Is mixed ANOVA the same thing as multilevel modeling? If not, how do they differ? I am trying to compare inter- and intra-individual differences and not sure which one is the better approach.
I don't have enough points to only respond in a comment, so I'll post as an answer.
I think that mixed ANOVA is something of a special case of multilevel modeling. Both can tell you about intra- and interindividual differences. One clear difference is that multilevel modeling uses maximum likelihood estimation, which gives you an advantage if you have missing data in your repeated-measure variable: mixed ANOVA will remove any incomplete cases from the analysis, whereas multilevel modeling makes use of all available information without needing to resort to listwise deletion (see Enders, 2011). Multilevel modeling won't give you an advantage if you have missing data on your predictors, however, in which case listwise deletion is also performed.
On the other hand, mixed ANOVA might be more accurate for small sample sizes. Maas & Hox (2005) showed that accuracy of parameter estimates (particularly of random effects, not so much of fixed effects) in multilevel modeling depends on sample size at level 2, but not so much at level 1; in your case, this would mean that you should probably hope for 50+ individuals in your sample. (FYI, if you're opting for multilevel modeling, more often than not you should use restricted maximum likelihood [REML] instead of full information maximum likelihood [FIML], particularly if you have small sample sizes. For large sample sizes, the two are equivalent, but for small sample sizes, restricted maximum likelihood is less biased. Be careful--REML is the default in lme4 and nlme in R, but FIML is the default in software like SAS, SPSS, and Mplus.)
If you have a number of missing data in your repeated-measure variable and have an adequate sample size, I would go with multilevel modeling.
Enders, C. K. (2011). Missing not at random models for latent growth curve analyses. Psychological Methods, 16, 1-16.
Maas, C. J. M., & Hox, J. J. (2005). Sufficient sample sizes for multilevel modeling. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 1, 86-92.