glottodist_subdata: Calculate construction-based distances between languages

In SietzeN/glottospace: Language Mapping and Geospatial Analysis of Linguistic and Cultural Data

Calculate construction-based distances between languages

Description

Calculate construction-based distances between languages

Usage

glottodist_subdata(
  glottosubdata,
  metric = NULL,
  index_type = NULL,
  avg_idx = NULL,
  fixed_idx = NULL
)

Arguments

glottosubdata	an glottosubdata object
metric	either "gower" or "anderberg"
index_type	either "mci" or "ri" or "fmi"
avg_idx	the feature indices over which the average of distances is computed, it must be given when index_type is either "ri" or "fmi".
fixed_idx	the feature indices over which the distance of two constructions is computed, it must be given when index_type is either "ri" or "fmi".

Value

object of class dist

Details

The function “glottodist_subdata” returns a “dist” object, the input is a glottosubdata object, it computes the construction-based distance between languages, we refer to the observations of each language as constructions. The distance d(A_i, B_j) between two constructions A_i in a language A and B_j in a language B is determined by the argument “metric”, whose value is either “gower” or “anderberg”. When “index_type” is “mci”, it returns the “matching constructions index”:

MCI(A, B) := \frac{1}{2|A|}\sum\limits_{A_i\in A}\min\limits_{B_j\in B}d(A_i, B_j) + \frac{1}{2|B|}\sum\limits_{B_i\in B}\min\limits_{A_j\in A}d(A_j, B_i). When “index_type” is “ri”, it returns the “relative index”:

RI(A, B) = \frac{1}{|M|}\sum\limits_{s\in M}\textrm{AVG}_{A_i(s) = 1 \textrm{ and } B_j(s) = 1}d(A_i^F, B_j^F), here M is the indices of a subset of variables given by the argument “avg_idx” and F is the indices of a subset of variables given by the argument “fixed_idx”, the restricted constructions A_i^F and B_j^F are defined as the constructions A_i, B_j restricted to “fixed_idx” F. When “index_type” is “fmi”, it returns the “form-meaning index”:

FMI(A, B) = \frac{1}{|M||F|} \sum\limits_{s\in M, p\in F} \Big(1 - SIM(\{(A_i^M(s)=1 \textrm{ and }A_i^F(p)=1)\}, \{B_j^M(s) = 1 \textrm{ and }B_j^F(p) = 1\})\Big), here SIM(X, Y)=\min(|X|/|Y|, |Y|/|X|), if both X and Y are empty, SIM(X, Y)=1.

Examples

glottosubdata_cnstn <- glottoget(glottodata = "demosubdata_cnstn")
glottodist_subdata(glottosubdata = glottosubdata_cnstn, metric = "gower", index_type = "mci")
glottodist_subdata(glottosubdata = glottosubdata_cnstn, metric = "gower", index_type = "ri",
                   avg_idx = 1:4, fixed_idx = 5:7)
glottodist_subdata(glottosubdata = glottosubdata_cnstn, index_type = "fmi",
                   avg_idx = 1:4, fixed_idx = 5:7)

SietzeN/glottospace documentation built on June 15, 2024, 10:45 p.m.