Maximum likelihood inference

Challenge

By looking at the (log) likelihoods for different dice models, try to work out which model fits best.

Is it the one where I blu-tacked 1 (so that 6 never turns up?). Or the one where I blu-tacked 4 (so that 3 never turns up)? Or another one?

Here is a way to do that using tribble() (a tibble specified row-wise) to put together the loglikeihood under all the possible models:

loglikelihoods = tibble::tribble(
    ~model, ~loglikelihood,
    "Normal dice",        total_loglikelihood( data$sum_of_dice, rep( 1/6, 6 ) ),
    "Omit 1",             total_loglikelihood( data$sum_of_dice, c(  0.0,  0.2,  0.2,  0.2,  0.2,  0.2 ) ),
    "Omit 2",             total_loglikelihood( data$sum_of_dice, c(  0.2,  0.0,  0.2,  0.2,  0.2,  0.2 ) ),
    "Omit 3",             total_loglikelihood( data$sum_of_dice, c(  0.2,  0.2,  0.0,  0.2,  0.2,  0.2 ) ),
    "Omit 4",             total_loglikelihood( data$sum_of_dice, c(  0.2,  0.2,  0.2,  0.0,  0.2,  0.2 ) ),
    "Omit 5",             total_loglikelihood( data$sum_of_dice, c(  0.2,  0.2,  0.2,  0.2,  0.0,  0.2 ) ),
    "Omit 6",             total_loglikelihood( data$sum_of_dice, c(  0.2,  0.2,  0.2,  0.2,  0.2,  0.0 ) )
)

print( loglikelihoods )

We could plot that:

(
    ggplot( data = loglikelihoods )
    + geom_point(
        aes( x = model, y = loglikelihood )
    )
    + theme(
        axis.text.x = element_text( angle = 60, hjust = 1, vjust = 1 )
    )
)

What does that mean?