Practical Identifiability of a Minimal Adaptive Learning-Gain Model for Binary Feedback: A Simulation Study

Abstract

Social learning is shaped by distinct computational components--baseline beliefs (prior mean), feedback sensitivity (learning gain), and temporal uncertainty (drift)--that empirical designs rarely disentangle. We evaluate practical identifiability and predictive performance of a parsimonious four-parameter adaptive learning-gain model for binary feedback, where a latent belief about positive-outcome probability updates deterministically between observations and an internal confidence-precision state decays each trial. {sigma}, {omega}, and {lambda} are internal, model-defined variables--not validated psychological constructs. Using fixed-seed simulations, we report four findings. Joint maximum-likelihood recovery is poor: on a 24-condition grid (T=80), {sigma} and {omega} show near-zero tolerance-based recovery ([≤]0.002) across tolerances 0.3-1.0, {lambda} recovers at 0.078-0.263, and longer sequences do not improve recovery. Profile-likelihood and trade-off diagnostics show flat regions for {sigma} and {omega} and an asymmetric {lambda} profile, indicating weak practical (not structural) identifiability. A fitting-parity audit fixed a return-order bug in the fixed-gain candidate. After correction, block-level model discrimination is 0.48 (72/150) under common bounds--above chance (p<0.001)--but is driven almost entirely by Rescorla-Wagner (0.88-0.90); the adaptive filter and its nested fixed-gain restriction remain indistinguishable. Across 50 held-out datasets, the model shows no predictive advantage over an empirical-frequency baseline (paired 95% CIs span zero). Ablations show the added update components provide no consistent benefit. These results caution against interpreting individual parameter estimates from this model class in short binary-feedback designs, and specify that mechanistic claims about clinical group differences in {sigma}, {omega}, or {lambda} require graded responses, manipulated volatility, multi-context sequences, and longitudinal replication.