stan_example

# Load Stuff -------------------------------------------------------------------
rm(list=ls(all.names = T))
gc()
library(brms)
library(tidyverse)
library(tidybayes)
library(future)
library(future.apply)

set.seed(19)

# Function to simulate data ----------------------------------------------------
# Source all simulation functions 
# List all .R files in the folder
# list.files(file.path("helper_functions"), pattern = "\\.R$", full.names = TRUE) %>%
#   lapply(., function(x) {print(x);source(x)})

# Simulate data by specifying the standardised loading - measurement error set to 1 - lambda^2

sim_factor_stnd = function(
    n_rows,              # SCALAR: Sample Size
    std_loading,         # SCALAR OR VECTOR: Standardized Factor Loading
    n_items,             # SCALARL Number of items,
    intercepts,
    debug = FALSE
    
){
  if (length(std_loading)==1 & n_items > 1){
    std_loading = rep(std_loading, n_items)
  }
  if (is.null(intercepts)){
    intercepts  = rep(0, n_items)
  }
  
  error_variance = 1^2 - std_loading^2        # Set the error variance to 1-loading^2 (because obs variance =1)
  
  true_scores = rnorm(n_rows)
  dat         = sapply(1:n_items, function(i) intercepts[i] + std_loading[i]*true_scores + rnorm(n_rows, sd = sqrt(error_variance[i]))) # Note the sd(true_score) and sd(error) must be kept at 1 for the loading calculation to make sense!
  dat         = data.frame(true_scores,dat) 
  
  if (debug){
    cat("Error Variance: \n")
    print(error_variance)
    
    cat("std_loading: \n")
    print(std_loading)
    
    dat$mean = dat %>%
      select(starts_with("X")) %>%
      apply(.,1,mean)
    
    cat("\nCor(t, x):\n")
    print(round(cor(dat), digits = 2))
    
    cat("\nCor(t, x) SQAURED :\n")
    print(round(cor(dat)^2, digits = 2))
    
    cat("\nCov(t, x):\n")
    print(round(cov(dat), digits = 2))
    
    
  }
  
  return(dat)
}



# Simulate Factor Data ---------------------------------------------------------

n_rows      = 10000
n_items     = 4
std_loading = c(.25,.4,.6,.75)
std_loading = c(.5,0,.2,.1)
std_loading = c(.8,.1,.1,.1)
intercepts  = c(0,0,0,0)

dat = sim_factor_stnd(
  debug       = T,
  n_rows      = n_rows,
  n_items     = n_items,
  std_loading = std_loading,
  intercepts  = intercepts
)

dat_scale = scale(dat, center = TRUE, scale = TRUE) %>%
  data.frame()

dat_long = dat_scale %>%
  dplyr::select(-true_scores, -mean) %>%
  tibble::rowid_to_column(., var = "pps") %>%
  tidyr::pivot_longer(cols = starts_with("X")) %>%
  mutate(name = factor(name))

library(rstan)

dat = list(
  n = nrow(dat_long),
  pps_n = length(unique(dat_long$pps)),
  item_n = length(unique(dat_long$name)),
  item   = match(dat_long$name, unique(dat_long$name)),
  pps    = dat_long$pps,
  y = dat_long$value
  )

# CMDSTANR version -------------------------------------------------------------
library(cmdstanr)
mod <- cmdstan_model(file.path("helper_functions","stan_factor_model_v5exp.stan"))

fit1 <- mod$sample(
  data = dat,
  seed = 123,
  chains = 7,
  parallel_chains = 7,
  refresh = 500, # print update every 500 iters
  iter_warmup = 1000,
  iter_sampling = 1000
)