Multilevel models (also hierarchical linear models, nested models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level. These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. Although not a new idea, they have been much more popular following the growth of computing power and availability of software.
Multilevel models are particularly appropriate for research designs where the data for participants is organized at more than one level (i.e., nested data). The units of analysis are usually individuals (at a lower level) who are nested within contextual/aggregate units (at a higher level). While the lowest level of data in multilevel models is usually an individual, repeated measurements of individuals may also be examined. As such, multilevel models provide an alternative type of analysis for univariate or multivariate analysis of repeated measures. Individual differences in growth curves may be examined (see growth model). Furthermore, multilevel models can be used as an alternative to ANCOVA, where scores on the dependent variable are adjusted for covariates (i.e., individual differences) before testing treatment differences. Multilevel models are able to analyze these experiments without the assumptions of homogeneity-of-regression slopes that is required by ANCOVA.
Multilevel models can be used on data with many levels, although 2-level models are the most common. The dependent variable must be examined at the lowest level of analysis.
Read more about Multilevel Model: Level 1 Regression Equation, Level 2 Regression Equation, Types of Models, Assumptions, Statistical Tests, Statistical Power, Alternative Ways of Analyzing Hierarchical Data, Error Terms
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... Multilevel models have two error terms, which are also known as disturbances ... The individual components are all independent, but there are also group components, which are independent between groups but correlated within groups ...
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