Finding multilevel model level three residuals

[tetroupploy]

Dear all,

Thank you for reading my conundrum. For my PhD research, I am computing variables using the ecometric technique (Raudenbusch & Sampson, 1999). This requires fitting a three-level multilevel item response model (items nested in subjects nested in neighborhoods) and extracting the level 3 residuals for use in further studies.

I discovered how to calculate level-2 residuals on the Bristol Centre for Multilevel Modelling's website. That is, multiplying the average 'raw' level-1 residuals by a shrinkage factor (see reference above for a detailed explanation), which takes into account the level-2 and level-1 variance, as well as the number of observations in each group. However, I am not sure how this approach applies to the extraction of level-3 residuals. My naive impulse would be to replace everything in the equations with the corresponding values from the upper level. To compute the shrinkage factor, take the average of the (adjusted, I assume?) level-2 residuals, the level-3 variance, and the number of level-2 observations. However, I suppose the solution is more sophisticated. Could one of you connect me to a resource that contains the answer to this question, or could you explain your thoughts on this calculation?

TL;DR: I'd like to calculate level-3 residuals from my multilevel model. I want to know how to calculate the shrinkage factor to alter the 'raw' average residuals at the third level.

I hope anyone can take the time to assist me; thank you in advance! I am happy to share more details upon request.

Best,

Kevin Wittenberg attends Utrecht University.

[ChrisCharlton]

If you're using MLwiN then you can request residuals at any level using the "Residuals" window (see chapter 3 of the MLwiN user guide: https://www.bristol.ac.uk/cmm/media/sof ... al-web.pdf), or by using RLEV command in combination with the RESI command.

[auditanything]

The shrinkage factor for level 3 residuals is similar to that for level 2 residuals but includes level 3 and level 2 variance. Unfortunately I can't write the formula out for you here. I can't edit in the comments.