UCS::AM::Parametric - Parametric association measures

use UCS; use UCS::AM::Parametric; @parametric_AMs = UCS::AM_Keys(); # MI.conf # MI.conf.<n> [<n> = 2, 3, 5, 10, 50, 100, 1000] # Poisson.mu.pv # Poisson.mu.<n>.pv [<n> = 2, 3, 5, 10, 50, 100, 1000, 10000]

This module contains some parametric **association measures**, which are parametrised extensions of measures defined in the basic **UCS::AM** module. Parametric measures are a recent development in cooccurrence statistics, and the choice of appropriate parameter values is still very much a research question. Parametric measures will often be computationally expensive and may be numerically unstable, so novice users are advised to use the basic measures from the **UCS::AM** module instead.

The following section gives a full listing of the parametric association measures defined in the **UCS::AM::Parametric** module with short explanations. Please refer to *http://www.collocations.de/AM/* for the full equations and references. When the module is imported, the additional measures are registered with the **UCS** core library (see the UCS manpage for details on how to access registered association measures).

The association scores of measures with the suffix **.pv** can be interpreted as probabilities (i.e. the likelihood of the observed data or the p-value of a statistical hypothesis test). Such probabilities are given as **negative base 10 logarithms**, ranging from 0 to *+inf* (*+inf* is represented by the return value of the built-in **inf** function (see the UCS::Expression::Func manpage).

**MI.conf**-
Conservative estimate for the base 10 logarithm of the

*mu*-value (whose maximum-likelihood estimate is given by the**MI**measure). The association score computed by**MI.conf**is the lower endpoint of a two-sided confidence interval for*mu*at significance level**alpha**, which is specified by the`ALPHA`

parameter (as a negative base 10 logarithm). The "usual" significance levels*.01*and*.001*correspond to`ALPHA=2`

and`ALPHA=3`

, respectively.Please duplicate the

**UCS::Expression**object returned by`UCS::AM_Expression("MI.conf")`

before modifying the`ALPHA`

parameter. **MI.conf.***ALPHA*-
Versions of

**MI.conf**with the`ALPHA`

parameter pre-set to the value specified as part of the name. Availablevalues are*ALPHA***2**,**3**,**5**,**10**,**50**,**100**, and**1000**. For instance,**MI.conf.10**computes a two-sided confidence interval at significance level 1E-10.Do not modify the

`ALPHA`

parameter of these association measures (in the**UCS::Expression**object returned by the**UCS::AM_Expression**function). **Poisson.mu.pv**-
Poisson test for

*O11*under the modified point null hypothesis*pi = p1 * p2 * mu*(rather than the independence hypothesis*pi = p1 * p2*used by the**Poisson.pv**measure). The (non-logarithmic) value of*mu*is given by the`MU`

parameter. For`MU=1`

, the association scores computed by**Poisson.mu.pv**are identical to those of**Poisson.pv**.Please duplicate the

**UCS::Expression**object returned by`UCS::AM_Expression("Poisson.mu.pv")`

before modifying the`MU`

parameter. **Poisson.mu.***MU*.pv-
Versions of

**Poisson.mu.pv**with the`MU`

parameter pre-set to the value specified as part of the name. Availablevalues are*MU***2**,**3**,**5**,**10**,**50**,**100**,**1000**, and**10000**.Do not modify the

`MU`

parameter of these association measures (in the**UCS::Expression**object returned by the**UCS::AM_Expression**function).

Copyright 2003 Stefan Evert.

This software is provided AS IS and the author makes no warranty as to its use and performance. You may use the software, redistribute and modify it under the same terms as Perl itself.