Calculate the lexical diversity or complexity of text(s).
textstat_lexdiv(x, measure = c("all", "TTR", "C", "R", "CTTR", "U", "S",
"Maas"), log.base = 10)an input object, such as a document-feature matrix object
a character vector defining the measure to calculate.
a numeric value defining the base of the logarithm (for measures using logs)
not used
textstat_lexdiv returns a data.frame of documents and
their lexical diversity scores.
textstat_lexdiv calculates a variety of proposed indices for lexical
diversity. In the following formulae, \(N\) refers to the total number of
tokens, and \(V\) to the number of types:
"TTR":The ordinary Type-Token Ratio: $$TTR = \frac{V}{N}$$
"C":Herdan's C (Herdan, 1960, as cited in Tweedie & Baayen, 1998; sometimes referred to as LogTTR): $$C = \frac{\log{V}}{\log{N}}$$
"R":Guiraud's Root TTR (Guiraud, 1954, as cited in Tweedie & Baayen, 1998): $$R = \frac{V}{\sqrt{N}}$$
"CTTR":Carroll's Corrected TTR: $$CTTR = \frac{V}{\sqrt{2N}}$$
"U":Dugast's Uber Index (Dugast, 1978, as cited in Tweedie & Baayen, 1998): $$U = \frac{(\log{N})^2}{\log{N} - \log{V}}$$
"S":Summer's index: $$S = \frac{\log{\log{V}}}{\log{\log{N}}}$$
"K":Yule's K (Yule, 1944, as cited in Tweedie & Baayen, 1998) is calculated by: $$K = 10^4 \times \frac{(\sum_{X=1}^{X}{{f_X}X^2}) - N}{N^2}$$ where \(N\) is the number of tokens, \(X\) is a vector with the frequencies of each type, and \(f_X\) is the frequencies for each X.
"Maas":Maas' indices (\(a\), \(\log{V_0}\) & \(\log{}_{e}{V_0}\)): $$a^2 = \frac{\log{N} - \log{V}}{\log{N}^2}$$ $$\log{V_0} = \frac{\log{V}}{\sqrt{1 - \frac{\log{V}}{\log{N}}^2}}$$ The measure was derived from a formula by Mueller (1969, as cited in Maas, 1972). \(\log{}_{e}{V_0}\) is equivalent to \(\log{V_0}\), only with \(e\) as the base for the logarithms. Also calculated are \(a\), \(\log{V_0}\) (both not the same as before) and \(V'\) as measures of relative vocabulary growth while the text progresses. To calculate these measures, the first half of the text and the full text will be examined (see Maas, 1972, p. 67 ff. for details). Note: for the current method (for a dfm) there is no computation on separate halves of the text.
Covington, M.A. & McFall, J.D. (2010). Cutting the Gordian Knot: The Moving-Average Type-Token Ratio (MATTR). Journal of Quantitative Linguistics, 17(2), 94--100.
Maas, H.-D., (1972). \"Uber den Zusammenhang zwischen Wortschatzumfang und L\"ange eines Textes. Zeitschrift f\"ur Literaturwissenschaft und Linguistik, 2(8), 73--96.
McCarthy, P.M. & Jarvis, S. (2007). vocd: A theoretical and empirical evaluation. Language Testing, 24(4), 459--488.
McCarthy, P.M. & Jarvis, S. (2010). MTLD, vocd-D, and HD-D: A validation study of sophisticated approaches to lexical diversity assessment. Behaviour Research Methods, 42(2), 381--392.
Michalke, Meik. (2014) koRpus: An R Package for Text Analysis. Version 0.05-5. http://reaktanz.de/?c=hacking&s=koRpus
Tweedie. F.J. & Baayen, R.H. (1998). How Variable May a Constant Be? Measures of Lexical Richness in Perspective. Computers and the Humanities, 32(5), 323--352.
# NOT RUN {
mydfm <- dfm(corpus_subset(data_corpus_inaugural, Year > 1980), verbose = FALSE)
(result <- textstat_lexdiv(mydfm, c("CTTR", "TTR", "U")))
cor(textstat_lexdiv(mydfm, "all")[,-1])
# }
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