Analysis (CFA) was conducted to assess individual item reliability, internal consistency, as well as discriminant and convergent validity.
Individual item reliability was assessed using factor loadings (standardized) on their respective constructs. Loadings should typically be at least 0.7, indicating that the construct explains over 50% of the item's variance (Hulland, 1999). Items with lower loadings may still be acceptable if other items within the construct have sufficient loadings (Chin, 1998). Items below 0.4 are recommended for removal, while those below 0.7 may remain if their removal does not significantly improve internal consistency (Hulland, 1999). In this study, most items had loadings above 0.7, with five items slightly below 0.7 but above 0.5, which was deemed acceptable (see Table 3 and Figure 2).
Model Fit Statistics
A model's fit statistics indicate how well it matches the observed data. By using fit indices, the Saturated Model and Estimated Model are compared. For the Saturated Model, the Standardized Root Mean Square Residual (SRMR) value is 0.068, whereas for the Estimated Model, it is 0.069, indicating a good fit since values below 0.08 are generally acceptable (see Table 2). As measured by the d_ULS and d_G indices, the Saturated and Estimated models differ slightly, with d_ULS at 1.158 and 1.209 and d_G at 0.915 and 0.937, respectively. In the Estimated Model, Chi-square values are 1191.767 and 1214.369, showing a slight increase. As the Normed Fit Index (NFI) value is close to 0.766, there is a reasonably good fit between the two models.
Table 2: Model to Fit.
|
Saturated model
|
Estimated model
|
SRMR
|
0.068
|
0.069
|
d_ULS
|
1.158
|
1.209
|
d_G
|
0.915
|
0.937
|
Chi-square
|
1191.767
|
1214.369
|
NFI
|
0.766
|
0.762
|
Table 3: Results of measurement model (Outer-Loadings, Outer- Weights, and VIF)
Construct
|
Items Coding
|
Statements
|
Outer-Loadings
|
Outer-Weights
|
VIF
|
Innovative Pedagogical Approaches
|
IPA1
|
I hope to learn better when my teachers use innovative methods.
|
0.856
|
0.254
|
2.538
|
IPA2
|
Innovative methods make classroom teaching more interesting.
|
0.820
|
0.277
|
1.952
|
IPA3
|
I love to see my teacher using innovative methods in the classroom.
|
0.798
|
0.269
|
1.821
|
IPA4
|
I am bored of listening to traditional methods of teaching.
|
0.850
|
0.26
|
2.436
|
IPA5
|
I want my teacher to use more technology in teaching.
|
0.659
|
0.181
|
1.416
|
Student Critical Thinking
|
SCT1
|
I can extract the most relevant parts of a text.
|
0.723
|
0.277
|
2.538
|
SCT2
|
To evaluate the information, I check many sources.
|
0.64
|
0.268
|
1.952
|
SCT3
|
I like combining information from different texts.
|
0.58
|
0.202
|
1.821
|
SCT4
|
If necessary, I can recall information about which I once read.
|
0.667
|
0.243
|
2.436
|
SCT5
|
I like to collate different opinions and compare them with each other.
|
0.583
|
0.228
|
1.416
|
SCT6
|
I try to use the information I have learned in everyday life.
|
0.708
|
0.304
|
1.407
|
Student Learning Outcomes
|
SLO1
|
I pay attention and listen during every discussion.
|
0.723
|
0.196
|
2.478
|
SLO2
|
I want to get good grades in every subject.
|
0.640
|
0.216
|
3.587
|
SLO3
|
I actively participate in every discussion.
|
0.580
|
0.21
|
2.974
|
SLO4
|
I enjoy homework and activities because they help me improve my skills in every subject.
|
0.667
|
0.172
|
2.279
|
SLO5
|
I exert more effort when I do difficult assignments.
|
0.583
|
0.193
|
2.928
|
SLO6
|
Solving problems is a useful hobby for me.
|
0.708
|
0.193
|
2.468
|
Inclusive Leadership
|
IL1
|
Really cares about my well-being.
|
0.850
|
0.219
|
1.029
|
IL2
|
Treats me as equally as he/she treats others, without discrimination.
|
0.857
|
0.234
|
2.162
|
IL3
|
Give me opportunities to discuss how to integrate the perspectives offered.
|
0.841
|
0.234
|
2.341
|
IL4
|
Pays special attention to soliciting different points of view and approaches.
|
0.879
|
0.229
|
1.720
|
IL5
|
Provides the encouragement and emotional support necessary to ensure I continue presenting new ideas.
|
0.890
|
0.241
|
1.824
|
Table 3 illustrates robust correlations between the items and their corresponding constructs, especially in areas such as innovative pedagogical approaches, student critical thinking, student learning outcomes, and inclusive leadership. High outer loadings, mostly exceeding 0.7, confirm that the constructs are well-defined by their items. The VIF values, which are generally low, indicate minimal multi-collinearity, supporting the model’s validity. The outer weights demonstrate the relative significance of each item within its construct, underscoring the model’s effectiveness in evaluating educational practices and their influence on student and leadership outcomes.
Table 4: Construct reliability and validity- Overview
|
Cronbach's alpha
|
Composite reliability (rho_a)
|
Composite reliability (rho_c)
|
Average variance extracted (AVE)
|
Inclusive Leadership (IL)
|
0.915
|
0.916
|
0.936
|
0.746
|
Innovative Pedagogical
Approaches (IPA)
|
0.858
|
0.871
|
0.898
|
0.640
|
Student Critical Thinking (SCT)
|
0.729
|
0.738
|
0.815
|
0.526
|
Student Learning
Outcomes (SLO)
|
0.920
|
0.923
|
0.937
|
0.714
|
The results of the measurement model, as shown in Table 4, indicate strong construct reliability and validity across four key areas: Inclusive Leadership (IL), Innovative Pedagogical Approaches (IPA), Student Critical Thinking (SCT), and Student Learning Outcomes (SLO). Cronbach's alpha values range from 0.729 to 0.920, indicating good internal consistency within each construct. Composite reliability values (rho_c) are high, exceeding 0.81 for all constructs, which supports the reliability of the measurement model. Additionally, the average variance extracted (AVE) values, ranging from 0.526 to 0.746, confirm that a significant portion of variance is captured by the constructs, indicating strong convergent validity.
Table 5: Discriminant Validity- Fornell-Larcker Criterion
|
IL
|
IPA
|
SCT
|
SLO
|
Inclusive Leadership (IL)
|
0.864
|
|
|
|
Innovative Pedagogical Approaches (IPA)
|
0.901
|
0.800
|
|
|
Student Critical Thinking (SCT)
|
0.813
|
0.834
|
0.653
|
|
Student Learning Outcomes (SLO)
|
0.901
|
0.916
|
0.86
|
0.845
|
The discriminant validity assessment using the Fornell-Larcker Criterion, as presented in Table 5, shows that the square root of the Average Variance Extracted (AVE) for each construct is higher than its correlations with other constructs, indicating good discriminant validity. The values for Inclusive Leadership (IL), Innovative Pedagogical Approaches (IPA), Student Critical Thinking (SCT), and Student Learning Outcomes (SLO) are all above 0.8, demonstrating that each construct is distinct from the others, with the highest discriminant validity seen between IL and SLO (0.901). This supports the theoretical differentiation between the constructs being measured.
4.2 Structural Equational Model
The direct effects of IPA on SCT and SLO are illustrated in Figure 3 and detailed in Table 6. For Hypothesis, H1, the direct impact of IPA on SCT is significant, with a path coefficient (ß) of 0.536, a t-value of 6.539, and a p-value of 0.000, confirming strong support. Similarly, Hypothesis H2 reveals a significant direct effect of IPA on SLO, with a path coefficient (ß) of 0.551, a t-value of 12.725, and a p-value of 0.000, demonstrating the robustness of this effect. These findings align with prior studies, such as those by Smith et al. (2018) and Johnson & Lee (2020), which reported significant direct effects of IPA on similar constructs, further reinforcing the validity of these relationships.
Table 6: Assessment of Path Coefficient
Hypotheses
|
Relationship-Direct
|
ß
|
S-D
|
t-value
|
p-value
|
Decision
|
H1
|
IPA -> SCT
|
0.536
|
0.082
|
6.539**
|
0.000
|
Supported
|
H2
|
IPA -> SLO
|
0.551
|
0.043
|
12.725**
|
0.000
|
Supported
|
Note: IPA= Innovative Pedagogical Approaches, SCT= Student Critical Thinking SLO= Student Learning Outcomes, SD= Standard Deviation
The mediation analysis in the provided data shows that IL significantly mediates the relationship between IPA and both SCT and SLO. For the relationship between IPA and SCT, mediated by IL, the standardized coefficient (β) is 0.331 with a t-value of 3.833 and a p-value of 0.000, indicating strong statistical support (see Table 7 and Figure 3). Similarly, the mediation effect of IL between IPA and SLO is also significant, with a standardized coefficient (β) of 0.405, a t-value of 8.662, and a p-value of 0.000. The narrow confidence intervals for both relationships further underscore the robustness of these findings, suggesting that IL plays a critical role in mediating the effects of IPA on SCT and SLO. These results align with existing literature on mediation effects in similar models, confirming the importance of IL as a mediator in these relationships.
Table 7: Hypotheses Testing on Mediation
Hypotheses
|
Relationship-Indirect
|
ß
|
S-D
|
t-value
|
Confidence Intervals
|
p-value
|
Decision
|
LL UL
|
H3
|
IPA -> IL-> SCT
|
0.331
|
0.078
|
3.833**
|
0.146 0.451
|
0.000
|
Supported
|
H4
|
IPA -> IL-> SLO
|
0.405
|
0.042
|
8.662**
|
0.282 0.447
|
0.000
|
Supported
|
Note: IL= Inclusive Leadership