Ellipse BRMS NL Attempt

### Object position BRMS model
# Load in results and libraries
library(brms)
library(loo)
mc.cores=2

# Set dictionary with dataset.txt
data <- read.table("dataset.txt", header = T)

# BRMS: Non-linear model - Ellipse
# Define Priors
prior1 <- prior(normal(0, 1, lb = 0), nlpar = "a") +
  prior(lognormal(0, 2), nlpar = "b")

priors <- c(set_prior("normal(0,2)", nlpar = "a", lb = 0),
            set_prior("normal(0,2)", nlpar = "b", lb = 0))

nlModel <- brm(bf(Distance ~ sqrt(a ^ 2 * sin(Angle)^2 + b^2 * cos(Angle)^2),
               a ~ 1, b ~ 1,
               nl = TRUE), data = data, prior = priors, cores = 2, chains = 2)
marginal_effects(nlModel)
pp_check(nlModel)
plot(nlModel)

# BRMS: Linear model - One category per angle
data$anglesF <- as.factor(data$Angle)
lModel <- mComplex <- brm(Distance ~-1+anglesF +(1|Part), data = data, chains = 2, iter=2000, cores = 2)
marginal_effects(lModel)
pp_check(lModel)

# Compare models with loo
loo(nlModel,lModel)