Dissention, for measuring dispersion in draws from ordinal distributions.

dissent(x)

# S3 method for default
dissent(x)

# S3 method for rvar
dissent(x)

## Arguments

x

(multiple options) A vector to be interpreted as draws from an ordinal distribution, such as:

## Value

If x is a factor or numeric, returns a length-1 numeric vector with a value between 0 and 1 (inclusive) giving the dissention of x.

If x is an rvar, returns an array of the same shape as x, where each cell is the dissention of the draws in the corresponding cell of x.

## Details

Calculates Tastle and Wierman's (2007) dissention measure:

$$-\sum_{i = 1}^{n} p_i \log_2 \left(1 - \frac{|x_i - \mathrm{E}(x)| }{\max(x) - \min(x)} \right)$$

This ranges from 0 (all probability in one category) through 0.5 (uniform) to 1 (bimodal: all probability split equally between the first and last category).

## References

William J. Tastle, Mark J. Wierman (2007). Consensus and dissention: A measure of ordinal dispersion. International Journal of Approximate Reasoning. 45(3), 531--545. doi:10.1016/j.ijar.2006.06.024 .

## Examples

set.seed(1234)

levels <- c("lowest", "low", "neutral", "high", "highest")

# a bimodal distribution: high dissention
x <- ordered(
sample(levels, 4000, replace = TRUE, prob = c(0.45, 0.04, 0.02, 0.04, 0.45)),
levels = levels
)
dissent(x)
#> [1] 0.9303737

# a unimodal distribution: low dissention
y <- ordered(
sample(levels, 4000, replace = TRUE, prob = c(0.95, 0.02, 0.015, 0.01, 0.005)),
levels = levels
)
dissent(y)
#> [1] 0.1046236

# both together, as an rvar
xy <- c(rvar(x), rvar(y))
xy
#> rvar_ordered<4000>[2] mode <dissent>:
#> [1] highest <0.93>   lowest <0.10>
#> 5 levels: lowest < low < neutral < high < highest
dissent(xy)
#> [1] 0.9303737 0.1046236