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Mixed analytical and automatic differentiation

This way of specifying our model is not ideal, however, because now also the maximum likelihood loss function lives inside a SemFiniteDiff model, and this means even though we have defined analytical gradients for it, we do not make use of them.

A more efficient way is therefore to specify our model as a combined model with multiple loss terms:

ml_term = SemML(
    SemObservedData(data = data, specification = partable),
    RAMSymbolic(partable)
)

ridge_term = SemRidge(
    α_ridge = 0.01,
    which_ridge = params(ml_term)
)

model_ml_ridge = Sem(ml_term, ridge_term)

model_ml_ridge_fit = fit(model_ml_ridge)

The results of both methods will be the same, but we can verify that the computation costs differ (the package BenchmarkTools has to be installed for this):

using BenchmarkTools

@benchmark fit(model)

@benchmark fit(model_ml_ridge)