10 Multilevel models

Psychological data often contains natural groupings. In intervention research, multiple patients may be treated by individual therapists, or children taught within classes, which are further nested within schools; in experimental research participants may respond on multiple occasions to a variety of stimuli.

Although disparate in nature, these groupings share a common characteristic: they induce dependency between the observations we make. That is, our data points are not independently sampled from one another.

When data are clustered int his way then multilevel, sometimes called linear mixed models, serve two purposes:

  1. They overcome limitations of conventional models which assume that data are independently sampled (read a more detailed explanation of why handling non-independence properly matters)

  2. They allow us to answer substantive questions about sources of variation in our data.

Repeated measures Anova and beyond

RM Anova is another technique which relaxes the assumption of independent sampling, and is widely used in psychology: it is common that participants make repeated responses which can be categorised by various experimental variables (e.g. time, condition).

However RM Anova is just a special case of a much wider family of models: linear mixed models, but one which makes a number of restrictions which can be invonvenient, inefficient, or unreasonable.

Substantive questions about variation

Additionally, rather than simply ‘managing’ the non-independence of observations — treating it is a kind of nuisance to be eliminated — mixed models can allow researchers to focus on the sources of variation in their data directly.

It can be of substantive interest to estimate how much variation in the outcome is due to different levels of the nested structure. For example, in a clinical trial researchers might want to know how much influence therapists have on their clients’ outcome: if patients are ‘nested’ within therapists then multilevel models can estimate the variation between therapists (the ‘therapist effect’) and variation ‘within’ therapists ( i.e. variation between clients).