I have collected some experimental data in which participants focus on a centre and have to identify surrounding objects. It has long been identified in the literature that some positions may be easier to identify than others. I have therefore made a staircase procedure that tries to move the objects back and forth until the accuracy is roughly equal amongst positions:

I have already used BRMS to compare models with different assumptions (for instance an upper/lower division vs a left/right division). However, I have not had success with modelling an underlying ellipsoid distribution. Investigating wiki, it seems like one relevant equation could be:

I believe it could be possible to estimate with rstan but I wonder if it would be possible to estimate using BRMS. I would much prefer to stay in this environment as I have already done most of the analysis here and it would be great to formally compare these models with loo to see which would be best to describe the data.

I have created a script which simulates ellipsoid data and attempts to analyse it here.

My thought of how a model should be specified should be something like:

brm(data = dat,

family = gaussian,

mvbind(xposa(cos(t)),

yposb(sin(t))) ~ 1 +(1|part), chains = 2, cores = 2, iter=500)

Which returns:

Error: The following variables are missing in ‘data’:

‘a’, ‘t’, ‘b’

I have seen unknown variables in rstan before but not in BRMS, is this possible?

My best (very sorry attempt) does not estimate the data very well:

brm(data = dat,

family = gaussian,

mvbind(xpos, ypos) ~ 1 +(1|part), chains = 2, cores = 2, iter=500)

Is there a way that I can progress without having to start the analysis from scratch? All your response will be appreciated, I am a bit stuck here.