diff --git a/src/additional_functions/helper.jl b/src/additional_functions/helper.jl
index d6a1fc6c8..60365def0 100644
--- a/src/additional_functions/helper.jl
+++ b/src/additional_functions/helper.jl
@@ -89,3 +89,37 @@ function nonunique(values::AbstractVector)
     end
     return res
 end
+
+# check that a model only has a single lossfun
+function check_single_lossfun(model::AbstractSemSingle; throw_error)
+    if (length(model.loss.functions) > 1) & throw_error
+        @error "The model has $(length(sem.loss.functions)) loss functions.
+            Only a single loss function is supported."
+    end
+    return isone(length(model.loss.functions))
+end
+
+# check that all models use the same single loss function
+function check_single_lossfun(models::AbstractSemSingle...; throw_error)
+    uniform = true
+    lossfun = models[1].loss.functions[1]
+    L = typeof(lossfun)
+    for (i, model) in enumerate(models)
+        uniform &= check_single_lossfun(model; throw_error = throw_error)
+        cur_lossfun = model.loss.functions[1]
+        if !isa(cur_lossfun, L) & throw_error
+            @error "Loss function for group #$i model is $(typeof(cur_lossfun)), expected $L.
+            Heterogeneous loss functions are not supported."
+        end
+        uniform &= isa(cur_lossfun, L)
+    end
+    return uniform
+end
+
+check_single_lossfun(model::SemEnsemble; throw_error) =
+    check_single_lossfun(model.sems...; throw_error)
+
+# scaling corrections for multigroup models
+mg_correction(::SemFIML) = 0
+mg_correction(::SemML) = 0
+mg_correction(::SemWLS) = -1
diff --git a/src/frontend/fit/fitmeasures/RMSEA.jl b/src/frontend/fit/fitmeasures/RMSEA.jl
index f9dae84ed..764b5e116 100644
--- a/src/frontend/fit/fitmeasures/RMSEA.jl
+++ b/src/frontend/fit/fitmeasures/RMSEA.jl
@@ -7,13 +7,24 @@ function RMSEA end
 
 RMSEA(fit::SemFit) = RMSEA(fit, fit.model)
 
-RMSEA(fit::SemFit, model::AbstractSemSingle) = RMSEA(dof(fit), χ²(fit), nsamples(fit))
+function RMSEA(fit::SemFit, model::AbstractSemSingle)
+    check_single_lossfun(model; throw_error = true)
+    return RMSEA(dof(fit), χ²(fit), nsamples(fit)+rmsea_correction(model.loss.functions[1]))
+end
 
-RMSEA(fit::SemFit, model::SemEnsemble) =
-    sqrt(length(model.sems)) * RMSEA(dof(fit), χ²(fit), nsamples(fit))
+function RMSEA(fit::SemFit, model::SemEnsemble)
+    check_single_lossfun(model; throw_error = true)
+    n = nsamples(fit)+model.n*rmsea_correction(model.sems[1].loss.functions[1])
+    return sqrt(length(model.sems)) * RMSEA(dof(fit), χ²(fit), n)
+end
 
-function RMSEA(dof, chi2, nsamples)
-    rmsea = (chi2 - dof) / (nsamples * dof)
-    rmsea > 0 ? nothing : rmsea = 0
+function RMSEA(dof, chi2, N⁻)
+    rmsea = (chi2 - dof) / (N⁻ * dof)
+    rmsea = rmsea > 0 ? rmsea : 0
     return sqrt(rmsea)
 end
+
+# scaling corrections
+rmsea_correction(::SemFIML) = 0
+rmsea_correction(::SemML) = -1
+rmsea_correction(::SemWLS) = -1
diff --git a/src/frontend/fit/fitmeasures/chi2.jl b/src/frontend/fit/fitmeasures/chi2.jl
index dc19467fc..9ebb06bd9 100644
--- a/src/frontend/fit/fitmeasures/chi2.jl
+++ b/src/frontend/fit/fitmeasures/chi2.jl
@@ -9,20 +9,21 @@ Return the χ² value.
 # Single Models
 ############################################################################################
 
-χ²(fit::SemFit, model::AbstractSemSingle) =
-    sum(loss -> χ²(loss, fit, model), model.loss.functions)
+function χ²(fit::SemFit, model::AbstractSemSingle)
+    check_single_lossfun(model; throw_error = true)
+    return χ²(model.loss.functions[1], fit::SemFit, model::AbstractSemSingle)
+end
 
-# RAM + SemML
-χ²(lossfun::SemML, fit::SemFit, model::AbstractSemSingle) =
+χ²(::SemML, fit::SemFit, model::AbstractSemSingle) =
     (nsamples(fit) - 1) *
-    (fit.minimum - logdet(obs_cov(observed(model))) - nobserved_vars(observed(model)))
+    (fit.minimum - logdet(obs_cov(observed(model))) - nobserved_vars(model))
 
 # bollen, p. 115, only correct for GLS weight matrix
-χ²(lossfun::SemWLS, fit::SemFit, model::AbstractSemSingle) =
+χ²(::SemWLS, fit::SemFit, model::AbstractSemSingle) =
     (nsamples(fit) - 1) * fit.minimum
 
 # FIML
-function χ²(lossfun::SemFIML, fit::SemFit, model::AbstractSemSingle)
+function χ²(::SemFIML, fit::SemFit, model::AbstractSemSingle)
     ll_H0 = minus2ll(fit)
     ll_H1 = minus2ll(observed(model))
     return ll_H0 - ll_H1
@@ -32,38 +33,28 @@ end
 # Collections
 ############################################################################################
 
-function χ²(fit::SemFit, models::SemEnsemble)
-    isempty(models.sems) && return 0.0
-
-    lossfun = models.sems[1].loss.functions[1]
-    # check that all models use the same single loss function
-    L = typeof(lossfun)
-    for (i, sem) in enumerate(models.sems)
-        if length(sem.loss.functions) > 1
-            @error "Model for group #$i has $(length(sem.loss.functions)) loss functions. Only the single one is supported"
-        end
-        cur_lossfun = sem.loss.functions[1]
-        if !isa(cur_lossfun, L)
-            @error "Loss function for group #$i model is $(typeof(cur_lossfun)), expected $L. Heterogeneous loss functions are not supported"
-        end
-    end
-
-    return χ²(lossfun, fit, models)
+function χ²(fit::SemFit, model::SemEnsemble)
+    check_single_lossfun(model; throw_error = true)
+    lossfun = model.sems[1].loss.functions[1]
+    return χ²(lossfun, fit, model)
 end
 
-function χ²(lossfun::SemWLS, fit::SemFit, models::SemEnsemble)
-    return (nsamples(models) - 1) * fit.minimum
+function χ²(::SemWLS, fit::SemFit, models::SemEnsemble)
+    return (nsamples(models) - models.n) * fit.minimum
 end
 
-function χ²(lossfun::SemML, fit::SemFit, models::SemEnsemble)
-    G = sum(zip(models.weights, models.sems)) do (w, model)
-        data = observed(model)
-        w * (logdet(obs_cov(data)) + nobserved_vars(data))
+function χ²(::SemML, fit::SemFit, models::SemEnsemble)
+    F = 0
+    for model in models.sems
+        Fᵢ = objective(model, fit.solution)
+        Fᵢ -= logdet(obs_cov(observed(model))) + nobserved_vars(model)
+        Fᵢ *= nsamples(model) - 1
+        F += Fᵢ
     end
-    return (nsamples(models) - 1) * (fit.minimum - G)
+    return F
 end
 
-function χ²(lossfun::SemFIML, fit::SemFit, models::SemEnsemble)
+function χ²(::SemFIML, fit::SemFit, models::SemEnsemble)
     ll_H0 = minus2ll(fit)
     ll_H1 = sum(minus2ll ∘ observed, models.sems)
     return ll_H0 - ll_H1
diff --git a/src/frontend/fit/fitmeasures/minus2ll.jl b/src/frontend/fit/fitmeasures/minus2ll.jl
index 9b211fb44..961822ef5 100644
--- a/src/frontend/fit/fitmeasures/minus2ll.jl
+++ b/src/frontend/fit/fitmeasures/minus2ll.jl
@@ -3,36 +3,31 @@
 
 Return the negative 2* log likelihood.
 """
-function minus2ll end
+minus2ll(fit::SemFit) = minus2ll(fit, fit.model)
 
 ############################################################################################
 # Single Models
 ############################################################################################
 
-minus2ll(fit::SemFit) = minus2ll(fit, fit.model)
-
 function minus2ll(fit::SemFit, model::AbstractSemSingle)
-    minimum = objective(model, fit.solution)
-    return minus2ll(minimum, model)
+    check_single_lossfun(model; throw_error = true)
+    F = objective(model, fit.solution)
+    return minus2ll(model.loss.functions[1], F, model)
 end
 
-minus2ll(minimum::Number, model::AbstractSemSingle) =
-    sum(lossfun -> minus2ll(lossfun, minimum, model), model.loss.functions)
-
 # SemML ------------------------------------------------------------------------------------
-function minus2ll(lossfun::SemML, minimum::Number, model::AbstractSemSingle)
-    obs = observed(model)
-    return nsamples(obs) * (minimum + log(2π) * nobserved_vars(obs))
+function minus2ll(::SemML, F, model::AbstractSemSingle)
+    return nsamples(model) * (F + log(2π) * nobserved_vars(model))
 end
 
 # WLS --------------------------------------------------------------------------------------
-minus2ll(lossfun::SemWLS, minimum::Number, model::AbstractSemSingle) = missing
+minus2ll(::SemWLS, F, ::AbstractSemSingle) = missing
 
 # compute likelihood for missing data - H0 -------------------------------------------------
-# -2ll = (∑ log(2π)*(nᵢ + mᵢ)) + F*n
-function minus2ll(lossfun::SemFIML, minimum::Number, model::AbstractSemSingle)
+# -2ll = (∑ log(2π)*(nᵢ*mᵢ)) + F*n
+function minus2ll(::SemFIML, F, model::AbstractSemSingle)
     obs = observed(model)::SemObservedMissing
-    F = minimum * nsamples(obs)
+    F *= nsamples(obs)
     F += log(2π) * sum(pat -> nsamples(pat) * nmeasured_vars(pat), obs.patterns)
     return F
 end
@@ -67,4 +62,7 @@ end
 # Collection
 ############################################################################################
 
-minus2ll(fit::SemFit, model::SemEnsemble) = sum(Base.Fix1(minus2ll, fit), model.sems)
+function minus2ll(fit::SemFit, model::SemEnsemble)
+    check_single_lossfun(model; throw_error = true)
+    return sum(Base.Fix1(minus2ll, fit), model.sems)
+end
diff --git a/src/types.jl b/src/types.jl
index 777165f37..3f695bfa3 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -192,10 +192,7 @@ end
 function SemEnsemble(models...; weights = nothing, groups = nothing, kwargs...)
     n = length(models)
     # default weights
-    if isnothing(weights)
-        nsamples_total = sum(nsamples, models)
-        weights = [nsamples(model) / nsamples_total for model in models]
-    end
+    weights = isnothing(weights) ? multigroup_weights(models, n) : weights
     # default group labels
     groups = isnothing(groups) ? Symbol.(:g, 1:n) : groups
     # check parameters equality
@@ -226,7 +223,25 @@ function SemEnsemble(; specification, data, groups, column = :group, kwargs...)
         model = Sem(; specification = ram_matrices, data = data_group, kwargs...)
         push!(models, model)
     end
-    return SemEnsemble(models...; weights = nothing, groups = groups, kwargs...)
+    return SemEnsemble(models...; groups = groups, kwargs...)
+end
+
+function multigroup_weights(models, n)
+    nsamples_total = sum(nsamples, models)
+    uniform_lossfun = check_single_lossfun(models...; throw_error = false)
+    if !uniform_lossfun
+        @info "Your ensemble model contains heterogeneous loss functions.
+                Default weights of (#samples per group/#total samples) will be used".
+        return [(nsamples(model)) / (nsamples_total) for model in models]
+    end
+    lossfun = models[1].loss.functions[1]
+    if !applicable(mg_correction, lossfun)
+        @info "We don't know how to choose group weights for the specified loss function.
+                Default weights of (#samples per group/#total samples) will be used".
+        return [(nsamples(model)) / (nsamples_total) for model in models]
+    end
+    c = mg_correction(lossfun)
+    return [(nsamples(model)+c) / (nsamples_total+n*c) for model in models]
 end
 
 param_labels(ensemble::SemEnsemble) = ensemble.param_labels