=head1 NAME Text::NSP::Measures::2D::MI::ll - Perl module that implements Loglikelihood measure of association for bigrams. =head1 SYNOPSIS =head3 Basic Usage use Text::NSP::Measures::2D::MI::ll; my $npp = 60; my $n1p = 20; my $np1 = 20; my $n11 = 10; $ll_value = calculateStatistic( n11=>$n11, n1p=>$n1p, np1=>$np1, npp=>$npp); if( ($errorCode = getErrorCode())) { print STDERR $errorCode." - ".getErrorMessage(); } else { print getStatisticName."value for bigram is ".$ll_value; } =head1 DESCRIPTION The log-likelihood ratio measures the deviation between the observed data and what would be expected if and 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 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 occur together, and n12 is the number of times 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)] =head2 Methods =over =cut package Text::NSP::Measures::2D::MI::ll; use Text::NSP::Measures::2D::MI; use strict; use Carp; use warnings; no warnings 'redefine'; require Exporter; our ($VERSION, @EXPORT, @ISA); @ISA = qw(Exporter); @EXPORT = qw(initializeStatistic calculateStatistic getErrorCode getErrorMessage getStatisticName); $VERSION = '0.97'; =item 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. =cut sub calculateStatistic { my %values = @_; # computes and sets the observed and expected values from # the frequency combination values. returns 0 if there is an # error in the computation or the values are inconsistent. if( !Text::NSP::Measures::2D::MI::getValues(\%values) ) { return; } # Now for the actual calculation of Loglikelihood! my $logLikelihood = 0; # dont want ($nxy / $mxy) to be 0 or less! flag error if so! $logLikelihood += $n11 * Text::NSP::Measures::2D::MI::computePMI( $n11, $m11 ); $logLikelihood += $n12 * Text::NSP::Measures::2D::MI::computePMI( $n12, $m12 ); $logLikelihood += $n21 * Text::NSP::Measures::2D::MI::computePMI( $n21, $m21 ); $logLikelihood += $n22 * Text::NSP::Measures::2D::MI::computePMI( $n22, $m22 ); return ( 2 * $logLikelihood ); } =item getStatisticName() - Returns the name of this statistic INPUT PARAMS : none RETURN VALUES : $name .. Name of the measure. =cut sub getStatisticName { return "Log-likelihood"; } 1; __END__ =back =head1 AUTHOR Ted Pedersen, University of Minnesota Duluth Etpederse@d.umn.eduE Satanjeev Banerjee, Carnegie Mellon University Esatanjeev@cmu.eduE Amruta Purandare, University of Pittsburgh Eamruta@cs.pitt.eduE Bridget Thomson-McInnes, University of Minnesota Twin Cities Ebthompson@d.umn.eduE Saiyam Kohli, University of Minnesota Duluth Ekohli003@d.umn.eduE =head1 HISTORY Last updated: $Id: ll.pm,v 1.23 2008/03/26 17:20:27 tpederse Exp $ =head1 BUGS =head1 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} @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} L L =head1 COPYRIGHT 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 L and is included in this distribution as GPL.txt. =cut