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mixed_differentiation.md

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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 an ensemble model:

model_ml = Sem(
    specification = partable,
    data = data,
    loss = SemML
)

model_ridge = SemFiniteDiff(
    specification = partable,
    data = data,
    loss = myridge
)

model_ml_ridge = SemEnsemble(model_ml, model_ridge)

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)