M2 Three-Way Reference Model: Response, RT, and Gaze
Source:vignettes/m2-three-way-reference-model-0-10.Rmd
m2-three-way-reference-model-0-10.RmdScope
The M2 milestone implements a likelihood-faithful three-way
response-process model motivated by Man, Harring, and Zhan (2022), DOI
10.1177/01466216221089344. The measurement layer combines a
Rasch response model, a lognormal response-time model, and a
negative-binomial fixation-count model. Person-side ability, speed, and
gaze-process effects are correlated; item difficulty, time intensity,
and gaze intensity are also correlated.
The implementation deliberately separates likelihood
fidelity from prior fidelity.
prior_profile = "regularized" uses regularizing Stan
priors. "paper_centered" centers priors near values
described in the source literature but is not claimed to reproduce every
published hyperprior exactly.
No process channel is automatically interpreted as attention, cognitive load, guessing, strategy, or difficulty.
Canonical specification
library(eyeprocess)
#> eyeprocess 0.11.1: vendor-neutral eye/process data harmonization with first-class Gazepoint support.
spec <- multimodal_m2_spec()
spec
#> <eye_multimodal_m2_spec>
#> model: M2 response + RT + gaze
#> backend: cmdstanr
#> likelihood: Rasch + lognormal RT + negative-binomial gaze
#> reference DOI: 10.1177/01466216221089344
#> prior profile: regularized
#> missingness: ignorable
#> lifecycle: experimental
#> boundary: process channels are observations, not automatic psychological constructsThe object is not a new specification ecosystem. It inherits the
existing eye_multimodal_irt_spec and
eye_irt_model_spec architecture and composes the
established irt_*_channel() constructors.
Simulation
sim <- simulate_multimodal_m2(
n_person = 80,
n_item = 10,
seed = 20260814
)
head(sim$data)
#> person_id item_id response rt gaze
#> 1 P0001 I001 1 2.978669 161
#> 2 P0002 I001 1 76.968523 114
#> 3 P0003 I001 0 48.517830 29
#> 4 P0004 I001 1 23.997114 64
#> 5 P0005 I001 0 71.585599 58
#> 6 P0006 I001 1 26.440118 63
sim
#> <eye_multimodal_m2_simulation>
#> persons: 80
#> items: 10
#> rows: 800
#> dropout: response=0.000, rt=0.000, gaze=0.000
#> seed: 20260814
#> generating likelihood: response-Rasch + lognormal-RT + NB-fixationThe complete generating data and all latent truth are retained
separately in sim$complete_data and
sim$truth.
Structural audit
audit <- audit_multimodal_m2_identifiability(sim$data)
audit
#> <eye_multimodal_m2_identifiability>
#> model: M2
#> persons: 80
#> items: 10
#> supported: TRUE
#> missing fractions: response=0.000, rt=0.000, gaze=0.000
#> 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 audit is a conservative pre-fit screen. Passing it does not prove global identifiability, empirical adequacy, or construct validity.
CmdStan fit
The estimator is gated. It fails explicitly if CmdStanR/CmdStan are unavailable and does not substitute another engine.
fit <- fit_multimodal_m2(
sim,
chains = 4,
parallel_chains = 4,
iter_warmup = 1000,
iter_sampling = 1000,
seed = 9001
)
summary(fit)
plot(fit, type = "person_correlations")
plot(fit, type = "item_correlations")
plot(fit, type = "item_parameters")Identification
The reference implementation fixes the person latent means to zero,
fixes the response discrimination to one, uses a fixed -1
speed loading in the log-time mean, and a fixed +1
gaze-process loading in the negative-binomial log mean. These
constraints define the channel scales. The structural covariance
parameters remain estimated.