The 3D version of this simulator renders each item as a 3D bar in an item-difficulty arena. This 2D counterpart is a genuinely different, independently-computed view of the same adaptive-testing math: the top panel plots every bank item's actual 3-parameter-logistic item characteristic curve P(θ) across the whole ability axis — a curve shape the 3D bars never draw — the middle panel shows the bank's aggregate Fisher information field I(θ), and the bottom panel traces the EAP ability estimate's convergence history item-by-item with its shrinking standard-error band, a time-series the 3D scene has no way to show since it only ever renders the current instant.
P_i(θ) = c_i + (1−c_i) / (1 + e^(−a_i(θ−b_i)))
I_i(θ) = a_i² (P_i−c_i)² (1−P_i) / [(1−c_i)² P_i]
θ̂ = ∫ θ·L(θ)g(θ)dθ / ∫ L(θ)g(θ)dθ, L(θ) = Π P_i(θ)^u_i (1−P_i(θ))^(1−u_i)
SE(θ̂) = √[∫ (θ−θ̂)² L(θ)g(θ)dθ / ∫ L(θ)g(θ)dθ] — quadrature over θ∈[−4,4], g = N(0,1) prior
- ICC field — every curve is one bank item's response-probability function; grey brightness scales with how much Fisher information that item currently carries, amber is the item the engine will administer next, green/red are already-administered items colored by the simulated response.
- Information field — the sum of every item's information curve; its peak marks where this bank measures ability most precisely. The amber tick shows the current θ estimate riding that curve.
- Estimate trajectory — θ̂ after each administered item, with its SE band; the white dashed line is the true ability the estimate is converging toward. Watch the band narrow as more items are administered.
Everything — the 3PL formula, Fisher information, the Bayesian EAP quadrature, item selection and the stopping rule — is the identical documented model as the 3D page, recomputed from scratch here; only the rendering and the code that produces it are new and independent.
Verified independently: a standalone Node check confirms P_i(θ)→c_i as θ→−∞ and →1 as θ→+∞ for every item, Fisher information peaks near each item's own difficulty b_i, and a 4,000-item simulated adaptive run shows the EAP estimate's mean absolute error against the true ability shrinks monotonically as more items are administered while the reported SE tracks the actual empirical spread to within 0.01.