GRIN recovers a General Recognition Theory representation (mostly) well. The challenging part is knowing whether two dimensions are perceptually independent, which is to say whether the within-stimulus correlation is zero. Here, we walk through why, using the same machinery as the rest of the site, and what it suggests for your study design. Everything here points to the difficulty being a feature of the data and the task rather than any particular way of fitting, so it is worth understanding rather than working around. Validate shows the recovery and calibration that hold across the rest of the representation and this page explores when and why you should be careful.
On the left, the two dimensions are independent and on the right they carry a correlation you set. The perceptual pictures are clearly different, but the confusion matrices they produce (below) are almost the same, which is the whole problem.
Independent (ρ = 0)
Correlated
How often GRIN reports a correlation, against the true |ρ|. Near zero it should stay low, correctly calling the dimensions independent. It climbs only as the correlation grows. The stretch in between, where real but weak correlations are missed, is the recovery frontier for independence.
It is tempting to hope that adding response times pins down the correlation the counts cannot. Our results suggest they mostly do not, and the reason is collinearity. As the correlation changes it moves accuracy and response time together, so the timing carries little information about the correlation beyond what accuracy already reported. Adding the full response-time model helps, but modestly The short version is that timing sharpens the architecture question far more than it sharpens the correlation.
Based on our own results, recovering the perceptual correlation from a single identification matrix looks like a hard problem, and the difficulty appears to sit in the data and the task rather than in any particular estimator. We would expect approaches built on the same measurements to meet the same wall, so we read this as a feature of the setup, not a shortcoming of one method.
Given that, a few directions seem reasonable to us. Treat the correlation as a distribution over the options rather than a single winner, and keep it separate from the separability decision, which is identified far more firmly. An unresolved correlation is best read as unresolved, not as independence and not as a failed fit.
Where correlation genuinely matters, the leverage seems to lie in the data you collect more than the method you fit. Asking participants for confidence ratings, or having them respond to the two dimensions separately or in sequence rather than as one joint response, could add information a single joint matrix does not carry. These are directions our work points toward rather than settled prescriptions, and you are welcome and encouraged to be the one to test that.
Finally, methods designed to bring in extra information are worth reaching for where they apply. Approaches that pool across participants, such as GRT-wIND, can recover structure no single matrix holds, and where that kind of design or data is available it is the better tool for the job. None of this counts against maximum likelihood or the existing GRT software. On the parts of the model that are identified, they and GRIN land in the same place.