contribution of a new loss function for squared Hellinger distance

CITATION.cff

@@ -21,3 +21,4 @@ authors:
 repository-code: >-
   https://github.com/StructuralEquationModels/StructuralEquationModels.jl
 license: MIT
+doi: 10.5281/zenodo.6719626

README.md

@@ -1,8 +1,9 @@
 # <img src="https://github.com/StructuralEquationModels/Data/blob/main/images/logo.png" width = 100> StructuralEquationModels.jl
 
-| **Documentation**                                                               | **Build Status**                                                                                |
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+| **Documentation**                                                               | **Build Status**                                                                                | Citation                                                                                        |
+|:-------------------------------------------------------------------------------:|:-----------------------------------------------------------------------------------------------:|:-----------------------------------------------------------------------------------------------:|
+| [![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://structuralequationmodels.github.io/StructuralEquationModels.jl/) [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://structuralequationmodels.github.io/StructuralEquationModels.jl/dev/) | [![Project Status: Active – The project has reached a stable, usable state and is being actively developed.](https://www.repostatus.org/badges/latest/active.svg)](https://www.repostatus.org/#active) [![Github Action CI](https://github.com/StructuralEquationModels/StructuralEquationModels.jl/workflows/CI_extended/badge.svg)](https://github.com/StructuralEquationModels/StructuralEquationModels.jl/actions/) [![codecov](https://codecov.io/gh/StructuralEquationModels/StructuralEquationModels.jl/branch/main/graph/badge.svg?token=P2kjzpvM4V)](https://codecov.io/gh/StructuralEquationModels/StructuralEquationModels.jl) | [![DOI](https://zenodo.org/badge/228649704.svg)](https://zenodo.org/badge/latestdoi/228649704) |
+
 
 This is a package for Structural Equation Modeling.
 It is still *in development*.

src/loss/other/hellinger.jl

@@ -0,0 +1,61 @@
+############################################################################################
+### Types
+############################################################################################
+"""
+Squared Hellinger distance loss. 
+
+# Constructor
+
+    Hellinger()
+
+# Examples
+```julia
+    my_hellinger = Hellinger()
+```
+
+# Extended help
+## Implementation
+Subtype of `SemLossFunction`.
+"""
+
+struct Hellinger <: SemLossFunction end
+
+using LinearAlgebra
+import StructuralEquationModels: Σ, μ, obs_cov, obs_mean, objective!
+
+function objective!(hell::Hellinger, parameters, model::AbstractSem) 
+
+    # get model-implied covariance matrices
+    Σᵢ = Σ(imply(model))
+
+    # get observed covariance matrix
+    Σₒ = obs_cov(observed(model))
+
+    # get model-implued mean vector
+    μᵢ = μ(imply(model))
+
+    # get observed mean vector
+    μₒ = obs_mean(observed(model))
+
+    Sig = (Σᵢ + Σₒ)/2
+
+
+
+    # compute the objective
+    if isposdef(Symmetric(Σᵢ)) # is the model implied covariance matrix positive definite?
+
+          loss = ( det(Σᵢ)^(1/4) * det(Σₒ)^(1/4) ) / sqrt(det(Sig)) 
+
+           if !isnothing(μᵢ) & !isnothing(μₒ)
+            μd = (μᵢ-μₒ)
+            loss = loss * exp(0.125 * (μd)*inv(Sig)*(μd)')
+          end
+
+          loss = 1 - loss
+
+          return loss
+
+    else
+        return Inf
+    end
+end