glm/src/families.js

Generalized Linear Models

exports.GLM.families = exports.GLM.families || {};

exports.GLM.families.Binomial = function (link) {
  // default to logit
  if (!link) { link = exports.GLM.links.Logit(); }

  model = {};

  model.initialMu = function (y) {
    var init = [];
    for (var i = 0; i < y.length; i++) { init.push((y[i] + 0.5) / 2); }
    return init;
  };

  model.deviance = function(endogenous, mu) {
    // formula for binomial deviance
    // 2 * sum{i \in y,mu}(log(Y/mu) + (n-Y)*log((n-Y)/(n-mu)))
    var dev = 0.0; 
    for (var i = 0; i < mu.length; i++) {
      var one = endogenous[i] == 1 ? 1 : 0; 
      dev += one * Math.log(mu[i] + 1e-200) + (1 - one) * Math.log(1 - mu[i] + 1e-200);
    }
    return 2 * dev;
  };

  // assign input link function
  model.link = link;
  model.predict = function (mu) {
    return model.link(mu);
  };
  model.weights = function (mu) {
    function fix(z) { if (z < 1e-10) { return 1e-10; } else { if (z > (1 - 1e-10)) { return 1 - 1e-10; } else { return z; } } }
    var variance = exports.GLM.utils.map(mu, function(m) { return fix(m) * (1 - fix(m)) ;} );
    return exports.GLM.utils.map(model.link.derivative(mu), function (m, i) { return 1.0 / (Math.pow(m, 2) * variance[i] ); });
  };
  model.fitted = function (eta) {
    return model.link.inverse(eta);
  };
  return model;
};

exports.GLM.families.Gaussian = function (link) {
  // default to identity link function
  if (!link) { link = exports.GLM.links.Identity(); }
  var model = {};

  model.deviance = function (endogenous, mu) {
    var dev = 0.0;
    for (var i = 0; i < endogenous.length; i++) {
      dev += Math.pow(endogenous[i] - mu[i], 2);
    }
    return dev;
  };

  model.initialMu = function (y) {
    var y_mean = exports.GLM.utils.mean(y), mu = [];
    for (var i = 0; i < y.length; i++) { mu.push((y[i] + y_mean) / 2.0); }
    return mu;
  };

  model.link = link;
  model.predict = function (mu) {
    return model.link(mu);
  };
  model.weights = function (mu) {
    // TODO write test & cleanup
    var variance = exports.GLM.utils.makeArray(mu.length, 1);
    return exports.GLM.utils.map(model.link.derivative(mu), function (m, i) { return 1.0 / (Math.pow(m, 2) / variance[i] ); });
  };
  model.fitted = function (eta) {
    return model.link.inverse(eta);
  };
  return model;
};