A set of statistical techniques used to estimate parameters about 1. fixed effects based on groups (i.e., mean differences and regressions) as well as 2. random effects based on individual differences (i.e., variance and covariances). A fixed effectamounts to something that remains the same if an experiment is repeated (e.g.,age, gender). A random effect issome entity than cannot be controlled and is likely to be different when anexperiment is carried out again (e.g., participants in the two experiments). Thereare arguments in favor preferring mixed-effect models over classical approachesto repeated ANOVA designs. These modelshave a number of advantages that make them preferable: they can apply to avariety of designs (e.g., balanced and unbalanced), they can more easilyaddress the problem of missing data (and thus can be readily extended tomultilevel models), if age is part of the design then it does not need to beconsistent across participants (e.g., whether an infant was followed-up at 6months and another at 8 months), and assumptions regarding sphericity orcompound symmetry are not required. There are a number of accessible texts that consider in more depth thestrengths and assumptions of mixed-effects.
See Analysis of variance (ANOVA), Compound symmetry, Multilevel modeling (MLM), Repeated measures analysis of variance, Sphericity assumption, Sphericity