Estimate profile likelihood and 95% CI

This function estimate the profile likelihood and 95% CI for a one or two parameter model

Usage

calculate_profile(
  log_likelihood,
  data_in,
  n_param,
  a_initial,
  b_initial = NULL,
  precision = 0.01
)

Arguments

log_likelihood

Log-likelihood function in form function(x,a) (one parameter model) or function(x,a,b) (two parameter model)

data_in

Vector of observations to be evaluated in log_likelihood, with overall likelihood given by sum(log_likelihood)

n_param

Number of parameters in log_likelihood model

a_initial

Initial guess for parameter a

b_initial

Initial guess for parameter b (if a two parameter model, otherwise default is NULL)

precision

Parameter defining how fine-scale the grid search is for the profile likelihood

Author

Adam Kucharski, Joshua W. Lambert

Examples

# example of a one parameter model
data_in <- rnorm(n = 100, mean = 1, sd = 2)
log_likelihood <- function(x,a) dnorm(x, a, 2, log = TRUE)
n_param <- 1
a_initial <- 0.5

calculate_profile(
  log_likelihood = log_likelihood,
  data_in = data_in,
  n_param = 1,
  a_initial = 4,
  precision = 0.1
)
#> $estimate
#> [1] 1.141578
#> 
#> $profile_out
#>        a1        a2 
#> 0.7495856 1.5335712 
#> 

# examle of a two parameter model
data_in <- rnorm(n = 100, mean = 1, sd = 1)
log_likelihood <- function(x,a,b) dnorm(x, a, b, log = TRUE)
n_param <- 2
a_initial <- 0.5
b_initial <- 1

calculate_profile(
  log_likelihood = log_likelihood,
  data_in = data_in,
  n_param = 2,
  a_initial = 4,
  b_initial = 2,
  precision = 0.1
)
#> $estimate
#>        a        b 
#> 1.115020 1.009153 
#> 
#> $profile_out
#>        a1        a2        b1        b2 
#> 0.9641402 1.3641402 0.8729176 1.1453889 
#>