gam.helpers {UCS} | R Documentation |

## Helper Functions for GAM Equations (gam)

### Description

`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.

### Usage

gam.yates(d)
gam.yates.inv(d.corr)
signed.sqrt(x)
b.star(b)
b.norm(b)
e.bar(e, b, N)

### Arguments

`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* |

### Details

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.

### Value

all functions return a vector of real numbers

### References

Evert, Stefan (2004). *The Statistics of Word Cooccurrences: Word
Pairs and Collocations.* PhD Thesis, IMS, University of Stuttgart.

### Examples

d <- runif(20, -2, 2)
d.corr <- gam.yates(d)
all(d == gam.yates.inv(d.corr))
signed.sqrt(-4:4)

[Package

*UCS* version 0.5

Index]