Calculating level-three residuals in multilevel model
Posted: Tue Jun 14, 2022 11:57 am
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
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