Setting prior for location of a psychometric curve in brms

brms_psychometric_location_prior.r

library(ggplot2)
library(data.table)
library(brms)
library(cmdstanr)
set_cmdstan_path('//wsl$/Ubuntu/home/andche/.cmdstan/cmdstan-2.35.0')


distr_fun_std <- function(x, mean, sigma, lambda){
  lambda+(1-2*lambda)*pnorm((x- mean)/sigma)
}

real_mean <- 50
real_sigma <- 50

exdata <- data.table(expand.grid(delay_ms = seq(-300,300, by = 10), repl_i = 1:100))
exdata[,fixated_right := ifelse(rnorm(.N, delay_ms-real_mean, sd = real_sigma)>0, 1, 0), by = delay_ms]

model_formula <- bf(
  fixated_right ~ Phi((delay_ms-eta)/exp(logsigma)),
  eta ~ 1,
  logsigma ~ 1,
  family = bernoulli(link="identity"),
  nl = TRUE
)

log_sigma_mean <- log(50)
p2 <- c(
  prior(normal(100, 100), coef = "Intercept",  nlpar = "eta"),
  prior(constant(3.91), class = "b", nlpar = "logsigma")
)
default_prior(model_formula, exdata)
fit <- brm(
  model_formula,
  data = exdata, 
  # control = list(adapt_delta = 0.99),
  prior = p2,
  cores = 4,
  backend = "cmdstanr",
  sample_prior = "only"
)
summary(fit)

coefs <- fixef(fit)[,'Estimate']
pred_df <-  data.table(delay_ms = seq(-200,200, by = 10))
pred_df[,pred:=pnorm((delay_ms-coefs['eta_Intercept'])/exp(coefs['logsigma_Intercept']))]
pred_df <- cbind(pred_df, predict(fit, newdata = pred_df ))
ggplot(exdata, aes(x = delay_ms, y = fixated_right))+
  geom_smooth(method = 'glm', method.args = list(family = binomial('probit')), aes(color = 'Data'), se = F)+
  stat_function(fun = distr_fun_std, args = list(mean = real_mean, sigma = real_sigma, lambda = 0), aes(color = 'Generative model'))+
  geom_line(data=pred_df, aes(y = Estimate, color = 'Fitted model with uncertainty'))+
  geom_line(data=pred_df, aes(y = pred, color = 'Fitted model'))