Finding multilevel model level three residuals
Posted: Tue May 21, 2024 3:15 am
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.
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.