Ellipse BRMS

### Ellipse simulation
### Simulate X ellipses with y points and attempt to estimate the shape

# Load library
library("brms")

# Set Seed
set.seed(42)

# Define ellipses
nlev <- 8 # Points
nr <- 10 # Participants
width <- 12
height <- 10

# Generate n Circles
angs <- seq(pi/2,-pi-2*pi/nlev,-2*pi/nlev)
capture <- matrix(NA,nlev,3)
capture[,1] <- 1
# Add noise per meassure
indvar <- rnorm(1)
random <- rnorm(nlev,indvar,sd=0.1)
capture[,2] <- cos(angs)*(width+random)
capture[,3] <- sin(angs)*(height+random)
captureTemp <- matrix(NA,nlev,3)
for(i in 2:nr){
  indvar <- rnorm(1)
  random <- rnorm(nlev,indvar,sd=0.1)
  captureTemp[,1] <- i
  captureTemp[,2] <- cos(angs)*(width+random)
  captureTemp[,3] <- sin(angs)*(height+random)
  capture <- rbind(capture,captureTemp)}
# Make data frame
dat <- data.frame(capture)
names(dat) <- c("part", "xpos", "ypos")

# Plot
limit <- max(capture)
plot(dat$xpos,dat$ypos, xlim = c(-limit,limit), ylim = c(-limit,limit))

# Brms (wrong method, surely)
m1 <- brm(data = dat,
                   family = gaussian,
                   mvbind(xpos, ypos) ~ 1 +(1|part), chains = 2, cores = 2, iter=500)
m1
# Attempt at better model
m2 <- brm(data = dat,
             family = gaussian,
             mvbind(xpos*a*(cos(t)),
                    ypos*b*(sin(t))) ~ 1 +(1|part), chains = 2, cores = 2, iter=500)