Calculating level-three residuals in multilevel model

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KevinWittenberg
Posts: 1
Joined: Tue Jun 14, 2022 8:11 am

Calculating level-three residuals in multilevel model

Post by KevinWittenberg »

Dear all,

Thanks for reading through my conundrum. For my PhD research, I am calculating variables based on the ecometric approach (Raudenbusch & Sampson, 1999). This basically entails that I fit a three-level multilevel item response model (items nested in subjects nested in neighbourhoods) and I want to extract the level 3 residuals from this model to use in further analyses.

From the website of the bristol centre for multilevel modelling, I have already found how to calculate level-2 residuals. That is, multiplying the average 'raw' level-1 residuals by a shrinkage factor (see reference above for detailed explanation), which uses the level-2 and level-1 variance, as well as the number of observations per group. However, I am uncertain how this approach generalizes to the extraction of level-3 residuals. My naive instinct would be to replace everything in the formula with the corresponding values of the higher level. That is, using the average of the (adjusted I would imagine?) level-2 residuals, the level-3 variance, and the number of level-2 observations to calculate the shrinking factor. However, I can imagine that the solution is a little more sophisticated. Could one of you direct me to a resource that has the answer to this question, or could you explain to me what your insight is with regard to this calculation?

TL;DR: I want to calculate level-3 residuals from my multilevel model. Specifically, I need to know how to calculate the shrinkage factor to adjust the 'raw' average residuals at the third level.

I hope anyone can take the time to help me out, thanks in advance! I gladly provide more information upon request.

Best,

Kevin Wittenberg
Utrecht University
ChrisCharlton
Posts: 1348
Joined: Mon Oct 19, 2009 10:34 am

Re: Calculating level-three residuals in multilevel model

Post by ChrisCharlton »

If you are using MLwiN then the residuals returned from the Model>Residuals menu are already shrunken (see chapter 3 of the MLwiN User's Guide). If you need an unshrunken version then the REFLATE command (see the MLwiN on-line help) is provided to calculate this, and more details of the formula used are provided in chapter 17.
grippingfossil
Posts: 9
Joined: Fri Jan 13, 2023 2:58 am

Re: Calculating level-three residuals in multilevel model

Post by grippingfossil »

Thanks ChrisCharlton, basket random
I can solve my issue.
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