One of the advantages of using multilevel models is their tolerance to heterogeneity of variances between groups (or points in time for multilevel models of change). And one of the main problems with having unequal sizes between groups is that this inequality can create heterogeneous variance.
I suspect that this means that multilevel models are more tolerant to differences in sample sizes than, say, ANOVAs. However, does any know how tolerant they are? I've looked around, but can't find good guidelines or suggestions for handling unequal sample sizes in multilevel models?
For example, how unequal is too unequal? Does it affect other assumptions or tests, e.g., does having more of the variance--homo- or heterogeneous--come from one group and not the other affect interpreting results?
Thanks
Hello
Kindly look at this paper ( Sufficient Sample Sizes for Multilevel Modeling), where simulation study is used to determine the influence of different sample sizes at the group level on the accuracy of the estimates (regression coefficients and variances) and their standard errorsand the influence of other factors .
http://www.joophox.net/publist/methodology05.pdf
And addition to this paper (Power and sample size in multilevel modeling) which was discussed sample size determination in multilevel designs
https://pdfs.semanticscholar.org/a769/1eb67c5806e154da58a74f7b1a1bc9ccb58a.pdf
Good Luck
Sorry but your question is very unclear; multilevel modelling can handle imbalanced data structure eg individuals at level 2 with a different number of time-occasioned observations at level 1 (under relatively forgiving MAR assumptions) and can explicitly model heterogeneity at the individual level and at the occasion level simultaneously.
You might like to try a course to appreciate fully these issues eg free online lemma course at Bristol which you can follow in R, MLwin and Stata.
http://www.bristol.ac.uk/cmm/learning/online-course/
and these resources consider power
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#datadesign
A lot will depend on what you mane by groups that is whether the classification is treated as fixed ( e g binary sex) or random ( eg schools at level 2).
Thank you both for your excellent answers.
You are right, Kelvyn, that my question was quite ambiguous--especially given the abilities of MLMs to handle hetergeneity and different numbers of waves of data for level 1 (within-subject) data.
My question was that which Saleh was nonetheless able to answer about their robustness to small or very divergent sample sizes, given that both of these conditions can affect the quality of predictions made in any model. (My current situation is indeed in variance between the number of students in classes and the number of classes in cities--not the number of waves in students.)
Most of my knowledge of MLMs comes from Singer & Willet's very readable Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence (https://global.oup.com/academic/product/applied-longitudinal-data-analysis-9780195152968?q=9780195152968&lang=en&cc=us)
but increasing my understanding, e.g., through those online courses/resources should help.
Thanks again.
- Badges
- Science topic
- Similar topics
- Philosophy
- Esthetics
- Interpretation