Questions about the calculation of da1, mu1, and mu1hat in HGF, specifically tapas_hgf_whatworld family of scripts.

[Heechberri]

Hi experts,

I am using the tapas_hgf_whatworld family of scripts (edited, edits explained below) to model the perceptual states of a pSRTT task (adapted from Marshall et al, 2016).

I am facing an awkward problem where the more accurate my subject's mu1hat is, the higher their da1 becomes.
Below is a graph to illustrate the problem:

the correct transitional probability of a high-frequency previous trial to a low-frequency current trial is 0.3 of the time, hence younger adults are marginally and significantly better at predicting mu1hat as compared to older adults in correct high-to-low frequency trials

However, younger adults have higher da1 as compared to older adults for correctly answered high-to-low frequency trials.

Have I done something wrong? Can anyone explain this?

Below is a description of my task and what I have done.

Description of my task
Briefly, this task contains 4 visual targets, appearing in different sequences of 50 trials each. For each trial within the 50 trials, one of the 4 visual targets will appear most frequently (70% of the time, high-frequency stimulus), while the rest of the 3 visual targets at 10% of the time (a total of 30%; low-frequency stimulus). The high-frequency stimulus changes every 50 trials, while the frequency of appearance stays the same between high and low-frequency stimuli. Low-frequency visual targets are looked at together as one whole low-frequency stimulus (appearing at an accumulative sum of 30% of the time).

To summarise, below is the transitional matrix between the previous trial (column) and the current trial (row)

()

Additionally, I have a 5th kind of trial-to-trial transition that is random (each visual targets is shown at 25% of the time) and used for dummy trials.

This is how I have set up my ttms in the tapas_hgf_whatworld_config.m, and how I have set up my input variables:

ttms

c.ttm = NaN(4,4,5);

c.ttm(:,:,1) = [
    0.70 0.70 0.70 0.70;...
    0.10 0.10 0.10 0.10;...
    0.10 0.10 0.10 0.10;...
    0.10 0.10 0.10 0.10;...
               ];

c.ttm(:,:,2) = [
    0.10 0.10 0.10 0.10;...
    0.70 0.70 0.70 0.70;...
    0.10 0.10 0.10 0.10;...
    0.10 0.10 0.10 0.10;...
               ];

c.ttm(:,:,3) = [
    0.10 0.10 0.10 0.10;...
    0.10 0.10 0.10 0.10;...
    0.70 0.70 0.70 0.70;...
    0.10 0.10 0.10 0.10;...
               ];

c.ttm(:,:,4) = [
    0.10 0.10 0.10 0.10;...
    0.10 0.10 0.10 0.10;...
    0.10 0.10 0.10 0.10;...
    0.70 0.70 0.70 0.70;...
               ];

c.ttm(:,:,5) = [
    0.25 0.25 0.25 0.25;...
    0.25 0.25 0.25 0.25;...
    0.25 0.25 0.25 0.25;...
    0.25 0.25 0.25 0.25;...
               ];

My input into the model consists of 2 columns.

1. Visual target 1,2,3,or 4
2. ttm 1,2,3,4 or 5

Thank you!
Regards.
Vae