R/int_llLognorm.R

In statConfR: Models of Decision Confidence and Measures of Metacognition

ll_lognorm <-
  function(p, N_SA_RA,N_SA_RB, N_SB_RA, N_SB_RB, nRatings, nCond){
    p <- c(t(p))
    ds <- cumsum(exp(p[1:(nCond)])) # enforce that sensitivity is ordered
    locA <- -ds/2
    locB <- ds/2
    theta <- p[nCond+nRatings]
    sigma <- exp(p[nCond + nRatings*2]) # sigma needs to be bounded between 0 and Inf
                                        # see whether the results converge.
    # average placement of the confidence criteria
    mu_cA <- theta + rev(cumsum(c(exp(p[(nCond+1):(nCond+nRatings-1)]))))
    mu_cB <- theta + cumsum(c(exp(p[(nCond+nRatings+1):(nCond + nRatings*2-1)])))

    # convert to the location parameter of the latent lognormal distribution
    loc_RA <-  c(Inf,log(abs(mu_cA - theta)) - .5*sigma^2, -Inf) # the order here is REVERSED!!!
    loc_RB <- c(-Inf, log(mu_cB - theta) - .5*sigma^2, Inf)

    p_SA_RA <- matrix(NA, nrow=nCond, ncol = nRatings)
    p_SA_RB <- matrix(NA, nrow=nCond, ncol = nRatings)
    p_SB_RA <- matrix(NA, nrow=nCond, ncol = nRatings)
    p_SB_RB <- matrix(NA, nrow=nCond, ncol = nRatings)

    P_SBRB <-  Vectorize(function(j,i){
      integrate(function(x) dnorm(x, locB[j]) *
                  (plnorm(x-theta, loc_RB[i], sigma) - plnorm(x-theta, loc_RB[i+1], sigma)),
                lower = theta, upper = Inf, rel.tol = 10^-8)$value
    })
    P_SBRA <-  Vectorize(function(j,i){
      integrate(function(x) dnorm(x, locB[j]) *
                  (plnorm(theta-x,  loc_RA[i+1], sigma) - plnorm(theta-x,  loc_RA[i], sigma)),
                lower = -Inf, upper =theta, rel.tol = 10^-8)$value
    })
    P_SARA <- Vectorize(function(j,i){
      integrate(function(x) dnorm(x, locA[j]) *
                  (plnorm(theta-x,  loc_RA[i+1], sigma) - plnorm(theta-x,  loc_RA[i], sigma)),
                lower = -Inf, upper =theta, rel.tol = 10^-8)$value
    })
    P_SARB <- Vectorize(function(j,i){
      integrate(function(x) dnorm(x, locA[j]) *
                  (plnorm(x-theta, loc_RB[i], sigma) - plnorm(x-theta, loc_RB[i+1], sigma)),
                lower = theta, upper = Inf, rel.tol = 10^-8)$value
    })


    p_SB_RB <- outer(1:nCond, 1:nRatings, P_SBRB)
    p_SB_RA <- outer(1:nCond, 1:nRatings, P_SBRA)
    p_SA_RA <- outer(1:nCond, 1:nRatings, P_SARA)
    p_SA_RB <- outer(1:nCond, 1:nRatings, P_SARB)

    p_SB_RB[(is.na(p_SB_RB))| is.nan(p_SB_RB)| p_SB_RB < 10^-64] <- 10^-64
    p_SB_RA[(is.na(p_SB_RA))| is.nan(p_SB_RA)| p_SB_RA < 10^-64] <- 10^-64
    p_SA_RB[(is.na(p_SA_RB))| is.nan(p_SA_RB)| p_SA_RB < 10^-64] <- 10^-64
    p_SA_RA[(is.na(p_SA_RA))| is.nan(p_SA_RA)| p_SA_RA < 10^-64] <- 10^-64

    negLogL <- - sum (c(log(p_SB_RB) * N_SB_RB, log(p_SB_RA) * N_SB_RA,
                        log(p_SA_RB) * N_SA_RB, log(p_SA_RA) * N_SA_RA))
    negLogL
  }