R/loglikelihood.r

In PAIRADISE: PAIRADISE: Paired analysis of differential isoform expression

#' loglikelihood
#'
#'
#' Used internally in PAIRADISE to compute the log-likelihood function 
#'
#' @name loglikelihood
#' @param M Number of replicates for the current exon. Positive integer. 
#' @param I1 Exon inclusion counts for group 1. Positive integers. 
#' @param S1 Exon skipping counts for group 1. Positive integers.
#' @param I2 Exon inclusion counts for group 2. Positive integers.
#' @param S2 Exon skipping counts for group 2. Positive integers.
#' @param l.iI Effective length of inclusion isoform. Positive integer.
#' @param l.iS Effective length of skipping isoform. Positive integer.
#' @param logit.psi1 Numeric vector with values of logit psi1.
#' @param logit.psi2 Numeric vector with values of logit psi2.
#' @param alpha Numeric vector with values of alpha.
#' @param s1 Group 1 standard deviation. Positive number.
#' @param s2 Group 2 standard deviation. Positive number.
#' @param s Overall standard deviation. Positive number.
#' @param mu Parameter mu.
#' @param delta Parameter delta.
#' @return log likelihood value at input.
#' @keywords internal

loglikelihood <- function(M, I1, S1, I2, S2, l.iI, l.iS, logit.psi1, logit.psi2, 
    alpha, s1, s2, s, mu, delta) {
    
    numerator1 <- l.iI * l.iS * sigmoid(logit.psi1) * (sigmoid(logit.psi1) - 1) * 
        (I1 + S1)
    numerator2 <- l.iI * l.iS * sigmoid(logit.psi2) * (sigmoid(logit.psi2) - 1) * 
        (I2 + S2)
    
    denominator1 <- (l.iI * sigmoid(logit.psi1) + l.iS * (1 - sigmoid(logit.psi1)))^2
    denominator2 <- (l.iI * sigmoid(logit.psi2) + l.iS * (1 - sigmoid(logit.psi2)))^2
    
    a1 <- M * (log(s1) + log(s2) + log(s))
    a2 <- sum((logit.psi1 - alpha)^2)/(2 * (s1^2))
    a3 <- sum((logit.psi2 - alpha - delta)^2)/(2 * (s2^2))
    a4 <- sum((alpha - mu)^2)/(2 * (s^2))
    
    b1 <- (1/s1^4) * ((1/(s2^2)) - numerator2/denominator2)
    b2 <- (1/(s1^2)) - (numerator1/denominator1)
    b3 <- (1/s2^4) + ((1/(s1^2)) + (1/(s2^2)) + (1/(s^2))) * ((numerator2/denominator2) - 
        (1/(s2^2)))
    
    c1 <- sum(I1 * log((l.iI * sigmoid(logit.psi1))/(l.iI * sigmoid(logit.psi1) + 
        l.iS * (1 - sigmoid(logit.psi1)))))
    c2 <- sum(S1 * log((l.iS * (1 - sigmoid(logit.psi1)))/(l.iI * sigmoid(logit.psi1) + 
        l.iS * (1 - sigmoid(logit.psi1)))))
    c3 <- sum(I2 * log((l.iI * sigmoid(logit.psi2))/(l.iI * sigmoid(logit.psi2) + 
        l.iS * (1 - sigmoid(logit.psi2)))))
    c4 <- sum(S2 * log((l.iS * (1 - sigmoid(logit.psi2)))/(l.iI * sigmoid(logit.psi2) + 
        l.iS * (1 - sigmoid(logit.psi2)))))
    
    result <- -(a1 + a2 + a3 + a4 + 0.25 * sum(log((b1 + b2 * b3)^2))) + c1 + c2 + 
        c3 + c4
    result
    
}

# loglikelihood <- function(M, I1, S1, I2, S2, l.iI, l.iS, logit.psi1,
# logit.psi2, alpha, s1, s2, s, mu, delta){ numerator1 <- l.iI *
# sigmoid(logit.psi1) numerator2 <- l.iS * (1 - sigmoid(logit.psi1)) numerator3
# <- l.iI * sigmoid(logit.psi2) numerator4 <- l.iS * (1 - sigmoid(logit.psi2))
# denominator1 <- (l.iI * sigmoid(logit.psi1) + l.iS * (1 - sigmoid(logit.psi1)))
# denominator2 <- (l.iI * sigmoid(logit.psi2) + l.iS * (1 - sigmoid(logit.psi2)))
# a1 <- sum(I1 * log(numerator1 / denominator1)) a2 <- sum(S1 * log(numerator2 /
# denominator1)) a3 <- sum(I2 * log(numerator3 / denominator2)) a4 <- sum(S2 *
# log(numerator4 / denominator2)) b1 <- M * (log(s1) + log(s2) + log(s)) b2 <-
# sum((logit.psi1 - alpha)^2) / (2*(s1^2)) b3 <- sum((logit.psi2 - alpha -
# delta)^2) / (2*(s2^2)) b4 <- sum((alpha - mu)^2) / (2*(s^2)) result <- a1 + a2
# + a3 + a4 - b1 - b2 - b3 - b4 result }