= Structural Equation Modeling = '''Structural equation modeling''' ('''SEM''') is a modeling framework that makes use of multiple prediction equations. It is also also known as '''covariance structure analysis''', '''analysis of moment structures''', or '''analysis of linear structural relationships'''. <> ---- == Description == SEM is used for measurement error adjustment. The first component is the '''measurement model''', which is essentially a [[Statistics/FactorAnalysis|CFA]]. Terminology is also common between the two, e.g. '''factors''', '''factor loadings''', '''indicators''', and so on. The most important distinction is that a causal direction is assumed; note the arrows below: {{attachment:path.png}} This is equivalent to a formulation like: * ''X = α,,1,, + β,,1,,x,,1,, + e,,1,,'' * ''X = α,,2,, + β,,2,,x,,2,, + e,,2,,'' * ''X = α,,3,, + β,,3,,x,,3,, + e,,3,,'' The second component is the '''structural model''' which specifies the [[Statistics/MediationAnalysis|mediation]] relationship of the latent factors. If a factor is predicted by other variables in the system, it is '''endogenous'''; otherwise it is '''exogenous'''. The simplest formulation of a structural model might be ''Y = α,,Y,, + β,,Y,,X + e,,Y,,'', but... * there can be multiple predictive factors, e.g. `Y ~ X + Z` * the outcome can itself have a measurement model, e.g. `Y ~= y1 + y2 + y3` Most model estimation strategies require assuming: 1. a uniform variance for the outcome construct's error, i.e. `e,,Y,,`. 2. a uniform variance for the latent constructs, e.g. `X` See [[https://www.youtube.com/watch?v=NOWdrfQVWAI&t=2045s]] for an demonstration of why assumptions are required, and how many are needed. ---- CategoryRicottone