Matrix representation of SEM

We saw path diagrams that allow for a conceptual representation of causal effects. However, to allow for computational solutions to SEM models based on data, a number of statisticians have developed different matrix representations of SEM models. There are numerous such representations, the most common of which are the LISREL model or the simple reticular action model (RAM). We will discuss two SEM packages in R here: the lavaan package and OpenMx. There is an older package called "sem", which was the first R package available on CRAN to perform SEM, which we will not actually discuss.

The lavaan package does not use any of the common matrix representations (though it uses something close to LISREL). OpenMx uses the RAM by default in its internal representation of path diagrams, but OpenMx also allows the user to customize a matrix representation. Various matrix representations largely achieve the same thing but differ in how they must be multiplied or added together...