Data (unit) level | The level of individual observations (data, units of the analysis) and the most basic or lowest level. The unexplained variability at the data level is expressed as the residual variance |

Data-level predictor | Explanatory or independent variable that varies at the data level, such that different observations take different values independent of any grouping level |

Factor | Categorical predictor (that can be fitted as a fixed or random effect) |

Fixed effect | Effects that are estimated at each factor level independently of all other factor levels, that is, only observations within each level contribute to the estimate. Factors can be fitted as fixed effects, but can still be conceptually random in the sense that they represent a random sample of levels rather than distinct treatments (e.g. block effects) |

Group-level predictor | Explanatory variable that varies at the grouping level, such that all observations within the same group take the same value |

Grouping level | Clusters of observations which constitute a hierarchical level above the data level. For example, individuals (data level: replicate observations per individual) or groups of individuals (data level: single observations per individual) |

Groups | Used in the statistical sense of any grouping (or clustering) of related observations. For example, individuals, species, blocks, plots |

Hyperparameter | An estimator at a higher hierarchical level that controls estimates at the group level. In classical mixed models, the group-level variance is a hyperparameter that estimates the variance of group-level means, which are themselves parameters of the model. Both the group-level variance and the group-level means are estimated from the data. (The term ‘hyperparameter’ has a second meaning in a Bayesian context that differs from the definition given here.) |

Main effect/marginal effect | The effect of a categorical predictor on the response when moving from one treatment level to another while holding all other predictors constant. The constancy of the marginal effect across values of other predictors distinguishes marginal effects from interaction effects that vary conditional on values of (one or more) other predictors |

Random effect | Effects that are estimated at each factor level, but where the distribution of the estimates is explicitly modelled by hyperparameters. The variance of the random effects can be considered the ‘unexplained’ variance at this level in the sense that the detailed causes of such random-effect variance are unknown. Estimates are influenced by shrinkage towards the population mean |

Random slopes | Most random effects that are fitted in mixed models are random intercept effects, that is, mean response value are allowed to vary among groups. Random slopes represent an interaction between a fixed factor and a random factor. Significant random-slope variance means that the magnitude of the between-group variance varies with values of a covariate or, equivalently, that the effect of a covariate varies among groups |

Shrinkage | A property of random-effect estimation in mixed models. Group means are not only influenced by observations from a particular group, but also by the population mean, such that the random-effect estimates for each group are closer to the population mean than the mean of the observations from a particular group (i.e. they are ‘shrunken’ towards the population mean). The effect is more pronounced for groups with a small number of observations |

Treatment | An experimental manipulation that is of primary interest in a study. We use the term in a wider sense, including also factors that are not under direct control of the experimenter (e.g. breeding status of an individual), therefore covering also quasi-experimental designs (Ryan 2007). Treatments will typically be fitted as fixed factors |