A mixed model is a statistical model containing both fixed effects and random effects. These models are useful in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units or where measurements are made on clusters of related statistical units. Due to their advantage to deal with missing values, mixed effect models are often preferred over the traditional approaches such as repeated measures ANOVA.
The matrix notation a mixed model can be represented as is:
y = Xβ + Zμ + Ɛ
y is a vector of observations
β is a vector of fixed effects
μ is a vector of random effects
Ɛ is a vector of IID random error terms
X and Z are matrices of regressors relating the observations y to β and μ