# Cognitive Models

The code here needs the LCA and C++-based PDA modules

This tutorial demonstrates the method of conducting maximum likelihood parameter estimation for the leaky competing accumulator model. You will need the subplex routines for optimization, because I use the PDA to construct the simulated PDF of the LCA model. The simulated PDF is an approximation of analytic PDF, so sPDF is noisy. The subplex is designed to handle such situation. The package can be downloaded from https://github.com/kingaa/subplex/ or CRAN.

rm(list = ls())
setwd('~/Documents/LCA5/tests/Group3/')
require(ggdmc); require(subplex)

model <- BuildModel(
p.map     = list(kappa = "1", beta = "1", Z="1", s = "1", t0 = "1",
I = "M", x0 = "1"),
match.map = list(M = list(s1 = 1, s2 = 2, s3=3)),
factors   = list(S = c("s1", "s2", "s3")),
constants = c(s = .1),
responses = c("r1", "r2", "r3"),
type      = "lca")

p.vector  <- c(kappa=1.15, beta=1, Z=0.5, t0=.200, I.true=1.2, I.false=1, x0 =.15)
nsim <- ntrial <- 1e2
## nsim <- ntrial <- 1e3

## I use the seed option to make sure I always replicate the result.
dat <- simulate(model, nsim = ntrial, ps = p.vector, seed = 123)
dmi <- BuildDMI(dat, model)
d <- data.table::data.table(dat)
## This is to create a column in the data frame to indicate
## correct and error responses.
## sapply(d[, .(S,R)], levels)

dmi$C <- ifelse(dmi$S == "s1" & dmi$R == "r1", TRUE, ifelse(dmi$S == "s2" & dmi$R == "r2", TRUE, ifelse(dmi$S == "s3" & dmi$R == "r3", TRUE, ifelse(dmi$S == "s1" & dmi$R == "s3", FALSE, ifelse(dmi$S == "s1" & dmi$R == "r2" ,FALSE, ifelse(dmi$S == "s2" & dmi$R == "r1", FALSE, ifelse(dmi$S == "s2" & dmi$R == "r3", FALSE, ifelse(dmi$S == "s3" & dmi$R == "r1", FALSE, ifelse(dmi$S == "s3" & dmi$R == "r2", FALSE, NA))))))))) prop.table(table(dmi$C))

## The maximum (log) likelihoods
## den <- likelihood(p.vector, dmi)
## sum(log(den))

objective_fun <- function(par, data) {
den <- likelihood(par, data)
return(-sum(log(den)))
}

init_par <- runif(length(p.vector))
init_par <- runif(1, 0, min(dmi$RT)) names(init_par) <- names(p.vector) ## Note the LCA PDF was calculated by using on PDA method (nsim = 16384) ## 8.1 hrs for 1e2 observations on Intel i5-6200U ## 5.14 hrs on Intel i7 res <- subplex(par = init_par, fn = objective_fun, data = dmi) str(res) round(res$par, 2)  ## remember to check res\$convergence

save(res, dat, p.vector, file = "LCA1S_MLE_1e2_subplex.RData")
save(res, dat, p.vector, file = "LCA1S_MLE_1e3_subplex.RData")

##      kappa    beta       Z      t0   I.true  I.false      x0
## True  1.15       1     0.5    0.20     1.2        1      .15
## 1e2   0.77    0.33    0.64    0.06    0.83     0.83     0.33
## 1e3   0.33    0.92    0.37    0.32    0.53     0.53     0.14