jstat/src/regression.js

Statistical Library for JavaScript

//To regress, simply build X matrix
//(append column of 1's) using
//buildxmatrix and build the Y
//matrix using buildymatrix
//(simply the transpose)
//and run regress.



//Regressions

jStat.extend({
  buildxmatrix: function buildxmatrix(){
    //Parameters will be passed in as such
    //(array1,array2,array3,...)
    //as (x1,x2,x3,...)
    //needs to be (1,x1,x2,x3,...)
    var matrixRows = new Array(arguments.length);
    for(var i=0;i<arguments.length;i++){
      var array = [1];
      matrixRows[i]= array.concat(arguments[i]);
    }
    return jStat(matrixRows);

  },

  builddxmatrix: function builddxmatrix() {
    //Paramters will be passed in as such
    //([array1,array2,...]
    var matrixRows = new Array(arguments[0].length);
    for(var i=0;i<arguments[0].length;i++){
      var array = [1]
      matrixRows[i]= array.concat(arguments[0][i]);
    }
    return jStat(matrixRows);

  },

  buildjxmatrix: function buildjxmatrix(jMat) {
    //Builds from jStat Matrix
    var pass = new Array(jMat.length)
    for(var i=0;i<jMat.length;i++){
      pass[i] = jMat[i];
    }
    return jStat.builddxmatrix(pass);

  },

  buildymatrix: function buildymatrix(array){
    return jStat(array).transpose();
  },

  buildjymatrix: function buildjymatrix(jMat){
    return jMat.transpose();
  },

  matrixmult: function matrixmult(A,B){
    var i, j, k, result, sum;
    if (A.cols() == B.rows()) {
      if(B.rows()>1){
        result = [];
        for (i = 0; i < A.rows(); i++) {
          result[i] = [];
          for (j = 0; j < B.cols(); j++) {
            sum = 0;
            for (k = 0; k < A.cols(); k++) {
              sum += A.toArray()[i][k] * B.toArray()[k][j];
            }
            result[i][j] = sum;
          }
        }
        return jStat(result);
      }
      result = [];
      for (i = 0; i < A.rows(); i++) {
        result[i] = [];
        for (j = 0; j < B.cols(); j++) {
          sum = 0;
          for (k = 0; k < A.cols(); k++) {
            sum += A.toArray()[i][k] * B.toArray()[j];
          }
          result[i][j] = sum;
        }
      }
      return jStat(result);
    }
  },

  //regress and regresst to be fixed

  regress: function regress(jMatX,jMatY){
    //print("regressin!");
    //print(jMatX.toArray());
    var innerinv = jStat.xtranspxinv(jMatX);
    //print(innerinv);
    var xtransp = jMatX.transpose();
    var next = jStat.matrixmult(jStat(innerinv),xtransp);
    return jStat.matrixmult(next,jMatY);

  },

  regresst: function regresst(jMatX,jMatY,sides){
    var beta = jStat.regress(jMatX,jMatY);

    var compile = {};
    compile.anova = {};
    var jMatYBar = jStat.jMatYBar(jMatX, beta);
    compile.yBar = jMatYBar;
    var yAverage = jMatY.mean();
    compile.anova.residuals = jStat.residuals(jMatY, jMatYBar);

    compile.anova.ssr = jStat.ssr(jMatYBar, yAverage);
    compile.anova.msr = compile.anova.ssr / (jMatX[0].length - 1);

    compile.anova.sse = jStat.sse(jMatY, jMatYBar);
    compile.anova.mse =
        compile.anova.sse / (jMatY.length - (jMatX[0].length - 1) - 1);

    compile.anova.sst = jStat.sst(jMatY, yAverage);
    compile.anova.mst = compile.anova.sst / (jMatY.length - 1);

    compile.anova.r2 = 1 - (compile.anova.sse / compile.anova.sst);
    if (compile.anova.r2 < 0) compile.anova.r2 = 0;

    compile.anova.fratio = compile.anova.msr / compile.anova.mse;
    compile.anova.pvalue =
        jStat.anovaftest(compile.anova.fratio,
                         jMatX[0].length - 1,
                         jMatY.length - (jMatX[0].length - 1) - 1);

    compile.anova.rmse = Math.sqrt(compile.anova.mse);

    compile.anova.r2adj = 1 - (compile.anova.mse / compile.anova.mst);
    if (compile.anova.r2adj < 0) compile.anova.r2adj = 0;

    compile.stats = new Array(jMatX[0].length);
    var covar = jStat.xtranspxinv(jMatX);
    var sds, ts, ps;

    for(var i=0; i<beta.length;i++){
      sds=Math.sqrt(compile.anova.mse * Math.abs(covar[i][i]));
      ts= Math.abs(beta[i] / sds);
      ps= jStat.ttest(ts, jMatY.length - jMatX[0].length - 1, sides);

      compile.stats[i]=[beta[i], sds, ts, ps];
    }

    compile.regress = beta;
    return compile;
  },

  xtranspx: function xtranspx(jMatX){
    return jStat.matrixmult(jMatX.transpose(),jMatX);
  },


  xtranspxinv: function xtranspxinv(jMatX){
    var inner = jStat.matrixmult(jMatX.transpose(),jMatX);
    var innerinv = jStat.inv(inner);
    return innerinv;
  },

  jMatYBar: function jMatYBar(jMatX, beta) {
    var yBar = jStat.matrixmult(jMatX, beta);
    return new jStat(yBar);
  },

  residuals: function residuals(jMatY, jMatYBar) {
    return jStat.matrixsubtract(jMatY, jMatYBar);
  },

  ssr: function ssr(jMatYBar, yAverage) {
    var ssr = 0;
    for(var i = 0; i < jMatYBar.length; i++) {
      ssr += Math.pow(jMatYBar[i] - yAverage, 2);
    }
    return ssr;
  },

  sse: function sse(jMatY, jMatYBar) {
    var sse = 0;
    for(var i = 0; i < jMatY.length; i++) {
      sse += Math.pow(jMatY[i] - jMatYBar[i], 2);
    }
    return sse;
  },

  sst: function sst(jMatY, yAverage) {
    var sst = 0;
    for(var i = 0; i < jMatY.length; i++) {
      sst += Math.pow(jMatY[i] - yAverage, 2);
    }
    return sst;
  },

  matrixsubtract: function matrixsubtract(A,B){
    var ans = new Array(A.length);
    for(var i=0;i<A.length;i++){
      ans[i] = new Array(A[i].length);
      for(var j=0;j<A[i].length;j++){
        ans[i][j]=A[i][j]-B[i][j];
      }
    }
    return jStat(ans);
  }
});