EconGeo (version 2.0)

z_score: Compute the z-score between technologies from an incidence matrix

Description

This function computes the z-score between pairs of technologies from a patent-technology incidence matrix. The z-score is a measure to analyze the co-occurrence of technologies in patent documents (i.e. knowledge combination). It compares the observed number of co-occurrences to what would be expected under the hypothesis that combination is random. A positive z-score indicates a typical co-occurrence which has occurred multiple times before. In contrast, a negative z-socre indicates an atypical co-occurrence. The z-score has been used to estimate the degree of novelty of patents (Kim 2016), scientific publications (Uzzi et al. 2013) or the relatedness between industries (Teece et al. 1994).

Usage

z_score(mat)

Value

A matrix of z-scores representing the co-occurrence of technologies in the input incidence matrix. The z-score measures the deviation of the observed co-occurrence from the expected co-occurrence under the assumption of random combination. Positive z-scores indicate typical co-occurrences, while negative z-scores indicate atypical co-occurrences.

Arguments

mat

A patent-technology incidence matrix with patents in rows and technologies in columns

Author

Lars Mewes

References

Kim, D., Cerigo, D. B., Jeong, H., and Youn, H. (2016). Technological novelty proile and invention's future impact. EPJ Data Science, 5 (1):1--15

Teece, D. J., Rumelt, R., Dosi, G., and Winter, S. (1994). Understanding corporate coherence. Theory and evidence. Journal of Economic Behavior and Organization, 23 (1):1--30

Uzzi, B., Mukherjee, S., Stringer, M., and Jones, B. (2013). Atypical Combinations and Scientific Impact. Science, 342 (6157):468--472

See Also

relatedness_density, co_occurrence

Examples

## Generate a toy incidence matrix
set.seed(2210)
techs <- paste0("T", seq(1, 5))
techs <- sample(techs, 50, replace = TRUE)
patents <- paste0("P", seq(1, 20))
patents <- sort(sample(patents, 50, replace = TRUE))
my_data <- data.frame(patents, techs)
my_dat <- unique(my_data)
mat <- as.matrix(table(my_data$patents, my_data$techs))

## run the function
z_score(mat)