qualvar (version 0.1.0)

DM: Deviation from the mode (DM)

Description

Computes the deviation from the mode for a vector of frequencies of categories.

Usage

DM(x, na.rm = TRUE)

Arguments

x

a vector of frequencies

na.rm

if TRUE, missing values are removed. If FALSE, NA is returned if there is any NA value.

Value

• The value of the DM statistics, which is normalised (varies between 0 and 1).

Details

According to Wilcox (1973, p. 327), 'the measure can be thought of as an index of deviation from the modal frequency, analogous to the variance as a measure of deviation from the mean'. The formula for the DM is: $$1 - \frac{\sum_{i = 1}^k (f_m - f_i)}{N(K-1)}$$

References

Wilcox, Allen R. 'Indices of Qualitative Variation and Political Measurement.' The Western Political Quarterly 26, no. 2 (1 June 1973): 325-43. doi:10.2307/446831.

Examples

x <- rmultinom(1, 100, rep_len(0.25, 4))
x <- as.vector(t(x))
names(x) <- c("a", "b", "c", "d")
DM(x)

df <- rmultinom(10, 100, rep_len(0.25, 4))
df <- as.data.frame(t(df))
names(df) <- c("a", "b", "c", "d")
apply(df, 1, DM)