Parameter recovery

Give the estimator an observer with a known amplitude. Does it hand the amplitude back?

Single synthetic observers were generated at nine amplitudes from −4° to +4° and three session lengths, forty times each, and fitted with the primary model. The largest absolute bias at any amplitude is 0.18° at 300 trials, 0.22° at 600 trials, 0.24° at 1200 trials. Bias is small everywhere; what trial count buys is precision. At a true amplitude of zero the root-mean-square error of a single observer’s estimate is 1.09° (300), 0.88° (600), 0.60° (1200) — which is why individual amplitudes should not be interpreted from short sessions, and why inference is at the group level.

Recovering the stimulus- and response-history amplitudes jointly is the harder test. Across a 3 × 3 grid of true values their recovery errors correlate at −0.40; hypothesis H5 requires |r| < 0.5, and the design passes. Mean bias is +0.03° for a_stim and −0.16° for a_resp.

Fig. 1 True versus recovered amplitude, 300 trials per observer

SIMULATED DATA

Faint points: individual simulations (jittered horizontally). Dark points: mean ± SD at each true value. The diagonal is perfect recovery.Source: results/parameter_recovery.parquet · run parameter_recovery-8964a2e-1000

Table view (9 rows)

true a (°)	mean estimate	SD	bias	RMSE	n
−4.0	−3.823	0.791	+0.177	0.801	40
−3.0	−2.970	0.695	+0.030	0.686	40
−2.0	−2.023	0.788	−0.023	0.778	40
−1.0	−1.001	1.024	−0.001	1.012	40
+0.0	+0.129	1.094	+0.129	1.088	40
+1.0	+0.976	1.351	−0.024	1.335	40
+2.0	+2.145	0.593	+0.145	0.603	40
+3.0	+2.859	0.651	−0.141	0.658	40
+4.0	+3.990	0.725	−0.010	0.716	40

Fig. 2 True versus recovered amplitude, 600 trials per observer

SIMULATED DATA

Table view (9 rows)

true a (°)	mean estimate	SD	bias	RMSE	n
−4.0	−3.881	0.573	+0.119	0.578	40
−3.0	−2.913	0.516	+0.087	0.517	40
−2.0	−1.838	0.514	+0.162	0.533	40
−1.0	−1.139	0.680	−0.139	0.686	40
+0.0	+0.034	0.886	+0.034	0.875	40
+1.0	+1.101	0.573	+0.101	0.575	40
+2.0	+1.900	0.541	−0.100	0.544	40
+3.0	+2.782	0.517	−0.218	0.555	40
+4.0	+3.856	0.578	−0.144	0.588	40

Fig. 3 True versus recovered amplitude, 1200 trials per observer

SIMULATED DATA

Table view (9 rows)

true a (°)	mean estimate	SD	bias	RMSE	n
−4.0	−3.781	0.360	+0.219	0.418	40
−3.0	−2.853	0.407	+0.147	0.427	40
−2.0	−1.880	0.301	+0.120	0.321	40
−1.0	−1.066	0.359	−0.066	0.361	40
+0.0	−0.064	0.608	−0.064	0.603	40
+1.0	+1.073	0.373	+0.073	0.376	40
+2.0	+1.965	0.401	−0.035	0.398	40
+3.0	+2.867	0.383	−0.133	0.401	40
+4.0	+3.762	0.360	−0.238	0.428	40