Implement likelihood (#45)

* implement likelihood functions

* export likelihood and loglikelihood

* add tests

* bump version

* add docs

Project.toml

@@ -1,7 +1,7 @@
 name = "ItemResponseFunctions"
 uuid = "18e85bec-f2a0-4122-b3a6-37651333b522"
 authors = ["Philipp Gewessler <[email protected]>"]
-version = "0.1.6"
+version = "0.1.7"
 
 [deps]
 AbstractItemResponseModels = "0ab3451c-659c-47cd-a7a9-a2d579e209dd"

docs/src/api.md

@@ -33,20 +33,13 @@ expected_score
 information
 ```
 ### Utilities
-#### Scoring functions
-```@docs
-partial_credit
-```
-
-#### Derivatives
 ```@docs
+ItemParameters
 derivative_theta
 derivative_theta!
+likelihood
+loglikelihood
+partial_credit
 second_derivative_theta
 second_derivative_theta!
 ```
-
-#### Item parameters
-```@docs
-ItemParameters
-```

src/ItemResponseFunctions.jl

@@ -45,7 +45,9 @@ export DichotomousItemResponseModel,
     derivative_theta,
     derivative_theta!,
     second_derivative_theta,
-    second_derivative_theta!
+    second_derivative_theta!,
+    likelihood,
+    loglikelihood
 
 include("model_types.jl")
 include("item_parameters.jl")
@@ -56,6 +58,7 @@ include("expected_score.jl")
 include("information.jl")
 include("scoring_functions.jl")
 include("derivatives.jl")
+include("likelihood.jl")
 
 include("precompile.jl")
 

src/likelihood.jl

@@ -0,0 +1,35 @@
+"""
+    $(SIGNATURES)
+
+Evaluate the likelihood of an item response model `M` at `theta`, given item parameters
+`betas` and response pattern `responses`.
+
+Items are assumed to be independent. Then, the likelihood function is defined as,
+
+``
+L(\\boldsymbol{u} | \\theta, \\boldsymbol{\\beta}) = \\prod_{j=1}^J P(Y_j = y | \\theta, \\boldsymbol{\\beta}_j)
+``
+
+See also [`loglikelihood`](@ref).
+"""
+function likelihood(M::Type{<:ItemResponseModel}, theta, betas, responses)
+    L = one(theta)
+
+    for (beta, y) in zip(betas, responses)
+        L *= irf(M, theta, beta, y)
+    end
+
+    return L
+end
+
+"""
+    $(SIGNATURES)
+
+Evaluate the log-likelihood of an item response model `M` at `theta`, given item parameters
+`betas` and response pattern `responses`,
+
+See also [`likelihood`](@ref).
+"""
+function loglikelihood(M::Type{<:ItemResponseModel}, theta, betas, responses)
+    return log(likelihood(M, theta, betas, responses))
+end

test/likelihood.jl

@@ -0,0 +1,11 @@
+@testset "likelihood" begin
+    betas = [(; b = 0.0) for _ in 1:4]
+    @test likelihood(OnePL, Inf, betas, ones(length(betas))) == 1.0
+    @test likelihood(OnePL, -Inf, betas, ones(length(betas))) == 0.0
+
+    @test likelihood(OnePL, Inf, betas, zeros(length(betas))) == 0.0
+    @test likelihood(OnePL, -Inf, betas, zeros(length(betas))) == 1.0
+
+    @test loglikelihood(OnePL, Inf, betas, ones(length(betas))) == 0.0
+    @test loglikelihood(OnePL, -Inf, betas, ones(length(betas))) == -Inf
+end

test/runtests.jl

@@ -26,4 +26,5 @@ using ForwardDiff: Dual
     include("models/rating_scale_model.jl")
     include("models/generalized_rating_scale_model.jl")
     include("derivatives.jl")
+    include("likelihood.jl")
 end