bootstrap LRT

Project.toml

@@ -6,13 +6,16 @@ version = "2.0.0"
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MixedModels = "ff71e718-51f3-5ec2-a782-8ffcbfa3c316"
+ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
 Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 
 [compat]
 MixedModels = "4"
+ProgressMeter = "1"
 StatsBase = "0.33, 0.34"
 StatsModels = "0.7.3"
 Tables = "1"

src/MixedModelsExtras.jl

@@ -2,11 +2,13 @@ module MixedModelsExtras
 
 using LinearAlgebra
 using MixedModels
+using Random
 using Statistics
 using StatsBase
 using StatsModels
 using Tables
 
+using MixedModels: replicate
 using StatsModels: termnames, vif, gvif
 export termnames, gvif, vif
 
@@ -24,4 +26,7 @@ export partial_fitted
 include("shrinkage.jl")
 export shrinkagenorm, shrinkagetables
 
+include("bootstrap.jl")
+export bootstrap_lrt
+
 end

src/bootstrap.jl

@@ -0,0 +1,90 @@
+"""
+    bootstrap_lrt(rng::AbstractRNG, n::Integer, m0::MixedModel, ms::MixedModel...;
+                  optsum_overrides=(;), progress=true)
+
+Bootstrapped likelihood ratio test applied to a set of nested models.
+
+The first model is used to simulate `n` dataset replicates, where the ground truth is that
+specified by the first model. Each of the other models is then refit to those
+null data and the underlying distribution of deviance differences is then captured.
+For final computation of the p-values, the observed deviance is differencce between the 
+original models is compared against this null distribution.
+
+!!! note
+    The precision of the resulting p-value cannot exceed ``1/n``. 
+
+!!! warn
+    This method is **not** thread safe. For efficiency , the models are modified 
+    during bootstrapping and the original fits are only restored at the end.
+
+!!! note
+    The nesting of the models is not checked.  It is incumbent on the user
+    to check this. This differs from `StatsModels.lrtest` as nesting in
+    mixed models, especially in the random effects specification, may be non obvious.
+
+This functionality may be deprecated in the future in favor of `StatsModels.lrtest`.
+"""
+function bootstrap_lrt(rng::AbstractRNG, n::Integer, m0::MixedModel, ms::MixedModel...;
+                          optsum_overrides=(;), progress=true)
+    y0 = copy(response(m0))
+    ys = [copy(response(m)) for m in ms]
+    local models
+    local devs
+    local dofs
+    local dofs
+    local formulas
+    local dofdiffs
+    local devdiffs
+    local pvals
+    try
+        models = [m0; ms...]
+        dofs = dof.(models)
+        formulas = string.(formula.(models))
+        ord = sortperm(dofs)
+        dofs = dofs[ord]
+        formulas = formulas[ord]
+        devs = deviance.(models)[ord]
+        dofdiffs = diff(dofs)
+        devdiffs = .-(diff(devs))
+
+        for (key, val) in pairs(optsum_overrides)
+            setfield!(m0.optsum, key, val)
+            for m in ms
+                setfield!(m.optsum, key, val)
+            end
+        end
+        nulldist = replicate(n; hide_progress=!progress) do
+            simulate!(rng, m0)
+            refit!(m0; progress=false)
+            for m in ms
+                refit!(m, response(m0); progress=false)
+            end
+            return [deviance(m) for m in models]
+        end
+        nulldist = stack(nulldist; dims=1)
+        nulldist = diff(nulldist; dims=2)
+        pvals = map(enumerate(devdiffs)) do (idx, dev)
+            if dev > 0
+                mean(>=(dev), view(nulldist, :, idx))
+            else
+                NaN
+            end
+        end
+    catch ex
+        rethrow(ex)
+    finally
+        # restore the original fits
+        if progress
+            @info "Bootstrapping complete, cleaning up..."
+        end
+        refit!(m0, y0; progress=false)
+        for (m, y) in zip(ms, ys)
+            refit!(m, y; progress=false)
+        end
+    end
+    return MixedModels.LikelihoodRatioTest(formulas,
+                                           (dof=dofs, deviance=devs),
+                                           (dofdiff=dofdiffs, deviancediff=devdiffs,
+                                            pvalues=pvals),
+                                           first(models) isa LinearMixedModel)
+end

test/bootstrap.jl

@@ -0,0 +1,18 @@
+using MixedModels
+using MixedModelsExtras
+using Random
+using Test
+
+using MixedModels: likelihoodratiotest
+
+progress = false
+sleepstudy = MixedModels.dataset(:sleepstudy)
+fm0 = fit(MixedModel, @formula(reaction ~ 1 + days + (1 | subj)), 
+          sleepstudy; progress)
+fm1 = fit(MixedModel, @formula(reaction ~ 1 + days + (1 + days | subj)), 
+          sleepstudy; progress)
+fmzc = fit(MixedModel, @formula(reaction ~ 1 + days + zerocorr(1 + days | subj)),
+           sleepstudy; progress)
+
+lrt = likelihoodratiotest(fm0, fm1, fmzc)
+boot = bootstrap_lrt(MersenneTwister(42), 1000, fm0, fm1, fmzc)