shannonEntropy: Shannon Entropy and Theil entropy decomposition

In n3ssuno/RKS: Regional Knowledge Space

Description

The function returns the Shannon information entropy of a given table. Optionally, it can return also the values for the entropy decomposed in the two constituents of within- and between-groups entropy.

Usage

shannonEntropy(occt, log_base = 2, Theil_decomp = NULL)

Arguments

occt	Contingency table (i.e., occurrence table or incidence matrix) on which you want to compute the indices. It can be a 2D array, in which the first dimension represents the units of analysis (like firms, regions, or countries), and the second dimension represents the events or characteristics of interest (like the classes of the patents produced by the regions, or the sectors in which the workers belongs). Lastly, the values in each cell represents the occurrences of each unit-event pair. Moreover, you can use also a 3D array if you like, in which the third dimension represents the time. The object is expected to be of "table" class.
log_base	Base of the logarithm used to compute the entropy (i.e., its unit of measure). The default value is 2. You can use any number you like (to use the natural logarithm, write exp(1)).
Theil_decomp	A list of groups . It should be of the same length of the second dimension of the occt provided.

Details

The function returns the Shannon information entropy of a given table. It computes internally the frequency of each observation and, if not specified differently, uses "bits" as units of measure. The function can compute either the entropy of a cross-section, or of a panel. If a vector of groups is provided, the function returns also the values for the entropy decomposed in the two constituents of within- and between-groups entropy, following the Theil's decomposition.

Value

data.table with the (total) entropy and (eventually) its decomposition in between- and within-group components.

References

Theil (1972) Statistical Decomposition Analysis, North-Holland.

Zadjenweber (1972) “Une Application de la Théorie de l'Information à l'Économie: La Mesure de la Concentration”, Revue d'Economie Politique, 82, 486–510.

Frenken (2007) “Entropy Statistics and Information Theory”, in Hanusch and Pyka (Eds.) Elgar Companion to Neo-Schumpeterian Economics, Edward Elgar.

Stirling (2007) “A General Framework for Analysing Diversity in Science, Technology and Society”, Journal of The Royal Society Interface, 4, 707–719.

Quatraro (2010) “Knowledge Coherence, Variety and Economic Growth: Manufacturing Evidence from Italian Regions”, Research Policy, 39, 1289-1302;

Examples

geo <- paste0("R", 10:50)
tech <- paste0("T", 10:90)
time <- 1:5
dat <- expand.grid(geo, tech, time)
colnames(dat) <- c("geo", "tech", "time")
set.seed(1)
dat$nPat <- sample(1:200, nrow(dat), replace = TRUE)
octab <- xtabs(nPat ~ geo + tech + time, dat)
octab[sample(1:length(octab), length(octab)/2)] <- 0
grps <- substr(attr(octab, "dimnames")$tech, 2, 2)
ETP <- shannonEntropy(octab,
                      log_base = exp(1),
                      Theil_decomp = grps)

n3ssuno/RKS documentation built on Jan. 15, 2020, 5:15 p.m.