model.md
In bsem: Bayesian Structural Equation Models

outer model (blocks): Xp × n = αp × kλk × n + εp × n where p is the number of variables (features), k is the number of latent factors and n is the sample size. X is the data matrix with variables in the rows and sample elements in the columns, α • × j is the column vector of loadings for the jth* latent variable and λj × • is the row vector of scores for the j*th unobserved variable, j = 1, …, k.

Normality and independence are assumed for the errors as εij ∼ N(0, σi2), for i = 1, …, p.
inner model:

paths:

**λ**<sub>j × • </sub> = **β**<sup>⊤</sup>**λ**<sup>( − j)</sup> + ν <br>
where **β** is a vector of constant coefficients and
**λ**<sup>( − j)</sup><sub>(k − 1) × n</sub> represent a subset of the matrix of scores, i.e. at least excluding the j<sup>*t**h*</sup> row scores.<br>
The error assumes standard normal distribution.

exogenous: Yl × • = γ0 + γ⊤λ + ξ
```
where l is the number of exogenous variables, **γ** is a vector of constant coefficients and
**γ**<sub>**0**</sub> is the intercept.
```
λk × n is the matrix of scores and the error assumes ξlj ∼ N(0, τl2), for j = 1, …, n.