R function for fitting a normal mixture model to exit velocities for balls in play for a specific baseball hitter.

fit_norm_mix_model.R

fit_norm_mix_model <- function(pname, statcast){
  require(dplyr)
  require(LearnBayes)
  library(magrittr)
  logpost <- function(theta, y){
    mu1 <- theta[1]
    sigma1 <- exp(theta[2])
    mu2 <- theta[3]
    sigma2 <- exp(theta[4])
    p <- exp(theta[5]) / (1 + exp(theta[5]))
    sum(log(p * dnorm(y, mu1, sigma1) +
              (1 - p) * dnorm(y, mu2, sigma2)))
  }
  invlogit <- function(y){
    exp(y) / (1 + exp(y))
  }
  statcast |> 
    filter(type == "X",
           player_name == pname) |> 
    filter(is.na(launch_speed) == FALSE) |> 
    pull(launch_speed) -> y_AB
  y1 <- y_AB[y_AB < median(y_AB)]
  y2 <- y_AB[y_AB > median(y_AB)]
  theta0 <- c(mean(y1), log(sd(y1)), 
              mean(y2), log(sd(y2)), 0)
  laplace(logpost, theta0, y_AB) |> 
    extract2(1) -> Mode
  data.frame(player_name = pname,
             mu1 = Mode[1], log_sd1 = Mode[2],
             mu2 = Mode[3], log_sd2 = Mode[4],
             logit_p = Mode[5]) |> 
    mutate(sd1 = exp(log_sd1),
           sd2 = exp(log_sd2),
           p = invlogit(logit_p)) |> 
    select(player_name, mu1, sd1, mu2, sd2, p)
}