rockchalk (version 1.6.2)

summarizeFactors: Extracts non-numeric variables, calculates summary information, including entropy as a diversity indicator.

Description

This function finds the non- numeric variables and ignores the others. (See summarizeNumerics for a function that handles numeric variables.) It then treats all non-numeric variables as if they were factors, and summarizes each. The main benefits from this compared to R's default summary are 1) more summary information is returned for each variable (entropy estimates ofdispersion), 2) the columns in the output are alphabetized. To prevent alphabetization, use alphaSort = FALSE.

Usage

summarizeFactors(dat = NULL, maxLevels = 5,
    alphaSort = TRUE, sumstat = TRUE,
    digits = max(3, getOption("digits") - 3))

Arguments

dat

A data frame

maxLevels

The maximum number of levels that will be reported.

alphaSort

If TRUE (default), the columns are re-organized in alphabetical order. If FALSE, they are presented in the original order.

sumstat

If TRUE (default), report indicators of dispersion and the number of missing cases (NAs).

digits

integer, used for number formatting output.

Value

• A list of factor summaries

Details

Entropy is one possible measure of diversity. If all outcomes are equally likely, the entropy is maximized, while if all outcomes fall into one possible category, entropy is at its lowest values. The lowest possible value for entropy is 0, while the maximum value is dependent on the number of categories. Entropy is also called Shannon's information index in some fields of study (Balch, 2000 ; Shannon, 1949 ).

Concerning the use of entropy as a diversity index, the user might consult Balch(). For each possible outcome category, let p represent the observed proportion of cases. The diversity contribution of each category is -p * log2(p). Note that if p is either 0 or 1, the diversity contribution is 0. The sum of those diversity contributions across possible outcomes is the entropy estimate. The entropy value is a lower bound of 0, but there is no upper bound that is independent of the number of possible categories. If m is the number of categories, the maximum possible value of entropy is -log2(1/m).

Because the maximum value of entropy depends on the number of possible categories, some scholars wish to re-scale so as to bring the values into a common numeric scale. The normed entropy is calculated as the observed entropy divided by the maximum possible entropy. Normed entropy takes on values between 0 and 1, so in a sense, its values are more easily comparable. However, the comparison is something of an illusion, since variables with the same number of categories will always be comparable by their entropy, whether it is normed or not.

References

Balch, T. (2000). Hierarchic Social Entropy: An Information Theoretic Measure of Robot Group Diversity. Auton. Robots, 8(3), 209-238.

Shannon, Claude. E. (1949). The Mathematical Theory of Communication. Urbana: University of Illinois Press.

See Also

summarizeFactors and summarizeNumerics

Examples

set.seed(21234)
x <- runif(1000)
xn <- ifelse(x < 0.2, 0, ifelse(x < 0.6, 1, 2))
xf <- factor(xn, levels=c(0,1,2), labels("A","B","C"))
dat <- data.frame(xf, xn, x)
summarizeFactors(dat)
##see help for summarize for more examples