Text::NSP::Measures::2D::MI::ll - Perl module that implements Loglikelihood measure of association for bigrams.
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; }
The log-likelihood ratio measures the deviation 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)]
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.
INPUT PARAMS : none
RETURN VALUES : $name .. Name of the measure.
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>
Last updated: $Id: ll.pm,v 1.23 2008/03/26 17:20:27 tpederse Exp $
@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>}
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http://www.d.umn.edu/~tpederse/nsp.html
Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli
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