M2 Recovery and Identifiability

Why recovery precedes promotion

A multimodal model is not validated because it compiles or produces finite estimates. The M2 evidence program therefore separates structural support, numerical diagnostics, parameter recovery, uncertainty calibration, and later empirical reproduction.

library(eyeprocess)

sim <- simulate_multimodal_m2(
  n_person = 100,
  n_item = 10,
  dropout = c(response = .02, rt = .05, gaze = .10),
  seed = 101
)

audit_multimodal_m2_identifiability(sim$data)
#> <eye_multimodal_m2_identifiability>
#>   model: M2
#>   persons: 100
#>   items: 10
#>   supported: TRUE
#>   missing fractions: response=0.017, rt=0.055, gaze=0.107
#>   boundary: This audit is a conservative structural/data-support screen. It does not establish global identifiability, construct validity, or robustness to MNAR channel missingness.

The simulation retains complete latent and item truth even after observed-channel dropout is applied.

Recovery experiment

multimodal_m2_recovery() repeatedly simulates and fits the complete M2 estimator. It summarizes bias, RMSE, posterior SD, and 95% interval coverage across person latent parameters, item locations, item dispersions, covariance parameters, and hyperparameters.

rec <- multimodal_m2_recovery(
  n_rep = 25,
  n_person = 150,
  n_item = 15,
  chains = 4,
  parallel_chains = 4,
  iter_warmup = 1000,
  iter_sampling = 1000,
  base_seed = 20261001
)

rec
plot(rec, type = "truth_vs_estimate")
plot(rec, type = "coverage")

A publication-grade recovery grid should vary sample size, item count, latent correlations, item correlations, count dispersion, RT discrimination, and channel dropout rather than relying on one favorable condition.

What recovery does not show

Recovery under the generating model establishes that the estimator can recover parameters when its assumptions are true. It does not show robustness to misspecified count distributions, local dependence, device artifacts, nonignorable missingness, or construct validity. Those are distinct validation layers.