Ted Pedersen

# NAME

Text::NSP::Measures::2D::MI::ll - Perl module that implements Loglikelihood measure of association for bigrams.

# SYNOPSIS

### Basic Usage

``````  use Text::NSP::Measures::2D::MI::ll;

my \$ll = Text::NSP::Measures::2D::MI::ll->new();

my \$npp = 60; my \$n1p = 20; my \$np1 = 20;  my \$n11 = 10;

\$ll_value = \$ll->calculateStatistic( n11=>\$n11,
n1p=>\$n1p,
np1=>\$np1,
npp=>\$npp);

if( (\$errorCode = \$ll->getErrorCode()))
{
print STDERR \$erroCode." - ".\$ll->getErrorMessage();
}
else
{
print \$ll->getStatisticName."value for bigram is ".\$ll_value;
}``````

# DESCRIPTION

The log-likelihood ratio measures the devitation between the observed data and what would be expected if <word1> and <word2> were independent. The higher the score, the less evidence there is in favor of concluding that the words are independent.

Assume that the frequency count data associated with a bigram <word1><word2> as shown by a 2x2 contingency table:

``````          word2   ~word2
word1    n11      n12 | n1p
~word1    n21      n22 | n2p
--------------
np1      np2   npp``````

where n11 is the number of times <word1><word2> occur together, and n12 is the number of times <word1> occurs with some word other than word2, and n1p is the number of times in total that word1 occurs as the first word in a bigram.

The expected values for the internal cells are calculated by taking the product of their associated marginals and dividing by the sample size, for example:

``````          np1 * n1p
m11=   ---------
npp``````

Then the deviation between observed and expected values for each internal cell is computed to arrive at the log-likelihood value.

`````` Log-Likelihood = 2 * [n11 * log(n11/m11) + n12 * log(n12/m12) +
n21 * log(n21/m21) + n22 * log(n22/m22)]``````

## Methods

calculateStatistic() - This method calculates the ll value

INPUT PARAMS : \$count_values .. Reference of an hash containing the count values computed by the count.pl program.

RETURN VALUES : \$loglikelihood .. Loglikelihood value for this bigram.

getStatisticName() - Returns the name of this statistic

INPUT PARAMS : none

RETURN VALUES : \$name .. Name of the measure.

# AUTHOR

Ted Pedersen, University of Minnesota Duluth <tpederse@d.umn.edu>

Satanjeev Banerjee, Carnegie Mellon University <satanjeev@cmu.edu>

Amruta Purandare, University of Pittsburgh <amruta@cs.pitt.edu>

Bridget Thomson-McInnes, University of Minnesota Twin Cities <bthompson@d.umn.edu>

Saiyam Kohli, University of Minnesota Duluth <kohli003@d.umn.edu>

# HISTORY

Last updated: \$Id: ll.pm,v 1.20 2006/06/17 18:03:23 saiyam_kohli Exp \$

# SEE ALSO

``````  @article{Dunning93,
author = {Dunning, T.},
title = {Accurate Methods for the Statistics of
Surprise and Coincidence},
journal = {Computational Linguistics},
volume = {19},
number = {1},
year = {1993},
pages = {61-74}
url = L<http://www.comp.lancs.ac.uk/ucrel/papers/tedstats.pdf>}

@inproceedings{moore:2004:EMNLP,
author    = {Moore, Robert C.},
title     = {On Log-Likelihood-Ratios and the Significance of Rare
Events },
booktitle = {Proceedings of EMNLP 2004},
editor = {Dekang Lin and Dekai Wu},
year      = 2004,
month     = {July},
address   = {Barcelona, Spain},
publisher = {Association for Computational Linguistics},
pages     = {333--340}
url = L<http://acl.ldc.upenn.edu/acl2004/emnlp/pdf/Moore.pdf>}``````

http://groups.yahoo.com/group/ngram/

http://www.d.umn.edu/~tpederse/nsp.html

Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to

``````    The Free Software Foundation, Inc.,
59 Temple Place - Suite 330,
Boston, MA  02111-1307, USA.``````

Note: a copy of the GNU General Public License is available on the web at http://www.gnu.org/licenses/gpl.txt and is included in this distribution as GPL.txt.