Hierarchical models, also called multi-level models, are models in which processes occur at different levels. The easiest way to imagine such models is by thinking of two or more coupled mathematical equations. Typical reasons to have hierarchical models is because we have a process described by a traditional regression, plus an observation model, because we cannot observe every outcome with equal probability. In this case, the two hierarchical levels are the regression and on top of that the observation model.
Mixed models
Occupancy models
State-space models
http://www.jstatsoft.org/v41/i04/paper
Structural Equation Models (SEMs)
Structural equation models (SEM) are a special class of hierarchical models. Starting initially only as correlation summaries for normally distributed variables, SEMs have branched out substantially and are now a pretty broad array of methods and software.
Terminology
- exogenous variables is not influenced by other variables. Opposite is an endogenous variable
- a manifest variable is observed directly (also called indicator variable)
- a latent variable is not observed directly
- moderation - something like an interaction, i.e. that one variable incfluences the effect of two other variables on each other.
Further links
Courses
An Introduction to Structural Equation Modeling for Ecology and Evolutionary Biology http://jarrettbyrnes.info/ubc_sem/
Statistics for Psychosocial Research: Structural Models http://ocw.jhsph.edu/courses/structuralmodels/lectureNotes.cfm
Examples / Papers
- http://www.consevol.org/pdf/Books/Chapter%208%20Modern%20Phylogenetic%20Comparative%20Methods%20book.pdf
- http://www.esajournals.org/doi/pdf/10.1890/08-1034.1
- http://www.esapubs.org/archive/ecol/E090/028/suppl-1.htm
- [http://www.imachordata.com/space-and-sems-2/] (http://www.imachordata.com/space-and-sems-2/)