{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Velicer MAP test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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     "text": [
      "Analysis 2016-03-26 10:24:24 +0000\n",
      "= Statsample::Factor::MAP\n",
      "  There are 2 real factors on data\n",
      "  == Principal Component Analysis\n",
      "    Number of factors: 1\n",
      "    Communalities\n",
      "+----------+---------+------------+--------+\n",
      "| Variable | Initial | Extraction |   %    |\n",
      "+----------+---------+------------+--------+\n",
      "| v0       | 1.000   | 0.883      | 88.326 |\n",
      "| v1       | 1.000   | 0.875      | 87.503 |\n",
      "| v2       | 1.000   | 0.856      | 85.559 |\n",
      "| v3       | 1.000   | 0.886      | 88.600 |\n",
      "| v4       | 1.000   | 0.887      | 88.659 |\n",
      "| v5       | 1.000   | 0.819      | 81.855 |\n",
      "| v6       | 1.000   | 0.852      | 85.159 |\n",
      "| v7       | 1.000   | 0.822      | 82.226 |\n",
      "| v8       | 1.000   | 0.861      | 86.081 |\n",
      "| v9       | 1.000   | 0.872      | 87.165 |\n",
      "+----------+---------+------------+--------+\n",
      "\n",
      "    Total Variance Explained\n",
      "+--------------+---------+---------+---------+\n",
      "|  Component   | E.Total |    %    | Cum. %  |\n",
      "+--------------+---------+---------+---------+\n",
      "| Component 1  | 8.611   | 86.113% | 86.113  |\n",
      "| Component 2  | 0.926   | 9.263%  | 95.377  |\n",
      "| Component 3  | 0.100   | 1.004%  | 96.380  |\n",
      "| Component 4  | 0.089   | 0.894%  | 97.274  |\n",
      "| Component 5  | 0.067   | 0.674%  | 97.948  |\n",
      "| Component 6  | 0.060   | 0.597%  | 98.545  |\n",
      "| Component 7  | 0.043   | 0.429%  | 98.974  |\n",
      "| Component 8  | 0.040   | 0.399%  | 99.373  |\n",
      "| Component 9  | 0.032   | 0.319%  | 99.692  |\n",
      "| Component 10 | 0.031   | 0.308%  | 100.000 |\n",
      "+--------------+---------+---------+---------+\n",
      "\n",
      "    Component matrix\n",
      "+----+------+\n",
      "|    | PC_1 |\n",
      "+----+------+\n",
      "| v0 | .940 |\n",
      "| v1 | .935 |\n",
      "| v2 | .925 |\n",
      "| v3 | .941 |\n",
      "| v4 | .942 |\n",
      "| v5 | .905 |\n",
      "| v6 | .923 |\n",
      "| v7 | .907 |\n",
      "| v8 | .928 |\n",
      "| v9 | .934 |\n",
      "+----+------+\n",
      "\n",
      "  Traditional Kaiser criterion (k>1) returns 1 factors\n",
      "  == Velicer's MAP\n",
      "    Eigenvalues\n",
      "+----------+\n",
      "|  Value   |\n",
      "+----------+\n",
      "| 8.611330 |\n",
      "| 0.926336 |\n",
      "| 0.100374 |\n",
      "| 0.089363 |\n",
      "| 0.067434 |\n",
      "| 0.059687 |\n",
      "| 0.042917 |\n",
      "| 0.039857 |\n",
      "| 0.031882 |\n",
      "| 0.030820 |\n",
      "+----------+\n",
      "\n",
      "    Velicer's Average Squared Correlations\n",
      "+----------------------+----------------------------+\n",
      "| number of components | average square correlation |\n",
      "+----------------------+----------------------------+\n",
      "| 0                    | 0.722719                   |\n",
      "| 1                    | 0.407274                   |\n",
      "| 2                    | 0.036444                   |\n",
      "| 3                    | 0.060324                   |\n",
      "| 4                    | 0.106041                   |\n",
      "| 5                    | 0.188101                   |\n",
      "| 6                    | 0.225866                   |\n",
      "| 7                    | 0.310435                   |\n",
      "| 8                    | 0.538523                   |\n",
      "| 9                    | 1.000000                   |\n",
      "+----------------------+----------------------------+\n",
      "\n",
      "    The smallest average squared correlation is : 0.036444\n",
      "    The number of components is : 2\n",
      "  Velicer's MAP Test returns 2 factors to preserve\n",
      "\n"
     ]
    }
   ],
   "source": [
    "require 'statsample'\n",
    "\n",
    "Statsample::Analysis.store(Statsample::Factor::MAP) do\n",
    "  \n",
    "  rng       = Distribution::Normal.rng\n",
    "  samples   = 100\n",
    "  variables = 10\n",
    "  \n",
    "  f1 = rnorm(samples)\n",
    "  f2 = rnorm(samples)\n",
    "  \n",
    "  vectors={}\n",
    "  \n",
    "  variables.times do |i|\n",
    "  vectors[\"v#{i}\".to_sym]= Daru::Vector.new(\n",
    "    samples.times.collect do |nv|    \n",
    "      if i<5\n",
    "        f1[nv]*5 + f2[nv] *2 +rng.call\n",
    "      else\n",
    "        f1[nv]*2 + f2[nv] *3 +rng.call\n",
    "      end\n",
    "    end)\n",
    "  end\n",
    "  \n",
    "  \n",
    "  ds = Daru::DataFrame.new(vectors)\n",
    "  cor=cor(ds)\n",
    "  pca=pca(cor)\n",
    "  \n",
    "  map=Statsample::Factor::MAP.new(cor)\n",
    "  \n",
    "  echo (\"There are 2 real factors on data\")\n",
    "  summary(pca)\n",
    "  echo(\"Traditional Kaiser criterion (k>1) returns #{pca.m} factors\")\n",
    "  summary(map)\n",
    "  echo(\"Velicer's MAP Test returns #{map.number_of_factors} factors to preserve\")\n",
    "end\n",
    "  Statsample::Analysis.run_batch"
   ]
  }
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