StructuralEquationModels · alyst · Mar 22, 2025 · Mar 22, 2025 · Mar 22, 2025 · Mar 22, 2025
diff --git a/Project.toml b/Project.toml
@@ -8,6 +8,7 @@ DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 LazyArtifacts = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
 LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -30,6 +31,7 @@ StenoGraphs = "0.2 - 0.3, 0.4.1 - 0.5"
 DataFrames = "1"
 Distributions = "0.25"
 FiniteDiff = "2"
+InteractiveUtils = "1.11.0"
 LineSearches = "7"
 NLSolversBase = "7"
 NLopt = "0.6, 1"

diff --git a/docs/make.jl b/docs/make.jl
@@ -1,7 +1,14 @@
-using Documenter, StructuralEquationModels
+using Documenter, StructuralEquationModels, NLopt, ProximalAlgorithms, ProximalOperators
+
+SEM = StructuralEquationModels
+SEMNLOptExt = Base.get_extension(StructuralEquationModels, :SEMNLOptExt)
+SEMProximalOptExt = Base.get_extension(StructuralEquationModels, :SEMProximalOptExt)
 
 makedocs(
     sitename = "StructuralEquationModels.jl",
+    modules = [
+        SEM, SEMNLOptExt, SEMProximalOptExt,
+    ],
     pages = [
         "index.md",
         "Tutorials" => [

diff --git a/docs/src/developer/optimizer.md b/docs/src/developer/optimizer.md
@@ -1,64 +1,74 @@
 # Custom optimizer types
 
-The optimizer part of a model connects it to the optimization backend. 
-Let's say we want to implement a new optimizer as `SemOptimizerName`. The first part of the implementation is very similar to loss functions, so we just show the implementation of `SemOptimizerOptim` here as a reference:
+The optimizer part of a model connects it to the optimization backend.
+Let's say we want to implement a new optimizer as `SemOptimizerMyopt`.
+The first part of the implementation is very similar to loss functions,
+so we just show the implementation of `SemOptimizerOptim` here as a reference:
 
 ```julia
 ############################################################################################
 ### Types and Constructor
 ############################################################################################
-mutable struct SemOptimizerName{A, B} <: SemOptimizer{:Name}
+struct SemOptimizerMyopt{A, B} <: SemOptimizer{:Myopt}
     algorithm::A
     options::B
 end
 
-SemOptimizer{:Name}(args...; kwargs...) = SemOptimizerName(args...; kwargs...)
+SemOptimizer(Val{:Myopt}, args...; kwargs...) = SemOptimizerMyopt(args...; kwargs...)
 
-SemOptimizerName(;
+SemOptimizer_impltype(::Val{:Myopt}) = SemOptimizerMyopt
+
+SemOptimizerMyopt(;
     algorithm = LBFGS(),
     options = Optim.Options(; f_reltol = 1e-10, x_abstol = 1.5e-8),
     kwargs...,
-) = SemOptimizerName(algorithm, options)
+) = SemOptimizerMyopt(algorithm, options)
+
+struct MyOptResult{O <: SemOptimizerMyopt} <: SEM.SemOptimizerResult{O}
+    optimizer::O
+    ...
+end
 
 ############################################################################################
 ### Recommended methods
 ############################################################################################
 
-update_observed(optimizer::SemOptimizerName, observed::SemObserved; kwargs...) = optimizer
+update_observed(optimizer::SemOptimizerMyopt, observed::SemObserved; kwargs...) = optimizer
 
 ############################################################################################
 ### additional methods
 ############################################################################################
 
-algorithm(optimizer::SemOptimizerName) = optimizer.algorithm
-options(optimizer::SemOptimizerName) = optimizer.options
+options(optimizer::SemOptimizerMyopt) = optimizer.options
 ```
 
-Note that your optimizer is a subtype of `SemOptimizer{:Name}`, where you can choose a `:Name` that can later be used as a keyword argument to `fit(engine = :Name)`.
-Similarly, `SemOptimizer{:Name}(args...; kwargs...) = SemOptimizerName(args...; kwargs...)` should be defined as well as a constructor that uses only keyword arguments:
+Note that your optimizer is a subtype of `SemOptimizer{:Myopt}`,
+where you can choose a `:Myopt` that can later be used as a keyword argument to `fit(engine = :Myopt)`.
+Similarly, `SemOptimizer{:Myopt}(args...; kwargs...) = SemOptimizerMyopt(args...; kwargs...)`
+should be defined as well as a constructor that uses only keyword arguments:
 
 ```julia
-SemOptimizerName(;
+SemOptimizerMyopt(;
     algorithm = LBFGS(),
     options = Optim.Options(; f_reltol = 1e-10, x_abstol = 1.5e-8),
     kwargs...,
-) = SemOptimizerName(algorithm, options)
+) = SemOptimizerMyopt(algorithm, options)
 ```
 A method for `update_observed` and additional methods might be usefull, but are not necessary.
 
 Now comes the substantive part: We need to provide a method for `fit`:
 
 ```julia
 function fit(
-    optim::SemOptimizerName,
+    optim::SemOptimizerMyopt,
     model::AbstractSem,
     start_params::AbstractVector;
     kwargs...,
 )
-    optimization_result = ...
-
     ...
 
+    optimization_result = MyoptResult(optim, ...)
+
     return SemFit(minimum, minimizer, start_params, model, optimization_result)
 end
 ```
@@ -68,7 +78,7 @@ The method has to return a `SemFit` object that consists of the minimum of the o
 In addition, you might want to provide methods to access properties of your optimization result:
 
 ```julia
-optimizer(res::MyOptimizationResult) = ...
-n_iterations(res::MyOptimizationResult) = ...
-convergence(res::MyOptimizationResult) = ...
+algorithm_name(res::MyOptResult) = ...
+n_iterations(res::MyOptResult) = ...
+convergence(res::MyOptResult) = ...
 ```
diff --git a/docs/src/performance/simulation.md b/docs/src/performance/simulation.md
@@ -67,7 +67,7 @@ For example,
 
 new_observed = SemObservedData(;data = data_2, specification = partable)
 
-my_optimizer = SemOptimizerOptim()
+my_optimizer = SemOptimizer()
 
 new_optimizer = update_observed(my_optimizer, new_observed)
 ```

diff --git a/docs/src/tutorials/backends/nlopt.md b/docs/src/tutorials/backends/nlopt.md
@@ -1,47 +1,36 @@
 # Using NLopt.jl
 
-[`SemOptimizerNLopt`](@ref) implements the connection to `NLopt.jl`.
-It is only available if the `NLopt` package is loaded alongside `StructuralEquationModels.jl` in the running Julia session.
-It takes a bunch of arguments:
+When [`NLopt.jl`](https://github.com/jump-dev/NLopt.jl) is loaded in the running Julia session,
+it can be used by the [`SemOptimizer`](@ref) by specifying `engine = :NLopt`
+(see [NLopt-specific options](@ref SEMNLOptExt.SemOptimizerNLopt)).
+Among other things, `NLopt` enables constrained optimization of SEMs, which is
+explained in the [Constrained optimization](@ref) section.
 
-```julia
-    •  algorithm: optimization algorithm
-
-    •  options::Dict{Symbol, Any}: options for the optimization algorithm
-
-    •  local_algorithm: local optimization algorithm
-
-    •  local_options::Dict{Symbol, Any}: options for the local optimization algorithm
-
-    •  equality_constraints::Vector{NLoptConstraint}: vector of equality constraints
-
-    •  inequality_constraints::Vector{NLoptConstraint}: vector of inequality constraints
-```
-Constraints are explained in the section on [Constrained optimization](@ref).
-
-The defaults are LBFGS as the optimization algorithm and the standard options from `NLopt.jl`.
-We can choose something different:
+We can override the default *NLopt* algorithm (LFBGS) and instead use
+the *augmented lagrangian* method with LBFGS as the *local* optimization algorithm,
+stop at a maximum of 200 evaluations and use a relative tolerance of
+the objective value of `1e-6` as the stopping criterion for the local algorithm:
 
 ```julia
 using NLopt
 
-my_optimizer = SemOptimizerNLopt(;
+my_optimizer = SemOptimizer(;
+    engine = :NLopt,
     algorithm = :AUGLAG,
     options = Dict(:maxeval => 200),
     local_algorithm = :LD_LBFGS,
     local_options = Dict(:ftol_rel => 1e-6)
 )
 ```
 
-This uses an augmented lagrangian method with LBFGS as the local optimization algorithm, stops at a maximum of 200 evaluations and uses a relative tolerance of the objective value of `1e-6` as the stopping criterion for the local algorithm.
-
 To see how to use the optimizer to actually fit a model now, check out the [Model fitting](@ref) section.
 
-In the NLopt docs, you can find explanations about the different [algorithms](https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/) and a [tutorial](https://nlopt.readthedocs.io/en/latest/NLopt_Introduction/) that also explains the different options.
+In the *NLopt* docs, you can find details about the [optimization algorithms](https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/),
+and the [tutorial](https://nlopt.readthedocs.io/en/latest/NLopt_Introduction/) that demonstrates how to tweak their behavior.
 
-To choose an algorithm, just pass its name without the 'NLOPT\_' prefix (for example, 'NLOPT\_LD\_SLSQP' can be used by passing `algorithm = :LD_SLSQP`).
+To choose an algorithm, just pass its name without the `NLOPT_` prefix (for example, `NLOPT_LD_SLSQP` can be used by passing `algorithm = :LD_SLSQP`).
 
-The README of the [julia package](https://github.com/JuliaOpt/NLopt.jl) may also be helpful, and provides a list of options:
+The *README* of [*NLopt.jl*](https://github.com/JuliaOpt/NLopt.jl) may also be helpful, and provides a list of options:
 
  - `algorithm`
  - `stopval`

diff --git a/docs/src/tutorials/backends/optim.md b/docs/src/tutorials/backends/optim.md
@@ -1,23 +1,23 @@
 # Using Optim.jl
 
-[`SemOptimizerOptim`](@ref) implements the connection to `Optim.jl`.
-It takes two arguments, `algorithm` and `options`.
-The defaults are LBFGS as the optimization algorithm and the standard options from `Optim.jl`.
-We can load the `Optim` and `LineSearches` packages to choose something different:
+[*Optim.jl*](https://github.com/JuliaNLSolvers/Optim.jl) is the default optimization engine of *SEM.jl*,
+see [`SEM.SemOptimizerOptim`](@ref) for a full list of its parameters.
+It defaults to the LBFGS optimization, but we can load the `Optim` and `LineSearches` packages
+and specify BFGS (!not L-BFGS) with a back-tracking linesearch and Hager-Zhang initial step length guess:
 
 ```julia
 using Optim, LineSearches
 
-my_optimizer = SemOptimizerOptim(
+my_optimizer = SemOptimizer(
     algorithm = BFGS(
-        linesearch = BackTracking(order=3), 
+        linesearch = BackTracking(order=3),
         alphaguess = InitialHagerZhang()
-        ),
-    options = Optim.Options(show_trace = true) 
-    )
+    ),
+    options = Optim.Options(show_trace = true)
+)
 ```
 
-This optimizer will use BFGS (!not L-BFGS) with a back tracking linesearch and a certain initial step length guess. Also, the trace of the optimization will be printed to the console.
+Note that we used `options` to print the optimization progress to the console.
 
 To see how to use the optimizer to actually fit a model now, check out the [Model fitting](@ref) section.
 

diff --git a/docs/src/tutorials/concept.md b/docs/src/tutorials/concept.md
@@ -21,13 +21,13 @@ So everything that can be used as the 'observed' part has to be of type `SemObse
 
 Here is an overview on the available building blocks:
 
-|[`SemObserved`](@ref)            | [`SemImplied`](@ref)  | [`SemLossFunction`](@ref) | [`SemOptimizer`](@ref)        |
-|---------------------------------|-----------------------|---------------------------|-------------------------------|
-| [`SemObservedData`](@ref)       | [`RAM`](@ref)         | [`SemML`](@ref)           | [`SemOptimizerOptim`](@ref)   |
-| [`SemObservedCovariance`](@ref) | [`RAMSymbolic`](@ref) | [`SemWLS`](@ref)          | [`SemOptimizerNLopt`](@ref)   |
-| [`SemObservedMissing`](@ref)    | [`ImpliedEmpty`](@ref)| [`SemFIML`](@ref)         |                               |
-|                                 |                       | [`SemRidge`](@ref)        |                               |
-|                                 |                       | [`SemConstant`](@ref)     |                               |
+|[`SemObserved`](@ref)            | [`SemImplied`](@ref)  | [`SemLossFunction`](@ref) | [`SemOptimizer`](@ref)     |
+|---------------------------------|-----------------------|---------------------------|----------------------------|
+| [`SemObservedData`](@ref)       | [`RAM`](@ref)         | [`SemML`](@ref)           | :Optim                     |
+| [`SemObservedCovariance`](@ref) | [`RAMSymbolic`](@ref) | [`SemWLS`](@ref)          | :NLopt                     |
+| [`SemObservedMissing`](@ref)    | [`ImpliedEmpty`](@ref)| [`SemFIML`](@ref)         | :Proximal                  |
+|                                 |                       | [`SemRidge`](@ref)        |                            |
+|                                 |                       | [`SemConstant`](@ref)     |                            |
 
 The rest of this page explains the building blocks for each part. First, we explain every part and give an overview on the different options that are available. After that, the [API - model parts](@ref) section serves as a reference for detailed explanations about the different options.
 (How to stick them together to a final model is explained in the section on [Model Construction](@ref).)
@@ -52,7 +52,7 @@ Available loss functions are
 ## The optimizer part aka `SemOptimizer`
 The optimizer part of a model connects to the numerical optimization backend used to fit the model.
 It can be used to control options like the optimization algorithm, linesearch, stopping criteria, etc.
-There are currently three available backends, [`SemOptimizerOptim`](@ref) connecting to the [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl) backend, [`SemOptimizerNLopt`](@ref) connecting to the [NLopt.jl](https://github.com/JuliaOpt/NLopt.jl) backend and [`SemOptimizerProximal`](@ref) connecting to [ProximalAlgorithms.jl](https://github.com/JuliaFirstOrder/ProximalAlgorithms.jl).
+There are currently three available engines (i.e., backends used to carry out the numerical optimization), `:Optim` connecting to the [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl) backend, `:NLopt` connecting to the [NLopt.jl](https://github.com/JuliaOpt/NLopt.jl) backend and `:Proximal` connecting to [ProximalAlgorithms.jl](https://github.com/JuliaFirstOrder/ProximalAlgorithms.jl).
 For more information about the available options see also the tutorials about [Using Optim.jl](@ref) and [Using NLopt.jl](@ref), as well as [Constrained optimization](@ref) and [Regularization](@ref) .
 
 # What to do next
@@ -102,7 +102,7 @@ SemConstant
 
 ```@docs
 SemOptimizer
-SemOptimizerOptim
-SemOptimizerNLopt
-SemOptimizerProximal
+SEM.SemOptimizerOptim
+SEMNLOptExt.SemOptimizerNLopt
+SEMProximalOptExt.SemOptimizerProximal
 ```