NAME

Text::NSP::Measures::2D::MI::ps - Perl module that implements Poisson-Stirling
measure of association for bigrams.

SYNOPSIS

Basic Usage

  use Text::NSP::Measures::2D::MI::ps;
  my $npp = 60; my $n1p = 20; my $np1 = 20;  my $n11 = 10;
  $ps_value = calculateStatistic( n11=>$n11,
                                      n1p=>$n1p,
                                      np1=>$np1,
                                      npp=>$npp);
  if( ($errorCode = getErrorCode()))
  {
    print STDERR $errorCode." - ".getErrorMessage()."\n"";
  }
  else
  {
    print getStatisticName."value for bigram is ".$ps_value."\n"";
  }

DESCRIPTION

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

The Poisson Stirling measure is a negative logarithmic approximation of the Poisson-likelihood measure. It uses the Stirling's formula to approximate the factorial in Poisson-likelihood measure.

Poisson-Stirling = n11 * ( log(n11) - log(m11) - 1)

which is same as

Poisson-Stirling = n11 * ( log(n11/m11) - 1)

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: ps.pm,v 1.9 2008/03/26 17:20:28 tpederse Exp $

BUGS

SEE ALSO

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

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

  @article{SmadjaMH96,
          author = {Quasthoff, Uwe and Wolff, Christian},
          title = {The Poisson collocation measure and its application},
          journal = {Workshop on Computational Approaches to Collocations},
          year = {2002},
          url = L<http://www.ofai.at/~brigitte.krenn/colloc02/PoissonCollocationMeasureQuasthoffWolff_final.pdf>}

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 <http://www.gnu.org/licenses/gpl.txt> and is included in this distribution as GPL.txt.