Conducting a three-level mediation analysis with the predictor (x) at level 3 and the mediator (m) at level 2 requires careful consideration of the modeling approach. I understand that you have already aggregated the mediator at the school level for the regression of m on x at level 3, while using the non-aggregated mediator for y on m at level 2. However, it's important to note that this approach may not be ideal and could potentially introduce issues in the analysis.

Instead of aggregating the mediator, a more appropriate approach would be to use multilevel structural equation modeling (MSEM) in Mplus to account for the nested structure of your data. Mplus provides the capability to specify mediation models at multiple levels using the MODEL command. Here's a general outline of how you can conduct a three-level mediation analysis in Mplus:

1. Data preparation:

- Organize your data in a nested format, with individuals (level 1) nested within classrooms (level 2) nested within schools (level 3).

- Ensure that all variables (x, m, and y) are correctly coded and formatted.

2. Specify the three-level data structure:

- Use the VARIABLE command in Mplus to define the variables and their levels of measurement.

- Use the CLUSTER command to specify the clustering structure of the data (e.g., individuals within classrooms and classrooms within schools).

3. Specify the mediation model:

- Define the model using the MODEL command. Specify the relationships among x, m, and y, including the mediation paths.

- Use the TYPE = TWOLEVEL RANDOM command to account for the multilevel structure of the data.

- Define the model equations, specifying the predictors and outcomes at their respective levels.

- Include the necessary direct and indirect paths in the model, representing the mediation effects.

- Make sure to account for the clustering at each level using appropriate commands (e.g., WITHIN, BETWEEN, or RANDOM statements).

4. Specify model constraints and estimation:

- Determine the specific constraints you want to impose on the model (e.g., equality constraints) and specify them using the MODEL CONSTRAINT command if necessary.

- Select an appropriate estimation method based on your data characteristics and research question. Mplus offers various estimation options, such as maximum likelihood (ML) or robust maximum likelihood (MLR).

5. Run the analysis:

- Execute the analysis in Mplus and review the output for model fit indices, parameter estimates, and significance levels.

- Assess the overall fit of the model using fit indices like chi-square, comparative fit index (CFI), Tucker-Lewis index (TLI), and root mean square error of approximation (RMSEA).

- Examine the estimated direct and indirect effects to evaluate the mediation hypotheses.

Keep in mind that this is a general outline, and you may need to modify it to fit your specific research question and data structure. It's also recommended to consult the Mplus user guide and relevant literature on multilevel mediation for more detailed guidance and examples.

mediation model

Using an aggregated mediator in a mediation model can be a reasonable approach in certain circumstances, but it depends on the specific context and assumptions of your analysis. Let's consider the pros and cons of using an aggregated mediator:

Pros:

1. Simplification: Aggregating the mediator at the school level reduces the complexity of the analysis, as you only need to specify the mediator once at the school level instead of at both the classroom and school levels.

2. Improved convergence: Aggregating the mediator can sometimes help with convergence issues that may arise in complex multilevel models, particularly if the sample size at the school or classroom level is small.

Cons:

1. Ecological fallacy: Aggregating the mediator at the school level assumes that the relationship between the predictor and mediator is similar across all individuals within the same school. This assumption may not hold if there is substantial within-school variability in the mediator-outcome relationship.

2. Loss of information: Aggregating the mediator discards the individual-level variability, potentially leading to a loss of information and reduced statistical power.

3. Violation of assumptions: Aggregating the mediator may violate the assumption of independence between the mediator and the outcome variable at the individual level, which is typically required for mediation analyses.

Considering these pros and cons, it's important to evaluate whether aggregating the mediator is justified in your specific research context. If the assumptions underlying the aggregation are reasonable and align with your theoretical framework, and if the benefits outweigh the limitations, then using the aggregated mediator may be an acceptable approach. However, it's always advisable to exercise caution and consider alternative approaches (e.g., multilevel modeling) if feasible and justifiable for your research question and data structure.

Mahesh Senadeera , thank you so mich for your very thorough answer!! This is really helpful. I will think the pros and cons for aggregating the mediator at level 3 through very thoroughly, but think that it may be possible in my specific model.

I will definitely conduct a multilevel SEM as the aggregation of the mediator is just to help with the problem that the mediator is both a predictor variable at level 2 (regression of outcome on mediator) and an outcome variable at level 3 (regression of mediator on predictor). It still remains a three-level model. The problem is that Mplus needs me to specify if the mediator is at level 2 or level 3, which I can't (as it is an outcome/predictor at both levels, as described above). This is why I decided to aggregate the mediator at level 3 for the regression of the mediator on the predictor at level 3 possible.