gam.helpers {UCS} | R Documentation |
gam.yates
and gam.yates.inv
implement an invertible
version of the discounting function used by Yates' correction.
signed.sqrt
, b.star
, b.norm
and e.bar
are
standard abbreviations used in the definition of generalised
association measures in terms of ebo-coordinates.
gam.yates(d) gam.yates.inv(d.corr) signed.sqrt(x) b.star(b) b.norm(b) e.bar(e, b, N)
d |
difference between observed and expected frequency, to which the generalised Yates' correction is applied |
d.corr |
difference between observed and expected frequency with generalised Yates' correction applied, from which the original difference can uniquely be reconstructed |
x |
a vector of positive or negative real numbers |
b |
a vector of balance (b) values in the ebo coordinate system |
e |
a vector of expectation (e) values in the ebo coordinate system |
N |
sample size N |
The standard discounting function for Yates' correction is d* := d - 1/2 for d ≥ 0 and d* := d + 1/2 for d < 0,
where d is the difference between observed and expected
frequency. This definition does not lead to a continuous and
invertible function of d, so a GAM with Yates' correction
applied does not satisfy the soundness conditions. The generalised
Yates' correction implemented by gam.yates
and
gam.yates.inv
is a monotonic (and hence invertible) function that
is identical to the standard discounting function for d >= 1 and uses linear interpolation for -1 < d < 1.
The functions signed.sqrt
, b.star
, b.norm
and
e.bar
compute the standard abbreviation +/-
sqrt(x), b*, ||b|| and
\bar{e} (“e bar”) used by Evert (2004) for the
definition of GAMs in terms of ebo-coordinates.
all functions return a vector of real numbers
Evert, Stefan (2004). The Statistics of Word Cooccurrences: Word Pairs and Collocations. PhD Thesis, IMS, University of Stuttgart.
d <- runif(20, -2, 2) d.corr <- gam.yates(d) all(d == gam.yates.inv(d.corr)) signed.sqrt(-4:4)