ABSTRACT
This chapter provides a more detailed description of the different types of fixed and random effects available in integrated nested Laplace approximation (INLA). Random effects are often adopted to take into account variation produced by variables in the model that are not our primary object of study. For example, in a study to investigate the effect of different irrigation systems on plant growth, measurement may include the type of irrigation, type of soil and variables associated with the trees, such as a numerical identifier of the tree and age. The list of random effects implemented in INLA is quite rich. In general, iid random effects are not suitable to model complex covariate structures that often appear in experimental design. For this reason, INLA provides a number of generic specifications for random effects, in addition to some specific ones. Random walks of order one and two are also available as latent effects in INLA.
