Question

How to find in R constant term c of log likelihood for given vectors x(1 x n) and y(1 x n)? Normal distribution.

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As c does not depend on β or σ, these parameters can be ignored.

Answer 1

R-Code:

# function for calculating log likelihood
l <- function(beta, sigma^2, X, y)
{
c <- 1 # constant value of c
# computing the likelihood
result <- ((-nlogσ-(1/2sigma^2)(y-Xbeta)^T(y-Xbeta) +c)
# return the result
return(result)
}

# number of rows of matrix X
N <- 2
# number of columns of matrix X and also for vector y
M <- 10

# initializing the matrix X with normal distribution with mean 0 and standard deviation 1
X <- matrix( rnorm(N*M,mean=0,sd=1), N, M)
# initializing the vector y with normal distribution with mean 0 and standard deviation 1
y <- rnorm(M, mean=0, sd=1)
# initializing vector beta
beta <- c(0.1,0.2)
# calling function l to compute likelihood
likely = l(beta, sigma^2, X, y)

I don't have R-studio software. Please execute the above code in R-studio. If have any queries, please let me know that queries. thank you.