We expect students to submit 4 functions for assignment 1:
i. simulate_data <- function(num_obs). This function takes the number of observations (num_obs) as input and outputs a dataframe with the columns i, k, e, latent, y.
ii. compute_loglikelihood_a1 <- function(b,df). This function inputs beta (b) and the simulated dataframe (df) and outputs the loglikelihood.
iii. plot_loglikelihood_a1 <- function(df). This function inputs the simulated dataframe (df) and outputs the ggplot.
iv. optim_beta <- function(df). This function inputs the simulated dataframe (df) and outputs the optimal beta.

We use testthat to test the function submitted by students and magick to compare each pixel of the plot. For data simulation, we do column-wise comparison so it gives more detailed feedback when an error arises.