M2 Process Information and Channel Ablation

A common response target

The central M2 question is not whether RT and gaze have their own likelihood information. It is whether they improve measurement of the scored-response trait under a joint model.

multimodal_m2_ablation() therefore fits a compatible sequence:

• M0: response only;
• M1: response + RT;
• M2: response + RT + gaze.

multimodal_m2_process_information() compares all three models on the same response observations.

library(eyeprocess)

sim <- simulate_multimodal_m2(
  n_person = 150,
  n_item = 15,
  seed = 220
)

abl <- multimodal_m2_ablation(
  sim,
  chains = 4,
  parallel_chains = 4,
  iter_warmup = 1000,
  iter_sampling = 1000,
  seed = 221
)

info <- multimodal_m2_process_information(abl)
info

plot(info, type = "response_elpd")
plot(info, type = "theta_variance")

Two complementary quantities

The evidence object reports:

1. response-target PSIS-LOO ELPD, using only the scored-response log-likelihood in every model and MCMC relative-efficiency adjustment, for held-out response cells among the observed persons and items;
2. the corresponding pointwise ELPD-difference uncertainty and maximum Pareto-k diagnostic; and
3. posterior variance of ability, summarized across persons.

This LOO target is conditional on the study’s observed person/item population. It is not a transport estimate for entirely new persons or new items.

A useful process channel may improve response-target held-out prediction, reduce posterior uncertainty, both, or neither. A destabilizing channel may worsen predictive performance or inflate uncertainty.

Non-additivity

The package does not sum channel Fisher information by default. Under correlated latent and item structures, information is generally not additive in the simple independent-channel sense. The ablation sequence preserves this point explicitly.

Interpretation

An incremental response-target gain supports a model-based measurement claim under the fitted assumptions. It does not by itself establish that gaze measures attention, that RT measures strategy, or that either channel is causally informative.