I'm just learning about SEM (specifically basic path analysis models) and wondering if/when a technique like gradient descent is ever used in any of the estimations?
For example, at some point in path analysis you need to get estimates of the model parameters. I believe maximum likelihood is typically used for this, but could gradient descent be used instead? If so, what would be the function you're trying to minimize/maximize?
Later on in the process, once you have your parameters you calculate a model implied covariance matrix and compare it to one from your sample. Does gradient descent step in here as well? Or could it be used instead for both parameter estimation and evaluation of model fit?
I think my confusion stems from having a system of equations for calculating the values in the covariance matrix, and not understanding how gradient descent might handle the solving of those equations to get parameter values?