Fit the same model with fixed or random effect

Modeling
1

I try to fit the same model (sort of logistic) using or a random or a fixed effect. It seems to be ok for random effect but is weird with fixed effect. Probably I do something wrong but I don’t understand where… if someone could help me (This is a toy example, true model is more complicated). I add also toy data (in dta).

dta <- data.frame(Te = c(27.85, 28.45, 28.65, 28.95, 29.65, 30.25, 
                         30.85, 28.05, 28.4, 29.55, 28, 28.5, 29, 29.5, 30, 28.7, 29, 
                         29.2, 30, 31, 32, 33, 27.2, 27.7, 28.2, 28.7, 29, 29.2, 29.5, 
                         30, 31, 32, 33, 27.2, 27.7, 28.2, 28.7, 29, 29.2, 29.5, 29.7, 
                         30, 31, 32, 33), 
                  M = c(18, 11, 9, 8, 8, 2, 0, 19, 17, 11, 26, 
                        27, 24, 13, 11, 2, 2, 1, 0, 0, 0, 0, 9, 9, 10, 6, 10, 7, 5, 4, 
                        1, 0, 0, 7, 7, 6, 6, 6, 5, 2, 3, 3, 0, 0, 0), 
                  S = c(18, 12, 11, 
                        13, 15, 4, 5, 28, 28, 31, 30, 34, 39, 27, 31, 5, 5, 5, 6, 6, 
                        7, 5, 9, 9, 10, 10, 10, 10, 8, 10, 10, 10, 10, 7, 7, 9, 10, 10, 
                        10, 10, 10, 7, 10, 10, 6), 
                  R = c("B", "B", "B", "B", "B", "B", 
                        "B", "B", "B", "B", "A", "A", "A", "A", "A", "A", "A", "A", "A", 
                        "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", 
                        "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A"
                  ))

The random effect model… works fine (R is the random effect):

prior_ini <- set_prior(prior = "uniform(20, 35)", class = "b", coef="", 
                       nlpar = "P", lb = 20, ub = 35, check = TRUE) + 
  set_prior(prior = "uniform(0, 12)", class = "b", coef="", 
            nlpar = "Sp", lb = 0, ub = 12, check = TRUE) + 
  set_prior(prior = "student_t(3, 0, 5.9)", class = "sd", 
            lb = 0, nlpar = "P")

lRE <- brm(bf(M | trials(S) ~ 1/(1+exp(-5.9*(P-Te) / Sp)), 
              P ~ (1 | R),
              Sp ~ 1, 
              nl = TRUE),
           family = binomial(link="identity"), 
           data = dta, 
           prior = prior_ini,
           warmup = 1000, 
           thin = 10, 
           iter = 20000, 
           chains = 1, 
           init=rep(list(list(b_P_Intercept=29.5, 
                              b_Sp_Intercept=1.4, 
                              sd_R__P_Intercept=0.5)),
                    1))

plot(lRE)
conditions <- make_conditions(lRE, vars="R")
plot(conditional_effects(lRE, categorical = FALSE, effects='Te', 
                         condition=conditions, robust = TRUE, 
                         re_formula=NULL, spaghetti = FALSE, ndraws = 100))

Now the same with R as fixed effect:

prior_ini <- set_prior(prior = "uniform(20, 32)", class = "b", coef="", 
                       nlpar = "P", lb = 20, ub = 32, check = TRUE) + 
  set_prior(prior = "uniform(0, 100)", class = "b", coef="", 
            nlpar = "Sp", lb = 0, ub = 100, check = TRUE) + 
  set_prior(prior = "uniform(-32, 32)", class = "b", coef="RB", 
            nlpar = "P", check = TRUE)


lFE <- brm(bf(M | trials(S) ~ 1/(1+exp(-5.9*(P-Te) / Sp)), 
              P ~ R,
              Sp ~ 1, 
              nl = TRUE),
           family = binomial(link="identity"), 
           data = dta, 
           prior = prior_ini,
           warmup = 1000, 
           thin = 10, 
           iter = 20000, 
           chains = 1, 
           init=rep(list(list(b_P_Intercept=29.5, 
                              b_P_RB=0.5, 
                              b_Sp_Intercept=1.4)),
                    1))

plot(lFE)
conditions <- make_conditions(lFE, vars="R")
plot(conditional_effects(lFE, categorical = FALSE, effects='Te', 
                         condition=conditions, robust = TRUE, 
                         re_formula=NULL, spaghetti = FALSE, ndraws = 100))

Result is clearly wrong.

Thanks
Marc