Based on your objectives, Moderation and Mediation Analysis using Regression Models would be the most appropriate statistical method. Here’s why:

Why Moderation and Mediation Analysis?

Direct Relationships:

Regression models can directly assess the relationships between:

Teacher EI and effectiveness.

Teacher effectiveness and student success.

Teacher EI and student success.

Moderation Analysis:

You can test whether one variable (e.g., teacher effectiveness) moderates the relationship between teacher EI and student success. Moderation analysis will determine if the strength or direction of the EI-student success relationship changes depending on levels of teacher effectiveness.

Simplicity and Clarity:

Compared to SEM, regression-based moderation and mediation analysis is simpler to implement, especially for studies with a limited sample size.

Statistical Tools:

Tools like the PROCESS macro for SPSS or R packages like lavaan and mediation make it easy to conduct such analyses.

Suggested Approach

Step 1: Analyze Direct Effects:

Perform separate regression analyses for:

Teacher EI → Teacher Effectiveness.

Teacher Effectiveness → Student Success.

Teacher EI → Student Success.

Step 2: Test Moderation:

Add an interaction term to the regression model (e.g., Teacher EI × Teacher Effectiveness) to assess moderation.

Example: Does the relationship between EI and student success depend on teacher effectiveness?

Step 3: Test for Mediation (Optional):

If you suspect teacher effectiveness mediates the relationship between EI and student success, mediation analysis can also be included.

You can use Structural Equation Modelling.

Suitable statistical methods include regression analysis (e.g., multiple regression) to examine the relationships between EI and the variables of interest, and structural equation modeling (SEM) to assess the direct and indirect effects. Additionally, ANOVA or MANOVA can be used to compare group differences if EI is categorized into levels.