comparative-judgement/lib/statutils.js

Comparative Judgement Algorithms

/* jshint -W024, expr:true */
/*jslint node: true */
/*global expect, fx, sinon*/
"use strict";
var _ = require('underscore');

var factorial = function (num) {
  // If the number is less than 0, reject it.
  if (num < 0) {
    return -1;
  }
  // If the number is 0, its factorial is 1.
  else if (num === 0) {
    return 1;
  }
  // Otherwise, call this recursive procedure again.
  else {
    return (num * factorial(num - 1));
  }
};

var rasch = function (ability, difficulty) {
  var ex = Math.exp(ability - difficulty);
  return ex / (1 + ex);
};

var average = function (a) {
  var r = {
      mean: 0,
      variance: 0,
      deviation: 0
    },
    t = a.length;
  for (var m, s = 0, l = t; l--; s += a[l]);
  for (m = r.mean = s / t, l = t, s = 0; l--; s += Math.pow(a[l] - m, 2));
  return r.deviation = Math.sqrt(r.variance = s / t), r;
};

var info = function (p) {
  return p * (1 - p);
};

var zsq = function (p) {
  var res = 1 - p;
  return Math.pow(res, 2) / info(p);
};

var wms = function (probs) {
  if (probs.length > 0) {
    var numer = 0;
    var denom = 0;
    for (var i = 0; i < probs.length; i++) {
      var inf = info(probs[i]);
      numer += inf * zsq(probs[i]);
      denom += inf;
    }
    return (numer / denom);
  } else {
    return 0;
  }
};

function k_combinations(set, k) {
  var i, j, combs, head, tailcombs;

  if (k > set.length || k <= 0) {
    return [];
  }

  if (k == set.length) {
    return [set];
  }

  if (k == 1) {
    combs = [];
    for (i = 0; i < set.length; i++) {
      combs.push([set[i]]);
    }
    return combs;
  }

  // Assert {1 < k < set.length}

  combs = [];
  for (i = 0; i < set.length - k + 1; i++) {
    head = set.slice(i, i + 1);
    tailcombs = k_combinations(set.slice(i + 1), k - 1);
    for (j = 0; j < tailcombs.length; j++) {
      combs.push(head.concat(tailcombs[j]));
    }
  }
  return combs;
}

var infoPR = function (info, wq) {
  // Weighted probabilities of selection
  var iPR = _.map(info, function (ii) {
    return Math.pow(ii, wq);
  });
  var totalInfoPR = _.reduce(iPR, function (memo, num) {
    return memo + num;
  }, 0);
  //if totalInfoPR == 0
  //then no information
  //w is probably wrong
  //choose pair with most info
  //will throw a divide by zero error
  //fix by not letting w be wrong
  var probSelect = _.map(iPR, function (i) {
    return i / totalInfoPR;
  });
  //console.log(probSelect);
  return probSelect;
};

var iI = function (theta, trueScores) {
  //Get probabiltities for every item
  var Ps = _.map(trueScores, function (trueScore) {
    return rasch(theta, trueScore);
  });
  //Convert probabilities into information
  var ii = _.map(Ps, function (p) {
    return (info(p));
  });
  return ii;
};

var wq = function (itemsAdministered, itemsExpected, AP) {
  var rng = _.range(1, itemsAdministered + 1);
  var numerator = _.reduce(rng, function (memo, num) {
    return memo + (Math.pow(num, AP));
  }, 0);
  rng = _.range(1, itemsExpected);
  var denominator = _.reduce(rng, function (memo, num) {
    return memo + (Math.pow(num, AP));
  }, 0);
  var wwq = itemsExpected * numerator / denominator;
  return wwq;
};

var calciPR = function (theta, items, done, thr, AP) {
  // Progressive selection probabilities
  if(done>=thr) done=thr-1;
  var info = iI(theta, items);
  //console.log('info: ',info);
  //console.log('done: ',done, 'thr: ',thr, 'AP: ',AP);
  var w = wq(done, thr, AP);
  // console.log('w: ',w);
  var iPr = infoPR(info, w);
  //console.log(iPr);
  return iPr;
};

var sampleVector = function (array, runif) {
  //Take a cumulative sum of the vector
  var rnd = runif;
  var cumulative = 0;
  var sums = _.map(array, function (num) {
    cumulative += num;
    return cumulative;
  });
  sums[sums.length-1] = 1.1;
  // Break
  for (var i = 0; i < sums.length; i++) {
    if (sums[i] > rnd) {
      break;
    }
  }
  return i;
};

module.exports = {
  sampleVector: sampleVector,
  calciPR: calciPR,
  infoPR: infoPR,
  iI: iI,
  wq: wq,
  factorial: factorial,
  rasch: rasch,
  average: average,
  info: info,
  zsq: zsq,
  wms: wms,
  k_combinations: k_combinations,
};