model-selection-sequence.puml

@startuml
skinparam shadowing false

title Relation-safe measurement-model selection

actor Analyst
participant "Factor Retention" as Retention
participant "Candidate Model Fits" as Fits
participant "Relation Classifier" as Relation
participant "Inferential Comparator" as Infer
participant "Held-out Validator" as CV
participant "Residual / DIF /\nScoreability Diagnostics" as Diagnostics
participant "Recovery Simulation" as Recovery
participant "Selection Policy" as Select

Analyst -> Retention : propose substantive factor counts
Retention --> Analyst : candidate counts + uncertainty
Analyst -> Fits : fit correlated MIRT / bifactor / higher-order / testlet / two-tier / facets / latent-space
Fits --> Analyst : exact fit artifacts + case/cluster likelihood evidence

Analyst -> Relation : classify from actual constraints/boundaries
Relation --> Analyst : regular_nested | boundary_nested | nonlinear_nested | non_nested | overlapping | unknown

alt regular nested
  Analyst -> Infer : LR / robust LR
else boundary or singular
  Analyst -> Infer : parametric-bootstrap / boundary-aware LR
else strictly non-nested or overlapping
  Analyst -> Infer : formal distinguishability first
  Infer --> Analyst : distinguishable?
  alt distinguishable
    Analyst -> Infer : non-nested selection statistic
  else not established
    Infer --> Analyst : no preferred model
  end
else unknown
  Relation --> Analyst : fail closed; establish relation
end

Analyst -> CV : leave-query/person/testlet/rater/domain-out as appropriate
CV --> Analyst : cluster-aware predictive evidence
Analyst -> Diagnostics : fit + local dependence + DIF/invariance + scoreability/stability
Diagnostics --> Analyst : interpretation evidence
Analyst -> Recovery : realistic true-structure simulation
Recovery --> Analyst : selection accuracy + bias/RMSE/coverage/convergence
Analyst -> Select : combine evidence under declared policy
Select --> Analyst : simplest supported model or indeterminate

note over Relation,Infer
Model names do not define nestedness.
A positive numeric likelihood-difference variance is not, by itself,
the formal Vuong distinguishability test.
end note

note over Select
A better in-sample fit does not automatically authorize a score interpretation.
end note

@enduml