than others. Bayesian nonlinear mixed-effects model Multilevel modeling is frequently used in diverse applications and it can be formulated by the Bayesian framework. Particularly, Bayesian nonlinear mixed-effects models have recently received significant attention. A basic version of the Bayesian nonlinear mixed-effects models is represented as the following three-stage: Stage 1: Individual-Level Model Stage 2: Population Model Stage 3: Prior Here, denotes the continuous response of the -th subject at the time point , and is the -th covariate of the -th subject. Parameters involved in the model are written in Greek letters. is a known function parameterized by the -dimensional vector . Typically, is a `nonlinear' function and describes the temporal trajectory of individuals. In the model, and describe within-individual variability and between-individual variability, respectively. If Stage 3: Prior is not considered, then the model reduces to a frequentist nonlinear mixed-effect model. A central task in the application of the Bayesian nonlinear mixed-effect models is to evaluate the posterior density: The panel on the right displays Bayesian research cycle using Bayesian nonlinear mixed-effects model. A research cycle using the Bayesian nonlinear mixed-effects model comprises two steps: (a) standard research cycle and (b) Bayesian-specific workflow. Standard research cycle involves literature review, defining a problem and specifying the research question and hypothesis. Bayesian-specific workflow comprises three sub-steps: (b)–(i) formalizing prior distributions based on background knowledge and prior elicitation; (b)–(ii) determining the likelihood function based on a nonlinear function ; and (b)–(iii) making a posterior inference. The resulting posterior inference can be used to start a new research cycle. See also Hyperparameter Mixed-design analysis of variance Random effects model Nonlinear mixed-effects model Restricted randomization References Further reading This concentrates on education. Includes SAS code External links Centre for Multilevel Modelling Analysis of variance Regression models