IPM_Najera_EC_v1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><font size=\"6\">IPM para Ecuador basado en Nájera</font></center>\n",
    "\n",
    "Ejercicio aplicado a datos de Ecuador basado en: https://github.com/hectornajera83/Taller-quito\n",
    "\n",
    "Notebook realizado en Jupyter con Kernel de R: IRkernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T15:47:29.856157Z",
     "start_time": "2019-06-20T15:47:29.823Z"
    }
   },
   "outputs": [],
   "source": [
    "rm(list=ls())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:16:19.179956Z",
     "start_time": "2019-06-20T16:16:19.134Z"
    },
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "#Librerias para IRT, Alpha de Cronbach y Omega\n",
    "library(\"psych\")\n",
    "library(\"ltm\")\n",
    "#Librería para Latent Variable Analysis\n",
    "library(\"lavaan\")\n",
    "#Para importar información desde Stata\n",
    "library('readstata13')\n",
    "#Para manejo de bases de datos (abajo dplyr)\n",
    "library('data.table')\n",
    "#Para usar pipes\n",
    "library(\"magrittr\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T15:47:33.390124Z",
     "start_time": "2019-06-20T15:47:33.354Z"
    }
   },
   "outputs": [],
   "source": [
    "#Directorio de bases de datos (bdd) de encuestas Ecuador\n",
    "    #A veces mejor setear directorio que un proyecto (?)\n",
    "dir = \"C:/Users/dvill/Desktop/MT/Taller Najera/Data\"\n",
    "setwd(dir)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T15:47:34.889031Z",
     "start_time": "2019-06-20T15:47:34.439Z"
    }
   },
   "outputs": [],
   "source": [
    "##Cargo información de ENEMDU diciembre 2018\n",
    "#Prefiero no trabajar con factores, aún falta mejoras para su uso en R (?)\n",
    "#Tengo 3 bdd:\n",
    "    #1) matriz de información de ENEMDU diciembre 2018: enem18dic (data.table)\n",
    "    #2) matriz con detalle de variables de enem18dic: enem18dic.var.labels (data.table)\n",
    "    #3) lista de información de etiquetas de valores de variables: \n",
    "        # enem18dic.val.labels (lista R-base)\n",
    "\n",
    "en18dic = fread(file = \"enem18dic.csv\")\n",
    "en18dic.var.labels = fread( file = \"enem18dic.var.labels.csv\")\n",
    "en18dic.val.labels = readRDS(file = \"enem18dic.val.labels.RDS\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T15:47:40.712227Z",
     "start_time": "2019-06-20T15:47:40.666Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.table: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>VarName</th><th scope=col>VarLabel</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>id_upm  </td><td>Identificador de la unidad primaria de muestreo</td></tr>\n",
       "\t<tr><td>id_viv  </td><td>Identificador de vivienda                      </td></tr>\n",
       "\t<tr><td>id_hogar</td><td>Identificador del hogar                        </td></tr>\n",
       "\t<tr><td>id_per  </td><td>Identificador de la persona                    </td></tr>\n",
       "\t<tr><td>area    </td><td>area                                           </td></tr>\n",
       "\t<tr><td>ciudad  </td><td>ciudad                                         </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.table: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       " VarName & VarLabel\\\\\n",
       " <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t id\\_upm   & Identificador de la unidad primaria de muestreo\\\\\n",
       "\t id\\_viv   & Identificador de vivienda                      \\\\\n",
       "\t id\\_hogar & Identificador del hogar                        \\\\\n",
       "\t id\\_per   & Identificador de la persona                    \\\\\n",
       "\t area     & area                                           \\\\\n",
       "\t ciudad   & ciudad                                         \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.table: 6 × 2\n",
       "\n",
       "| VarName &lt;chr&gt; | VarLabel &lt;chr&gt; |\n",
       "|---|---|\n",
       "| id_upm   | Identificador de la unidad primaria de muestreo |\n",
       "| id_viv   | Identificador de vivienda                       |\n",
       "| id_hogar | Identificador del hogar                         |\n",
       "| id_per   | Identificador de la persona                     |\n",
       "| area     | area                                            |\n",
       "| ciudad   | ciudad                                          |\n",
       "\n"
      ],
      "text/plain": [
       "  VarName  VarLabel                                       \n",
       "1 id_upm   Identificador de la unidad primaria de muestreo\n",
       "2 id_viv   Identificador de vivienda                      \n",
       "3 id_hogar Identificador del hogar                        \n",
       "4 id_per   Identificador de la persona                    \n",
       "5 area     area                                           \n",
       "6 ciudad   ciudad                                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(en18dic.var.labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T15:47:46.699452Z",
     "start_time": "2019-06-20T15:47:46.661Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>59350</li>\n",
       "\t<li>427</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 59350\n",
       "\\item 427\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 59350\n",
       "2. 427\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 59350   427"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#En diciembre 2018 se levantaron 59 mil encuestas\n",
    "dim(en18dic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T15:47:48.651832Z",
     "start_time": "2019-06-20T15:47:48.614Z"
    }
   },
   "outputs": [],
   "source": [
    "#Lista de variables candidatas para IPM\n",
    "vars = \"dim1_ind1_h dim1_ind2_h dim1_ind3_h dim2_ind1_h dim2_ind2_h \n",
    "        dim2_ind3_h dim3_ind1_h dim3_ind2_h dim4_ind1_h dim4_ind2_h \n",
    "        dim4_ind3_h dim4_ind4_h\"\n",
    "vars = vars %>% strsplit(split = \" \") %>% unlist\n",
    "vars = vars[vars %in% c(\"\\n\", \"\")==F]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confiabilidad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Análisis Factorial Exploratorio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploración de variables propuestas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:46:53.601103Z",
     "start_time": "2019-06-20T16:46:53.178Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 12 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>VarLab</th><th scope=col>mean</th><th scope=col>w.mean</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Inasistencia a educaciÃ³n general bÃ¡sica y bachillerato -nivel de hogar  </td><td>0.10805392</td><td>0.12811452</td></tr>\n",
       "\t<tr><td>VulneraciÃ³n del acceso a educaciÃ³n superior -nivel de hogar             </td><td>0.08439764</td><td>0.08064356</td></tr>\n",
       "\t<tr><td>Logro educativo incompleto -nivel de hogar                                </td><td>0.54766639</td><td>0.57179540</td></tr>\n",
       "\t<tr><td>Empleo infantil y adolescente -nivel de hogar                             </td><td>0.06638585</td><td>0.07682566</td></tr>\n",
       "\t<tr><td>Desempleo y empleo inadecuado -nivel de hogar                             </td><td>0.69405223</td><td>0.69559640</td></tr>\n",
       "\t<tr><td>No contribuciÃ³n al sistema de pensiones -nivel de hogar                  </td><td>0.66424600</td><td>0.68181382</td></tr>\n",
       "\t<tr><td>Pobreza extrema por ingresos -nivel de hogar                              </td><td>0.07127211</td><td>0.08349788</td></tr>\n",
       "\t<tr><td>Hogares sin provisiÃ³n de agua por red pÃºblica -nivel de hogar           </td><td>0.21590564</td><td>0.21382864</td></tr>\n",
       "\t<tr><td>Personas en condiciÃ³n de hacinamiento -nivel de hogar                    </td><td>0.13039596</td><td>0.16728352</td></tr>\n",
       "\t<tr><td>Viviendas en condiciones inadecuadas -nivel de hogar                      </td><td>0.48414490</td><td>0.48742508</td></tr>\n",
       "\t<tr><td>Viviendas sin adecuado sistema de eliminaciÃ³n de excretas -nivel de hogar</td><td>0.18990733</td><td>0.22652001</td></tr>\n",
       "\t<tr><td>Viviendas sin acceso a recolecciÃ³n de basura -nivel de hogar             </td><td>0.18711036</td><td>0.18259807</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 12 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " VarLab & mean & w.mean\\\\\n",
       " <chr> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Inasistencia a educaciÃ³n general bÃ¡sica y bachillerato -nivel de hogar   & 0.10805392 & 0.12811452\\\\\n",
       "\t VulneraciÃ³n del acceso a educaciÃ³n superior -nivel de hogar              & 0.08439764 & 0.08064356\\\\\n",
       "\t Logro educativo incompleto -nivel de hogar                                 & 0.54766639 & 0.57179540\\\\\n",
       "\t Empleo infantil y adolescente -nivel de hogar                              & 0.06638585 & 0.07682566\\\\\n",
       "\t Desempleo y empleo inadecuado -nivel de hogar                              & 0.69405223 & 0.69559640\\\\\n",
       "\t No contribuciÃ³n al sistema de pensiones -nivel de hogar                   & 0.66424600 & 0.68181382\\\\\n",
       "\t Pobreza extrema por ingresos -nivel de hogar                               & 0.07127211 & 0.08349788\\\\\n",
       "\t Hogares sin provisiÃ³n de agua por red pÃºblica -nivel de hogar            & 0.21590564 & 0.21382864\\\\\n",
       "\t Personas en condiciÃ³n de hacinamiento -nivel de hogar                     & 0.13039596 & 0.16728352\\\\\n",
       "\t Viviendas en condiciones inadecuadas -nivel de hogar                       & 0.48414490 & 0.48742508\\\\\n",
       "\t Viviendas sin adecuado sistema de eliminaciÃ³n de excretas -nivel de hogar & 0.18990733 & 0.22652001\\\\\n",
       "\t Viviendas sin acceso a recolecciÃ³n de basura -nivel de hogar              & 0.18711036 & 0.18259807\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 12 × 3\n",
       "\n",
       "| VarLab &lt;chr&gt; | mean &lt;dbl&gt; | w.mean &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| Inasistencia a educaciÃ³n general bÃ¡sica y bachillerato -nivel de hogar   | 0.10805392 | 0.12811452 |\n",
       "| VulneraciÃ³n del acceso a educaciÃ³n superior -nivel de hogar              | 0.08439764 | 0.08064356 |\n",
       "| Logro educativo incompleto -nivel de hogar                                 | 0.54766639 | 0.57179540 |\n",
       "| Empleo infantil y adolescente -nivel de hogar                              | 0.06638585 | 0.07682566 |\n",
       "| Desempleo y empleo inadecuado -nivel de hogar                              | 0.69405223 | 0.69559640 |\n",
       "| No contribuciÃ³n al sistema de pensiones -nivel de hogar                   | 0.66424600 | 0.68181382 |\n",
       "| Pobreza extrema por ingresos -nivel de hogar                               | 0.07127211 | 0.08349788 |\n",
       "| Hogares sin provisiÃ³n de agua por red pÃºblica -nivel de hogar            | 0.21590564 | 0.21382864 |\n",
       "| Personas en condiciÃ³n de hacinamiento -nivel de hogar                     | 0.13039596 | 0.16728352 |\n",
       "| Viviendas en condiciones inadecuadas -nivel de hogar                       | 0.48414490 | 0.48742508 |\n",
       "| Viviendas sin adecuado sistema de eliminaciÃ³n de excretas -nivel de hogar | 0.18990733 | 0.22652001 |\n",
       "| Viviendas sin acceso a recolecciÃ³n de basura -nivel de hogar              | 0.18711036 | 0.18259807 |\n",
       "\n"
      ],
      "text/plain": [
       "   VarLab                                                                    \n",
       "1  Inasistencia a educaciÃ³n general bÃ¡sica y bachillerato -nivel de hogar  \n",
       "2  VulneraciÃ³n del acceso a educaciÃ³n superior -nivel de hogar             \n",
       "3  Logro educativo incompleto -nivel de hogar                                \n",
       "4  Empleo infantil y adolescente -nivel de hogar                             \n",
       "5  Desempleo y empleo inadecuado -nivel de hogar                             \n",
       "6  No contribuciÃ³n al sistema de pensiones -nivel de hogar                  \n",
       "7  Pobreza extrema por ingresos -nivel de hogar                              \n",
       "8  Hogares sin provisiÃ³n de agua por red pÃºblica -nivel de hogar           \n",
       "9  Personas en condiciÃ³n de hacinamiento -nivel de hogar                    \n",
       "10 Viviendas en condiciones inadecuadas -nivel de hogar                      \n",
       "11 Viviendas sin adecuado sistema de eliminaciÃ³n de excretas -nivel de hogar\n",
       "12 Viviendas sin acceso a recolecciÃ³n de basura -nivel de hogar             \n",
       "   mean       w.mean    \n",
       "1  0.10805392 0.12811452\n",
       "2  0.08439764 0.08064356\n",
       "3  0.54766639 0.57179540\n",
       "4  0.06638585 0.07682566\n",
       "5  0.69405223 0.69559640\n",
       "6  0.66424600 0.68181382\n",
       "7  0.07127211 0.08349788\n",
       "8  0.21590564 0.21382864\n",
       "9  0.13039596 0.16728352\n",
       "10 0.48414490 0.48742508\n",
       "11 0.18990733 0.22652001\n",
       "12 0.18711036 0.18259807"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res1 = data.frame(\"VarLab\" = NA, \"mean\" = NA, \"w.mean\" = NA)\n",
    "#loops en R <3\n",
    "i = 0\n",
    "for (x in vars){\n",
    "    i = i + 1\n",
    "    res1[i,\"VarLab\"] = en18dic.var.labels[VarName == x, VarLabel]\n",
    "    res1[i,\"mean\"] = en18dic[, mean(get(x))]\n",
    "    res1[i,\"w.mean\"] = en18dic[, weighted.mean(get(x), fexp)] #sin summarize\n",
    "}\n",
    "res1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Acá el objetivo es encontrar variables que potencialmente tengan prevalencias poco intuitivas. Este es un ejercicio subjetivo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###\tAlpha de Cronbach "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:46:56.864594Z",
     "start_time": "2019-06-20T16:46:55.961Z"
    }
   },
   "outputs": [],
   "source": [
    "alpha1<-psych::alpha(en18dic[,mget(vars)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:46:57.369087Z",
     "start_time": "2019-06-20T16:46:57.328Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 1 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>raw_alpha</th><th scope=col>std.alpha</th><th scope=col>G6(smc)</th><th scope=col>average_r</th><th scope=col>S/N</th><th scope=col>ase</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>median_r</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.7132027</td><td>0.7070646</td><td>0.715708</td><td>0.16746</td><td>2.413722</td><td>0.001668119</td><td>0.2869615</td><td>0.1912352</td><td>0.1571697</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       " raw\\_alpha & std.alpha & G6(smc) & average\\_r & S/N & ase & mean & sd & median\\_r\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.7132027 & 0.7070646 & 0.715708 & 0.16746 & 2.413722 & 0.001668119 & 0.2869615 & 0.1912352 & 0.1571697\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 9\n",
       "\n",
       "| raw_alpha &lt;dbl&gt; | std.alpha &lt;dbl&gt; | G6(smc) &lt;dbl&gt; | average_r &lt;dbl&gt; | S/N &lt;dbl&gt; | ase &lt;dbl&gt; | mean &lt;dbl&gt; | sd &lt;dbl&gt; | median_r &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 0.7132027 | 0.7070646 | 0.715708 | 0.16746 | 2.413722 | 0.001668119 | 0.2869615 | 0.1912352 | 0.1571697 |\n",
       "\n"
      ],
      "text/plain": [
       " raw_alpha std.alpha G6(smc)  average_r S/N      ase         mean     \n",
       " 0.7132027 0.7070646 0.715708 0.16746   2.413722 0.001668119 0.2869615\n",
       " sd        median_r \n",
       " 0.1912352 0.1571697"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Alpha total para conjunto de variables propuesto\n",
    "    #Reliability analysis \n",
    "alpha1$total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los valores de Alpha recomendados son XXXX, según XXXX. Este indicador tiene debilidades, siempre se recomienda profundizar con el análisis del indicador Omega."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:46:59.364041Z",
     "start_time": "2019-06-20T16:46:59.313Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 12 × 8</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>raw_alpha</th><th scope=col>std.alpha</th><th scope=col>G6(smc)</th><th scope=col>average_r</th><th scope=col>S/N</th><th scope=col>alpha se</th><th scope=col>var.r</th><th scope=col>med.r</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>dim1_ind1_h</th><td>0.7059350</td><td>0.6978981</td><td>0.7037743</td><td>0.1735625</td><td>2.310141</td><td>0.001713868</td><td>0.010382162</td><td>0.1653083</td></tr>\n",
       "\t<tr><th scope=row>dim1_ind2_h</th><td>0.7205153</td><td>0.7226378</td><td>0.7277772</td><td>0.1914972</td><td>2.605394</td><td>0.001650879</td><td>0.007889410</td><td>0.1673545</td></tr>\n",
       "\t<tr><th scope=row>dim1_ind3_h</th><td>0.6784367</td><td>0.6746547</td><td>0.6845662</td><td>0.1586134</td><td>2.073657</td><td>0.001888858</td><td>0.010459241</td><td>0.1407375</td></tr>\n",
       "\t<tr><th scope=row>dim2_ind1_h</th><td>0.7015845</td><td>0.6911956</td><td>0.6983986</td><td>0.1690773</td><td>2.238296</td><td>0.001744849</td><td>0.010731996</td><td>0.1574396</td></tr>\n",
       "\t<tr><th scope=row>dim2_ind2_h</th><td>0.6851860</td><td>0.6814128</td><td>0.6845692</td><td>0.1627888</td><td>2.138859</td><td>0.001834308</td><td>0.009757477</td><td>0.1568998</td></tr>\n",
       "\t<tr><th scope=row>dim2_ind3_h</th><td>0.7033710</td><td>0.6958411</td><td>0.6976880</td><td>0.1721702</td><td>2.287755</td><td>0.001717750</td><td>0.009397127</td><td>0.1653083</td></tr>\n",
       "\t<tr><th scope=row>dim3_ind1_h</th><td>0.7022749</td><td>0.6935633</td><td>0.7034902</td><td>0.1706448</td><td>2.263316</td><td>0.001742410</td><td>0.011255602</td><td>0.1431168</td></tr>\n",
       "\t<tr><th scope=row>dim3_ind2_h</th><td>0.6795186</td><td>0.6730502</td><td>0.6731709</td><td>0.1576415</td><td>2.058573</td><td>0.001863801</td><td>0.007354594</td><td>0.1521943</td></tr>\n",
       "\t<tr><th scope=row>dim4_ind1_h</th><td>0.6990778</td><td>0.6911010</td><td>0.6998233</td><td>0.1690151</td><td>2.237304</td><td>0.001750441</td><td>0.011232718</td><td>0.1574396</td></tr>\n",
       "\t<tr><th scope=row>dim4_ind2_h</th><td>0.6785415</td><td>0.6743875</td><td>0.6836793</td><td>0.1584510</td><td>2.071135</td><td>0.001887624</td><td>0.009923074</td><td>0.1453322</td></tr>\n",
       "\t<tr><th scope=row>dim4_ind3_h</th><td>0.6935830</td><td>0.6870359</td><td>0.6956614</td><td>0.1663670</td><td>2.195255</td><td>0.001782048</td><td>0.010261445</td><td>0.1574396</td></tr>\n",
       "\t<tr><th scope=row>dim4_ind4_h</th><td>0.6836468</td><td>0.6764205</td><td>0.6779742</td><td>0.1596915</td><td>2.090431</td><td>0.001838861</td><td>0.007892802</td><td>0.1521943</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 12 × 8\n",
       "\\begin{tabular}{r|llllllll}\n",
       "  & raw\\_alpha & std.alpha & G6(smc) & average\\_r & S/N & alpha se & var.r & med.r\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tdim1\\_ind1\\_h & 0.7059350 & 0.6978981 & 0.7037743 & 0.1735625 & 2.310141 & 0.001713868 & 0.010382162 & 0.1653083\\\\\n",
       "\tdim1\\_ind2\\_h & 0.7205153 & 0.7226378 & 0.7277772 & 0.1914972 & 2.605394 & 0.001650879 & 0.007889410 & 0.1673545\\\\\n",
       "\tdim1\\_ind3\\_h & 0.6784367 & 0.6746547 & 0.6845662 & 0.1586134 & 2.073657 & 0.001888858 & 0.010459241 & 0.1407375\\\\\n",
       "\tdim2\\_ind1\\_h & 0.7015845 & 0.6911956 & 0.6983986 & 0.1690773 & 2.238296 & 0.001744849 & 0.010731996 & 0.1574396\\\\\n",
       "\tdim2\\_ind2\\_h & 0.6851860 & 0.6814128 & 0.6845692 & 0.1627888 & 2.138859 & 0.001834308 & 0.009757477 & 0.1568998\\\\\n",
       "\tdim2\\_ind3\\_h & 0.7033710 & 0.6958411 & 0.6976880 & 0.1721702 & 2.287755 & 0.001717750 & 0.009397127 & 0.1653083\\\\\n",
       "\tdim3\\_ind1\\_h & 0.7022749 & 0.6935633 & 0.7034902 & 0.1706448 & 2.263316 & 0.001742410 & 0.011255602 & 0.1431168\\\\\n",
       "\tdim3\\_ind2\\_h & 0.6795186 & 0.6730502 & 0.6731709 & 0.1576415 & 2.058573 & 0.001863801 & 0.007354594 & 0.1521943\\\\\n",
       "\tdim4\\_ind1\\_h & 0.6990778 & 0.6911010 & 0.6998233 & 0.1690151 & 2.237304 & 0.001750441 & 0.011232718 & 0.1574396\\\\\n",
       "\tdim4\\_ind2\\_h & 0.6785415 & 0.6743875 & 0.6836793 & 0.1584510 & 2.071135 & 0.001887624 & 0.009923074 & 0.1453322\\\\\n",
       "\tdim4\\_ind3\\_h & 0.6935830 & 0.6870359 & 0.6956614 & 0.1663670 & 2.195255 & 0.001782048 & 0.010261445 & 0.1574396\\\\\n",
       "\tdim4\\_ind4\\_h & 0.6836468 & 0.6764205 & 0.6779742 & 0.1596915 & 2.090431 & 0.001838861 & 0.007892802 & 0.1521943\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 12 × 8\n",
       "\n",
       "| <!--/--> | raw_alpha &lt;dbl&gt; | std.alpha &lt;dbl&gt; | G6(smc) &lt;dbl&gt; | average_r &lt;dbl&gt; | S/N &lt;dbl&gt; | alpha se &lt;dbl&gt; | var.r &lt;dbl&gt; | med.r &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| dim1_ind1_h | 0.7059350 | 0.6978981 | 0.7037743 | 0.1735625 | 2.310141 | 0.001713868 | 0.010382162 | 0.1653083 |\n",
       "| dim1_ind2_h | 0.7205153 | 0.7226378 | 0.7277772 | 0.1914972 | 2.605394 | 0.001650879 | 0.007889410 | 0.1673545 |\n",
       "| dim1_ind3_h | 0.6784367 | 0.6746547 | 0.6845662 | 0.1586134 | 2.073657 | 0.001888858 | 0.010459241 | 0.1407375 |\n",
       "| dim2_ind1_h | 0.7015845 | 0.6911956 | 0.6983986 | 0.1690773 | 2.238296 | 0.001744849 | 0.010731996 | 0.1574396 |\n",
       "| dim2_ind2_h | 0.6851860 | 0.6814128 | 0.6845692 | 0.1627888 | 2.138859 | 0.001834308 | 0.009757477 | 0.1568998 |\n",
       "| dim2_ind3_h | 0.7033710 | 0.6958411 | 0.6976880 | 0.1721702 | 2.287755 | 0.001717750 | 0.009397127 | 0.1653083 |\n",
       "| dim3_ind1_h | 0.7022749 | 0.6935633 | 0.7034902 | 0.1706448 | 2.263316 | 0.001742410 | 0.011255602 | 0.1431168 |\n",
       "| dim3_ind2_h | 0.6795186 | 0.6730502 | 0.6731709 | 0.1576415 | 2.058573 | 0.001863801 | 0.007354594 | 0.1521943 |\n",
       "| dim4_ind1_h | 0.6990778 | 0.6911010 | 0.6998233 | 0.1690151 | 2.237304 | 0.001750441 | 0.011232718 | 0.1574396 |\n",
       "| dim4_ind2_h | 0.6785415 | 0.6743875 | 0.6836793 | 0.1584510 | 2.071135 | 0.001887624 | 0.009923074 | 0.1453322 |\n",
       "| dim4_ind3_h | 0.6935830 | 0.6870359 | 0.6956614 | 0.1663670 | 2.195255 | 0.001782048 | 0.010261445 | 0.1574396 |\n",
       "| dim4_ind4_h | 0.6836468 | 0.6764205 | 0.6779742 | 0.1596915 | 2.090431 | 0.001838861 | 0.007892802 | 0.1521943 |\n",
       "\n"
      ],
      "text/plain": [
       "            raw_alpha std.alpha G6(smc)   average_r S/N      alpha se   \n",
       "dim1_ind1_h 0.7059350 0.6978981 0.7037743 0.1735625 2.310141 0.001713868\n",
       "dim1_ind2_h 0.7205153 0.7226378 0.7277772 0.1914972 2.605394 0.001650879\n",
       "dim1_ind3_h 0.6784367 0.6746547 0.6845662 0.1586134 2.073657 0.001888858\n",
       "dim2_ind1_h 0.7015845 0.6911956 0.6983986 0.1690773 2.238296 0.001744849\n",
       "dim2_ind2_h 0.6851860 0.6814128 0.6845692 0.1627888 2.138859 0.001834308\n",
       "dim2_ind3_h 0.7033710 0.6958411 0.6976880 0.1721702 2.287755 0.001717750\n",
       "dim3_ind1_h 0.7022749 0.6935633 0.7034902 0.1706448 2.263316 0.001742410\n",
       "dim3_ind2_h 0.6795186 0.6730502 0.6731709 0.1576415 2.058573 0.001863801\n",
       "dim4_ind1_h 0.6990778 0.6911010 0.6998233 0.1690151 2.237304 0.001750441\n",
       "dim4_ind2_h 0.6785415 0.6743875 0.6836793 0.1584510 2.071135 0.001887624\n",
       "dim4_ind3_h 0.6935830 0.6870359 0.6956614 0.1663670 2.195255 0.001782048\n",
       "dim4_ind4_h 0.6836468 0.6764205 0.6779742 0.1596915 2.090431 0.001838861\n",
       "            var.r       med.r    \n",
       "dim1_ind1_h 0.010382162 0.1653083\n",
       "dim1_ind2_h 0.007889410 0.1673545\n",
       "dim1_ind3_h 0.010459241 0.1407375\n",
       "dim2_ind1_h 0.010731996 0.1574396\n",
       "dim2_ind2_h 0.009757477 0.1568998\n",
       "dim2_ind3_h 0.009397127 0.1653083\n",
       "dim3_ind1_h 0.011255602 0.1431168\n",
       "dim3_ind2_h 0.007354594 0.1521943\n",
       "dim4_ind1_h 0.011232718 0.1574396\n",
       "dim4_ind2_h 0.009923074 0.1453322\n",
       "dim4_ind3_h 0.010261445 0.1574396\n",
       "dim4_ind4_h 0.007892802 0.1521943"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Alpha total para conjunto de variables propuesto\n",
    "    #Reliability if an item is dropped\n",
    "alpha1$alpha.drop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se puede considerar que las variables que al ser removidas reducen \"muy poco\" (cuanto es muy poco?) a Alpha, son redudantes y ayudan poco a comprender la variable latente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Item Response Theory - IRT de 2 parámetros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:06.167436Z",
     "start_time": "2019-06-20T16:47:01.663Z"
    }
   },
   "outputs": [],
   "source": [
    "rel_irt<-ltm::ltm(en18dic[,mget(vars)] ~ z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:07.236336Z",
     "start_time": "2019-06-20T16:47:07.185Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.table: 12 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Intercept</th><th scope=col>z1</th><th scope=col>VarName</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>-2.4634266</td><td>0.9963838</td><td>dim1_ind1_h</td></tr>\n",
       "\t<tr><td>-2.4579136</td><td>0.4254302</td><td>dim1_ind2_h</td></tr>\n",
       "\t<tr><td> 0.2646775</td><td>1.5494915</td><td>dim1_ind3_h</td></tr>\n",
       "\t<tr><td>-3.6229075</td><td>1.6441192</td><td>dim2_ind1_h</td></tr>\n",
       "\t<tr><td> 1.1220191</td><td>1.4406508</td><td>dim2_ind2_h</td></tr>\n",
       "\t<tr><td> 0.7943118</td><td>0.8925539</td><td>dim2_ind3_h</td></tr>\n",
       "\t<tr><td>-3.4240290</td><td>1.5361891</td><td>dim3_ind1_h</td></tr>\n",
       "\t<tr><td>-2.2309780</td><td>2.2365091</td><td>dim3_ind2_h</td></tr>\n",
       "\t<tr><td>-2.3299460</td><td>1.1597437</td><td>dim4_ind1_h</td></tr>\n",
       "\t<tr><td>-0.1030767</td><td>1.5931866</td><td>dim4_ind2_h</td></tr>\n",
       "\t<tr><td>-1.9087812</td><td>1.3458469</td><td>dim4_ind3_h</td></tr>\n",
       "\t<tr><td>-2.4378971</td><td>2.1218278</td><td>dim4_ind4_h</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.table: 12 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " Intercept & z1 & VarName\\\\\n",
       " <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t -2.4634266 & 0.9963838 & dim1\\_ind1\\_h\\\\\n",
       "\t -2.4579136 & 0.4254302 & dim1\\_ind2\\_h\\\\\n",
       "\t  0.2646775 & 1.5494915 & dim1\\_ind3\\_h\\\\\n",
       "\t -3.6229075 & 1.6441192 & dim2\\_ind1\\_h\\\\\n",
       "\t  1.1220191 & 1.4406508 & dim2\\_ind2\\_h\\\\\n",
       "\t  0.7943118 & 0.8925539 & dim2\\_ind3\\_h\\\\\n",
       "\t -3.4240290 & 1.5361891 & dim3\\_ind1\\_h\\\\\n",
       "\t -2.2309780 & 2.2365091 & dim3\\_ind2\\_h\\\\\n",
       "\t -2.3299460 & 1.1597437 & dim4\\_ind1\\_h\\\\\n",
       "\t -0.1030767 & 1.5931866 & dim4\\_ind2\\_h\\\\\n",
       "\t -1.9087812 & 1.3458469 & dim4\\_ind3\\_h\\\\\n",
       "\t -2.4378971 & 2.1218278 & dim4\\_ind4\\_h\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.table: 12 × 3\n",
       "\n",
       "| Intercept &lt;dbl&gt; | z1 &lt;dbl&gt; | VarName &lt;chr&gt; |\n",
       "|---|---|---|\n",
       "| -2.4634266 | 0.9963838 | dim1_ind1_h |\n",
       "| -2.4579136 | 0.4254302 | dim1_ind2_h |\n",
       "|  0.2646775 | 1.5494915 | dim1_ind3_h |\n",
       "| -3.6229075 | 1.6441192 | dim2_ind1_h |\n",
       "|  1.1220191 | 1.4406508 | dim2_ind2_h |\n",
       "|  0.7943118 | 0.8925539 | dim2_ind3_h |\n",
       "| -3.4240290 | 1.5361891 | dim3_ind1_h |\n",
       "| -2.2309780 | 2.2365091 | dim3_ind2_h |\n",
       "| -2.3299460 | 1.1597437 | dim4_ind1_h |\n",
       "| -0.1030767 | 1.5931866 | dim4_ind2_h |\n",
       "| -1.9087812 | 1.3458469 | dim4_ind3_h |\n",
       "| -2.4378971 | 2.1218278 | dim4_ind4_h |\n",
       "\n"
      ],
      "text/plain": [
       "   Intercept  z1        VarName    \n",
       "1  -2.4634266 0.9963838 dim1_ind1_h\n",
       "2  -2.4579136 0.4254302 dim1_ind2_h\n",
       "3   0.2646775 1.5494915 dim1_ind3_h\n",
       "4  -3.6229075 1.6441192 dim2_ind1_h\n",
       "5   1.1220191 1.4406508 dim2_ind2_h\n",
       "6   0.7943118 0.8925539 dim2_ind3_h\n",
       "7  -3.4240290 1.5361891 dim3_ind1_h\n",
       "8  -2.2309780 2.2365091 dim3_ind2_h\n",
       "9  -2.3299460 1.1597437 dim4_ind1_h\n",
       "10 -0.1030767 1.5931866 dim4_ind2_h\n",
       "11 -1.9087812 1.3458469 dim4_ind3_h\n",
       "12 -2.4378971 2.1218278 dim4_ind4_h"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "irtC = rel_irt$coefficients  %>% data.table\n",
    "irtC = irtC  %>% setnames(\"(Intercept)\", \"Intercept\")\n",
    "irtC[, VarName := vars]\n",
    "irtC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el contexto de IRT z1 es discriminación, el intercepto representa severidad. Una buena regla de dedo según XXXXX viene a ser:\n",
    "* Discriminación menor a 0.9 significa que el indicador representa muy poco de la variable latente, se puede considerar sacar al indicador\n",
    "* Severidad mayor a 3 o menor a -3 significa que el indicador es \"tan severo\" que aporta poco a nuestra comprensión de la variable latente, se puede considerar sacar al indicador"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:10.803509Z",
     "start_time": "2019-06-20T16:47:10.768Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'dim2_ind1_h'</li>\n",
       "\t<li>'dim3_ind1_h'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'dim2\\_ind1\\_h'\n",
       "\\item 'dim3\\_ind1\\_h'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'dim2_ind1_h'\n",
       "2. 'dim3_ind1_h'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"dim2_ind1_h\" \"dim3_ind1_h\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Variables \"malas\" según severidad\n",
    "irtC[abs(Intercept)>3, VarName]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:11.643380Z",
     "start_time": "2019-06-20T16:47:11.608Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'dim1_ind2_h'</li>\n",
       "\t<li>'dim2_ind3_h'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'dim1\\_ind2\\_h'\n",
       "\\item 'dim2\\_ind3\\_h'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'dim1_ind2_h'\n",
       "2. 'dim2_ind3_h'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"dim1_ind2_h\" \"dim2_ind3_h\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Variables \"malas\" según discriminación\n",
    "irtC[z1<0.9, VarName]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimador Omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:50:10.964638Z",
     "start_time": "2019-06-20T16:50:10.726Z"
    }
   },
   "outputs": [],
   "source": [
    "o0<-psych::omega(en18dic[,mget(vars)], plot = F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:50:15.240959Z",
     "start_time": "2019-06-20T16:50:15.183Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$`Omega Total`</dt>\n",
       "\t\t<dd>0.753475580177457</dd>\n",
       "\t<dt>$`Omega Jerárquico`</dt>\n",
       "\t\t<dd>0.42970449733992</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$`Omega Total`] 0.753475580177457\n",
       "\\item[\\$`Omega Jerárquico`] 0.42970449733992\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$`Omega Total`\n",
       ":   0.753475580177457\n",
       "$`Omega Jerárquico`\n",
       ":   0.42970449733992\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`Omega Total`\n",
       "[1] 0.7534756\n",
       "\n",
       "$`Omega Jerárquico`\n",
       "[1] 0.4297045\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o0.i = list(\"Omega Total\" = o0$omega.tot, \"Omega Jerárquico\" = o0$omega_h)\n",
    "o0.i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se considera un Omega \"bueno\", cuando este es mayor a 0.9. Se comprueba la necesidad de este valor en las simulaciones propuestas por Nájera (XXXX)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estructura factorial ideal dados los datos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:18.964818Z",
     "start_time": "2019-06-20T16:47:18.607Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zKyoZ2/mh+cpaacZeFtpCkkWMmHZMWi9lHwZqM0ZzF75YIaE3ZL7iSrlJOR3BtC\neBsZt8dLfoO5YSVHUtXJzUfOuYWVQf9lF8r/XXn6PB/VKbnR3bCSE4mqROqjsE3FpenuyzaU\nkTR14aVt0pSI0kdBW8lWG+Qlvz0aWGmLJAVy8ZFr1QcUwOGXnJf8a9Fgt7ROkuqIlU9rCw3J\ngpXfreHxkn8jGlhphRS1IfNRSBs5pgsVwC62d6C84uVEgspQ+ShYq/A4CuIlv0M0OMKzkJ4s\n2z5y7MeiCMa0cZ+Meckfez+eMsmJ4uAjp2x2F1zOjzR7UFxzE+L2HnP1zJaX/O7XC7qUqhDt\nu1NCu2mjEHjVpAOGcTYrCWyZ7C+2fLLI/HkH/Yx9731HPYIXPoFrQrzkAuVhlMWQmpEofHTk\n2ORvuEdhOYfsff7QnjL463485kK01VeZpp4/NawkEqv+LR+5NOdDRb7Lu+b+id9T4eSs5l4/\n5nnwFeJb6pkQ/6SFmulZR2WRVgPY9JFDFsdKXMsH+rzF7ME8nYvKaz718GSjnxA38Y4YTnSS\nMtJxHx3ecyhPFhne3Q1PW8ycnxCjEhfR3Qd1K/QUKV0j7fERwQGYZqS2O6gp8MTA8Isi78wt\nbtc8kJKR1n10zsA2k5GedSUMT9LOG4ORus6GW3lK9CRkpA0fba5OUlTtiKbnVtyxncFI3TnS\nx/Ak5CJIx0jHfETVrVaJtr/6s1xcXmdVpRtJiJZO6NRIp9jC+Na6ZPk1WTHlecD3d1d5nHZ5\n7afvtZsJ0c3F5HlVNyeSKfYhH9FFIeR1pNfUuyCvIxV4RPNQhegXfGAk3qz5aOsuVLIyfnMy\nj2xo6uLOkTQhvr8lTdfZ8K/MnVIiZV710fqaVCUc2sdFHr5cp6yraUFRaEI81AVFkUaJd/uI\nqkanX9lGDnqeZ/5dcCltf9SahHhdxwUFWimN8grDO9sC5y/dt15cq6CgMNWSKKzdR6uVRVKT\nhbUHUkqSLoWirvhobS2CosFFBylHwATKaT9BWgmeZFhdAuLwpxAV+Zdyn48Ob7WQ+j+DIrTk\nX0Tbgd1K7RytuCJq/lTyF5R9Aa0+sq9x2EbH1gcmcv9x4l46bx8drK/c6zsmWUvLvGz+Pjq0\ntayrmgEZC8y7YBYfWavjSD1lXMmcyFVl3sUS2hvtw3z5/sLAReeRp9asy+Tlo/3Vk2fNciZD\nwTmXyM9HezcStVLpHpJKwpkFP29bp8C4PEYfWSpgZ72c2naMAcTdvMKp0UTXnhbGhRHKf/X9\nbOleG+1ajZL4Ecw5OxoGFUAG36I4+2hfdfD4QeQQw8T50fCoBQrYlsPdR3sy51J/TMIYiOIU\noNEAACAASURBVBINl6o4CNdSuPpo31QqeyIKAp9IOiJFw6lCdsO0CAYfmdT2rwFmlcYqmIjR\n8KqVPTAtgFj8U97+FvkGz8xFLTf5I18IiLj14/CM3s1HnnlyrCleIcW+FsBLDT9Yxu7iIz/V\nWbqoXR/tZA75eVFmbm0tKeXC+QS368nXojkNrtXkAMfANR/p8noJzrh6vI10lyMQlIla7Ub6\nTXC7mXwtmjPhW1frMAxb95GWws9GRwMKiO/427ecyevZPd11M2sxTXDrljmTxsC6wqwwDFrM\nXpfvbAtW8mJeK75GqsXq12oW/YPJ1dTMjcS/1kzwi3jLR+4ic60PsfIjIR/cev8d2n3/HqJ6\nyEO6uzGH8aMQn1qmnGcxfK1MOfP95j4mXX5h28D5RA/AF3bxKj5y/jXV8uFcFb/g9Biv3UlN\nPRlJPlH7JZf+nNQojxrvU8rzocciC4k2we0wSaX+mOUxKBbS8YjCGW7Bqj5SvnUMN4FK6CPU\nwvw3TPLwM9K1+Z4S9a+/HctTzqCyzGtIc1lk0RonuJ2Sql9MgbGAUSibMAt1w0dueSSifxen\nFmkt50l5TUb6kyk/7axZfSpD78GYcpFFa5zgdkqqRsROO27x2GEW59JI+pnAdgbJKC9jtXVI\nzs6R2uXr98CuUueQWaacZdGjTnC7zG4joOgwDMkErygXPloq6NZRxas4Fqb7UXcZ6aodk20Y\nSZ3gdsVIY3B7ihUMbvEYOT/Eldualz5aruSS7+HYXJDTAs0uiBoHDxjRSm44tNs00udy/ZhW\nWjGSqZPPemi3CHW1OKoQ7btTQguOBJK6DXpD/clGmhVDL9GKjxwyPhiZK7JLbH6ibhw8sMBW\ngcJQsFr2I/xZjfQyzQ24TDnLwjzB7YqRtN8ve8vThHiZBl2QcdQAqy2PgHONpHYeCP1bg482\ny33ivt88h6w2eOAXl/0XUGjNtuOl9tr9ksrXj3GOzWXKWRbmCW5XjWQeZq8XQxOirb4LvttS\n+wjpOFLL6y2PgDONZDkqX4SiHZZslvncI+i7/Ln/N3WEmQYPuBxDLHa/M+QlnpvNSDdj1krK\nKQvzBLfrRloZbTHfsibEP2kh9XyMlr1VvdHyKDixEZo3JRZvtKrcKO/p56G17Il+a8PXqiEa\n14Nw0wFsz0MZ2dAuz38cjDRlYZ7gdsNIG5oPAWhC3FYPb6nYVeGWlkfadM5rh9Yfutk/3Uer\nOUbozdHP5Ns9Z7FC+c8Dob1ZSduXeCr0RXQGvgU6RVps2XcF7y92cFpN2jc0nSyoPlqTLFKf\nqGakvkF5nhj4tNgTEYZ31rTDbu2nxDDwKOSR3bRtH93WGtHhUEJktX87op11GM2aqH2FaFcW\netcvdz+GwQPO2R0IxHyYdyS5V/M0/aJ01wJ2KuGJewNwOFOl4KQGudlhMKaZ/cDZE8dz0dgU\n1RDUwQPOOR6OhZGR3mGv1GgBuBX80NfunNMmt7YixOLgbm2NKOdFU/uoTOdI+zuruB7abaMJ\nMXfWSYZy2MBmCqoYeRhpvMa/tTs6dWdk/AnvO6s+2nWjnYGlayRNCNM9h8H9tJl5XkZy6QSa\npbOIc5aLVn9OH/LyyWvqXTAPHnDe1q61QuETjSZEv8B4xTjoDmo1W9eWRxAGTTaHNzKdd5iF\nOeM4waW6zSMbtMEDzhvdtVYofKLRhPj+ljRdZ8O/lfzD+Gkly7yM5Hg2bE8c0kVep+xtd7mk\n49qv2r0aBw84b33faoHwikYT4uEqRIAdlO0gxmldmghIciHYhnV3FMhFe2uzkYOehyzkP9Pg\nAecodq4XBq9odCFe13GB4+YoDWXMJy8jOW7C0KkcwEW+O6DAMAljIFI0VDViaD5u6x3eMlUm\nJJvQpSRs7sz880PwgoUWh7JYfnRc68AWaTMh2YKSjqZaWbQQ4MWhOlusV6aR/G5B2sgKBkqf\nvVU4u0bsuob3NsLkQbSF2TXynVHBPxmyo06H1Lt+wvfCzkj7foPgn+zxq+TfoDOnxHtjIs6D\nagu+j1XDDqhEXOvcp10QtKDgjdBjA44lh3+Ayw7Kp+URxHM8C98NKI94d44F/gE69kYhFgn6\nJLNp2oSe9FAcx7Pw3IB8jNPN3UjYAYFtDI3EYKTfNG2f5vt181GSHgrgeBZ+G3gtHvFuTwr/\ngB3MWs3PSL8vp2narqK+1NO4wBSNVA/D721Ggn8AAVMTmjWl2S1T75u4/f0e1JKikVZuloCB\nACG6kdppyauaz42Tm5FCxwJKwmYkOU3b49beHmpSgq2FA0YCcVA6G37L1Wna2jSNtHWOBAAN\nFiNp07S1aRrJtdcOgGOYD+30adraNI00TAeCzgYQEmOvXYc+TVubqJG6kQ3XP3R/gxCsXkcy\nT9PWpmqkfvHWDhYXZIEHayMbpkXGadraNI0kuuc1meejwhAh4I3DWLvfEvM0bW2aRuof2mR8\nwi8GrQJntluDbiTzNG1tGkbStvC8CnExPrXJMRbsoorGvfK1K5bWlpOkkY4n/K0ARxWEf2WH\na3mB8iDawv5QYKiM2V+5MNLuTcFRGXG8Ll3XzctIlM0fjkoYurrLy0j7n7RKsW3mhhK8YKEF\nYY6kyU7IhGQTgnanpGTOoqno8IonUjThqsYtz1SM5LYN+90VpDBzFJMwBk6OJnxVeLS8UzZ1\nxjbW5kcKAQ9DFWmk86TPzEguG5kO7E5u2967KDktULNc9rc35pSNpArR3IS4vVfzP/23y63l\nnbSlUzYiZuni7CYcHdXfBbIci99UBRpJE6KfutDkpHh7/8yMtL0VdVbzoNFssFrt2tSpHfXu\nNpKukcyT6d6X073HP3x2aHknbeiUrfweeS5mC2Jj3EXd5Z3y/8Rjtuzf/rbCoJgzfKLRhOin\ndx/mgYjvoIHMjLQ9sHtMIzhZaWDuqFp0N4a95z+8H3Et0EgGITgZ6MdWyztpO2SsbmfYH4ll\nSlb1IZnayTy2q/gUaCSta0gKcxd7p6UOxlbLO2MzlNg3NNsdKSl5NTNJH+zsV1e+9TWS0N4Y\nNmPL9KktN9/X1i009qRZo/VRfjqGm5Z9j3F9ZjU/iZWyEDaw89rqRu2ZncTOStoPcXdw439E\ns9WrsmKkt/nRoeZIjT1p20Zy6ewS+k/Is64WJ49MsJaGsnWd2FLNm1pWnuokdlbSjHSpmtlS\nZ0OJxT/bZgyYn2RmycLUk7ZtpPUNLPtg1LQ3fsd21pZH2rTObKcbz7KbO4mtlSolwJvsvFJi\ndDGU9pOh5GD54uncs9Elm/ekOWS+FdO8UKoQA43xIQKxOeEpiue2Uv2gRPtg+Knm5KS+s+rz\n+5EXYsU1q36aPzJqzm8etuHvIaqHnNlHnn4Y52jrU35qmbLVpnJT27bsFKgMx2DzCtDLsVym\nCrEoFj/WW16IDYRlWR/qD/nstV1JF5PH8MTl8aR61UhKGm25SX45YKCejCQfFvOSS7ttvk1q\n9Cnl+dBjkYVE60mTXwrDMZhm7ZWiqUIMe7+PMD2AkQGrLY8if+oMt7dob3tWJ/GxknFkg2N4\nWrGFLv+/6YnO/d+1+R7O9a+VbWOzlJdFFq2xJ21Kqn4xDR3ePDY1j2xoao7nSAMrLY8gc/os\nD7B0EksrXWRFyOejza+h+GQx1aa+Xi1b5msy0p9c4TPbiM1If8O7WRatsSdtSmrMx7GhaUJU\n04ICYdI8R5anu6Yjv9g0ctCzfLvXSNNa1p7s2TlSu3y1G2n5bpZM7UlbZrcRkBVdiO+CC9/9\nUWB4tM4fSr+R2hl2bjCBkZdh9IW/f2RGUnvS7EZqgxz1FAE33VadlJOVhLmLLISR9N55czat\nbTnYhp1qqpNUK50aTCh+P/yGc6SuM+zviJFmWZh70taN1GK3tAd+kilOynCnJKyFW8zDttdI\nsyzMPWlbRjJ/CVZhKNiGk7KqZL0o8hLP7YiRZlmYe9IcjAR8YaiddtRjO5HIAENBHsrIhtbb\nSFMW5p40GCkAHLXTnaQ3ndOCCQuvcvCKJi1Yaqefiee6U+JVCl7RpAVP7RyclIeV9pfBc7yL\nU/IcFI0FU+1cnJSDlWCkXGCqnVD+t2bbMI3eHV4F4BVNWnDVzuCkHHdKvMLnFU1asNXO0UmJ\nW4lX8LyiSQu+2rk6KWkr8QqdVzRpwVc7ob1pbeHyLcQWvCLnFU1aMNbO7KS8dkq84uYVTVpw\n1s7oJNtOiXNB7AhexJYjYVhr5+Mk3iUBucO7+fk5iXdZQNbwbnyWEeA2y8BKIBbMm57tXgpb\n2LASiAP3hufrJPYFAnnCvt35O4l9kUCG8G91VifBSoAP/Nuc/VYKe+ywEjiZBFrcHielUC6Q\nEyk0ONvB3bqTUigZyIYkmtuKk2AlwIIkGtvqU1DW1kuidCAH0mhqe52USPFA+iTS0vY7KZEC\ngsRJpZ2tOglWArFJppWtOWmjFMmUEaRLMo1s/YbzDSclU0qQKuk0sSNOgpVAYBJqYIecBCuB\noKTUvDactGkl0mAAmJNU69p4MBd2SiAaSbWtrSc3bBYGVgKBSKtlHXYSrATCkFi72nSSg5XI\nggHgR2rNavO5XNgpgRik1qi2H9zgUCI+Vor9aFWF2HIkTHLakTiJjZWYhDHAK5q0SE87Byc5\nWYkkmKPwiGKEVzRpkaB2Do/lSmanxCGGCV7RpEWK2hE5iYOV4kcwh1c0aZGidi7PEnIrV/TS\nRw9gAa9o0iJJ7ZyclMROiZf8vKJJizS1c3GS604pqgK85OcVTVokqh2hk6JaiZf8vKJJi1S1\no3RSRBF4yc8rmrRIVTs1bouTuO+UbNvtArIF9dSWG1P2C58XUd0bh+Rr0YBtktXOaZfksVOK\nI8QOI7315XYj3eXIn6rZTr4WDdgmXe2InRTHSmtGMvOuHAPtkr3Frel2YTe3zNNtDPFJWDtq\nJ8XQwttIT3H1MFItTLnBSAFIWDu30yQvJ52uhmGD90rcf4d237+HqB7yGO0uV7gbouxTfmqZ\ncp7F7Ptl8vuYdCsa4EjK2jk7ia+V9M1du5OaejLSo/v8kks7J71NMfYpqy7NY5FFTyOuSvK6\nS/F0iAa4krR2rk7yKeW5VtI29k9U7+E8qP+7Nt/Duf61skU4S3lZZNHzFC8l+Zh0KxrgTNra\nhXDSqZJo26rF3/f1NRmp+/g9bGsnA9mM9NeOJ0a/LCSfqlaTj0m3ogHOJK5dGCedJ4qtJ3t2\njtQuX+1GWr77JWuqqyE5jERM4trpbcqakqWVTjDSVTuEg5ECkLp27k7yK+pJugQ30udy/Zi3\nASORkrx2wZx0ijKGc6SuY+DviJFmWXzPlNTjOi27tWiAM+lrF8pJp1hJ28RL7bWbInE10iyL\nj8lHMFIIMtDOx0ncrKRvQF7iuR0x0iyLm/E5WzBSADLQzqtBeJY3tDyG/B/KyIbW20jzLGCk\nk8hBu6BOCisQL/l5RZMWWWgX0klhrcRLfl7RpEUe2vk5iZGV9ufs+aBhp+R5NIY45KGdoRRr\nBfMudDCVYKRcyES74E4KpBMv+XlFkxa5aBfaSYGsxEt+XtGkRTba+TqJh5V4yc8rmrTIRztP\nJ+0pOb1YvOTnFU1a5KOdqSTkTqKWi5f8vKJJi4y0O8NJ1FbiJT+vaNIiJ+1OcVIrquUjF5ub\nELf3npzaRa80B3aWAuRlpB1O8i++fLLI/HkH8pkjYq+TQCZkZSTvDgf/8v919yiI/qkHknv3\n9MW7qNdWAvmTvZGInXSXd839m3ZllegO83BUVDqZNYDgTqrlA33eolbuTKi8cgHZkZmRdjnJ\nRwPlySIDd8PTFkFR5GakPU7yEcFkpH/D44RBwRRhJEInmYz0rCtheJI2KInsjBTYSZqR+jc3\nHNsVTn5G2ukkRyEqbY8k3zbobSicDI20z0mOSvS9dp/FdaPZUxlBqWRZ/wGd9JDXkV5T74K8\njrQc6wAKpBwj0Tjpb3j64nJkQ1PjHKlwsjTSbic5qHGRQ+uuU/J+rJ3rhJQgUzKt/p1OckjR\n3LvR333iPvV3weXZ4jSpbHKt/HBOCrUySJps6z6Ok7KVE2yQbc1bCubgJFgJ+JNvve920kFN\nYKUiybjWYzkpZ02BjZwrPZ6TclYVGMm5ym1lC+8kWKk4sq7wI046bKWD64O0yLu+DzgJOyXg\nQ+a1HdNJsFJJ5F7XUZ0EK5VD7jVtLZ+TkwistLUFVhwubrlkr90hJwXfKfGSn1c0aZG/dkcO\n7kj0SWeySV7RpEUB2kV30oqVeMnPK5q0KEG7g04isdKhEM6CVzRpUYJ2R/cHAXdKvOTnFU1a\nFKEdByeZrcRLfl7RpEUZ2rFw0jIXQZgxFbyiSYtCtDvsJPqdkvDY/EnwiiYtCtHOXkxXAYh2\nSlM2MFJWlKIdFycpTw239uYJ+17wqS03n34Jr+RjRGAfxWjHxkm/fHYa6a0vXzOSa/J5ZMCf\ncrQjcBLxTkmsG8nMu3IMo09mSg4jBaAg7Y47iW6nNJ4geRvp6fxMV5nMmBxGCkBB2lEMeSOT\na3CSIb97Je6/Q7vv30NUj+4R4/1z+4fvlMxkyk8tU86zsCa/j0n1oKYsgQcl6cXLScJspGt3\nO0M9GenRfX7JpZ2T3qY23qeUDyF/LLKwJa+7FPpj/39nb7CRN0UpxspJXQvXG+y/YbaLn5Gu\nzff4rH+tfuvpOY0pL4ssbMnHpOoX/bdFtQkqyhKNxEmUVtLyquWEMa/JSH8y3We2YZuR/oZ3\nsyxsyf+My7s9JFy0k8J0o3DSUc1W70mdzVE7dYHPX+1GWr7bSG42Emy0m8KUWyuuoxTfM3lx\nb6bPzU2I25sqnshGanHH+U5KE+2wk+SZ/Pz8op9obKeTmBlpHEoLN3lTnF4HnfS3PJMfpr68\nLyZnPhJNLeeo/TtipFkW9uQWI80Cgpu8KE+qY066y1b6TzzGpHIy5t09ENpqL7XXrm19jfTa\n7rUzL+8HLYllUrjJjfJUWi3xphy17EB7f/dAywZXUQUjL/HcjhhploU9udVIxsNNuGmTAgU6\n5CTlBGTgvndSc8PmHsrIhtbbSFMW9uQrRjJrADetU6I2R5xkMtK/YfgOdSinI5T/egK4yUaR\nshxwkslIz7oShpFrhyM5HaG9MaaCmwyUqch+J5kP7drbzmO7/fJ7PmjYKblHNHCTQplibOx1\nVr6rFCMN/5udvQ3JGmnK1HOdXClUh927pL7X7jNdN7Ke0h+P43R2RQM3SUqVYK+THvI60mvq\nXeiv13wMY6kPh3E6B/ePhJGkR7Gl3+mkcWTD37jgLm6iberTz5FCcDCaot1UbMH3Oukim8tV\nJpKpqmkBcRCnQxFNqW4qscw9Ozscmnslqv7Abmgw3XDwnddjmclPFk2BbiqsuHP2d90ZUu/U\nkZf8tNFwdFO4gLiV9EwonbRTSMGLXWXYLqCyTO7TGyXNCZ4T/VCqQAWlzzIdGDipCJZtV72j\n632KkZYboN9a0dW/Na6ONLfSGc2i9Xu+997M5bVxbQn1FojzSws46WSkm4Y7usZlz70DFT22\n6rrwwDZIc0sOYicVrqYT9XAk99sNPXf3eTpiqxXS6iq96mmdVLycDvyG/Y5a1eJ1G68oBNng\nrq8It1IGcNLJaOPnh13Uzkva29vb/SXdZkpgSwA4iRjNSHLf1Oy+yXhzewe+JdtMCZA7CZKu\nYrqjS+kQJ93coa/JtlMC1E6Cpquod3SNhLmYtJkh1RZR6XDSuWh3dA2Mj2QhtdN2TjASIXDS\niRju6OqGCy2cReYmh0yI6gpV3obY/+NEyYrhjq677Gx4KQkJ3OSyOoxESIAjaQhrQ72jq+nv\n6DJfSDrmJqc1aWoK9S2Bk85Du6OrW3BZ6/ze7SYY6XTgJO7scJNj8rPOxoogRPcOTpTI8evU\ng5EiEKSjFOoGwdVNrvJTVBOqegROSottN1HvuYLnkQlwUnqsuglGikSQ4SQQODg2N8FIkQgz\nngRdDqdg6IZwF56gilDLMwKNzILGpzF3k4fsMBIxcFIODG4Ss0+Dv5qbELdhAvrFbRwEGz2e\nRU7ASbnw2zPNjdQPRvo66dN866T5/BITbO94FlkRyknQ+XR+RvotuYtb91J3z9arL/V0dzuM\nRE6wcffmtQQvdpWMK7qR+hs25IL3Tdz+GiUpwdbAyLlO4iU/r2iOohtpWNBNrviqnrP7NmCk\nAJzqJF7y84rmKBYj9U9Zedza20NNSrA1MBHOSfpqvOTnFc1RlM6G/tM/441PMFIINiSRd9PM\n0sy7VL2z5iX/SdGos1H4KOjC0jrLT8+6MjwhGUYKwqomw1wK8zPYjp1O4iX/OdGos1H4KWjC\n3GViO0e66U/Qg5HCsCLK74kDY5qpS3VP1rzkPyUa0yy8PgpKXDobbUZqZG+DKekReNUkF+yq\n3H9zKQxpZl2qbln/UorVDcXglGju6mwUTgru6Ke3GSnMHC+8apINVln6p7JpU/roP3LbeRdq\nJEcFj1/hsl1H+ujPdIWRQmGVxfTA3bFL1TdzwU3+U6KxKkh9bdgysqGpcY50IjZdTM3A3KW6\nnfmKkfrZTk3fPC/LLi8tGnXh0+HQZhlXWEwP0Q8xrELoRhq6NfR5L2CkcNjOYA1GMnepbme+\nx0h32RSqRktti/Ttco6wCGv5jhzTTsdfwe2N/FSel8Xy4C8YKSBmZcwHJqYu1fXMRb+JjR2f\nxlvcmm4nc3PdxLvaYSTqWSFN5ztHFVzfXv/feQWKjRLkkSlGadS5FIb/hi5Vh9z9jVSbW6E1\ni6e4+hvpaJswGueHZTYKfwWtG/+9dV6HYrsEeWSKURptLgVrJ6tL9qa1vkcf99+h3ffvIaqH\nPKSbnYep91TLlJ9appxn0Y7/1eT3MakW0p6SePWwrc9GcQxl4645wkhhMWljnUvBf5os82mQ\nvO5fT0Z6dJ9fculvm41yvtynlGfSj0UW7dt8HUXONqkfSrl2yB/qmiZUUItKXeK44sEN02WS\nKwZxDNflhblL1Z7rfBSY+uW/If+fka7N9/isf/0d+zyVmRtmKS+LLMYv1QDGpOoXlvbgt8vZ\nwDyywUtBc4iGhY7rHtkwaSbZYlBHnUvB2qW6mu/QHvXar2UDe01G+pPJP+0s8adSL2bOUi6y\naFuzkf6My6ezdErjaJAouMAaolPkNMWDkdYwqKPNpWDrUnXI3dAAZn1ak9Pmr900KGqbW6ZU\nusVs2zAbKYBxVAgVnGdi/Mpp/d1bps8lW0IfHOwx0lUf4UJlJOqO7/Cs297phI8oEJpssiWw\nk/yN9LlcP6aVaIxE03l2Fts7T4fCwEjnENZJhnOkrh/hz2qkl+lcYplylsW0sprcaqRkrOR0\nCLqdhKqwaYgWk6BO0tZ6qb12MtXv9WM8J1+mfG332pmXhxrZEADnE7nNZDDSWbgqtEtJfSV5\niedmM9LN2B+gpJyymFZWk68aibmVfLpDCI79aDYEgu6SDCs9lJEN7fL8x8FIUxbTIjX5hpH4\n4tupuJEaRjqRgE7iJT+vaAzs6ZpfXYOuxOy140A4J/GSn1c0KnsvcK2sRVhg3tpxIZiT9svv\nOfDAKTnjxnDkMrF1TcryMtaOEcE6HGAkF44OtjCvTduhwlU7ZoRyEi/5eUUzQDFkyTgc6nCu\ny/xos8uWQE7iJT+vaDrIBv4p2dB37/PTjilhnMRLfl7R0LlIySzIsFxm2vHFWSgvRXnJzyma\nAK096OB2TtrxJoiTeMnPJxrWIyuMJBdwPEI4iZf8TKIJfkdUCBIMORoBnKTeixqZXbJ4o07r\nsnjo5WlREJNm1JEIc55UGtq0LtNDL1N1UYsq94Ju0HHBaA8/GR96mbCLWtS4H3DScbRpXeRD\nLxO3ESrcEzjpMIZpXcTsDvlUSTv684GTjqI8UmJ8pz70MjVQ3Z7ASQfRjNSjPvQyNVDbniR7\nkYgLPyMt5NEeepkaqGxf4KRjCFPfgv7Qy9RAXXsDJx2iEoa+Bf2hl6mBqvYHTjqAEPq0LqaH\nXqYGatofGGkv3b5Im9bF/NDL1EBN7wBO2sNwWqSNbDA/9DI1UNF7gJN8mXUuqNO6mB96mRpp\nRx8NOMmHpUnUaV1OHnseiLSjj0F/E8CkW/P9Rb29V1YoXOLUHeJIEYWkZLgJYNKtn28OTjJS\niIvaoit5F79T5VE4OQPqXZuje0GhIpfjorbYOt7NdBPAoFw/J/dGkylQ5aJc1BZZxYcw3ATQ\nMc04bqYwmUtzUVtcDR/GPHb5vjm3fUE6F+iitqgKJsFkpH9idpneumKggJhRpovaYuqXDJOR\nnnU13ThtXzNQRIwo1kVtEdVLiuW2tNvmsV32Upfsojb72iWnMhup2eptkCsFiIcJhbuozbpy\ng1ArNwGM+jk1pEzFhovabOs2GNpNAEJeR/oIpzvTclQbLpJABT+0mwDkyIamdjhH6lDlpnva\nMAnecuxZJ0+ggyfqTQCDF1xvqRGrHyPjGQ1cNANSeKLeBNCNahAXt/2RTL3yKTY+0cBFS6DG\ncfw0FNYP0XGOBi7SgCAE7HcSL/ndooGLTEATCvY5SXCT3yEauMgCZKGgECPBRXagDAm7nJSW\nkeCiVSAODTudxEt+ofyffQMXbQB9iNjjJLuRVicM+lO/MKYcFz61L60Zi8W/WXq0kk0gERG+\nFzP7lz1GaiofI731LzeMpFzpgoucgEpU7HDSupFs1G5Nu0/1rnyNtOidh4tcgVBk7HHSDiP9\nc2zdMtVTXD2NJGbJ0DjcgVZ0+DvJ1FTvlbj/Du3kQ+erRzc2dhhw/jFYo0/5qWXKeRbt+F9N\nfh+TagUYz5PgIj8gFyGOYo5tVJiMJB9AWU9GenSfX3Lpvf/+YzGSfFLlY5FF+zaZVX4pDOPV\nx/54uMgfKEaIz1i1/shOW+PfcJvGz0jX5nt81r92N+E+xD/dGrOUl0UW45dq8jGpFr+Ai3YC\n0SjxUdN8B1At73R6TUb6k0k/bf9ZPlDPYqS/4d0si/FLNfmfcXm7754k0AHdSPE9gfxP7gAA\nBK9JREFUTbJ1BMzOkdr566VqrEZavmvXjGRejp3RAaAcLXsuJy0WrBrpJm90D2ck234SbALN\niPET1NNIlpvCCY00poCZPIFexBw0Ui33OX9HjDTLYlpZTb5uJOANtKPGS1Et8UvttZOpli1/\n49Dutd1rZ16OxnAAaEeOV9edtkRe4rkdMdIsC2NqGCkE0I4eD00NSR/KyIbW20hTFsbUMFII\noB09x4wUEV7RpAW0C4C7qLzk5xVNWkC7EDirul9+z+ejOiVHY9gPtAuCq6wwUi5AuzA46spL\nfl7RpAW0CwOMVBjQLhBuwvKSn1c0aQHtQuF26hI6Ci94RZMW0C4YLtLykp9XNGkB7cLhoC0v\n+XlFkxbQLhwwUkFAu4Bsi2ucgDIeJ2iSK9AuJFC3GFDVQYG8pYCaDgrkLQXUdFigbyGgogMD\ngcsA9RwaKFwEqObgQOISQC0HBxKXAGo5PNC4AFDJJwCR8wd1fAZQOXtQxacAmXMHNXwKkDl3\nUMPnAJ0zBxV8EhA6b1C/ZwGlswbVexqQOmdQu6cBqXMGtXse0DpjULknArHzBXV7JlA7W1C1\nZwK1swVVeyqQO1dQs+cCvTMFFXsyEDxPUK9ns1A89qNVFWJpkgHQ7myE9UN0eEWTFtDudITl\nfXx4RZMW0O58hPEtA3hFkxbQLgLC8I4DvKJJC2gXg1F1Zqf3vKJJC2gXAxgpO6BdFAbZYaRs\ngHZx6HWHkbIB2kVCCm81UveF8cvmJsTtbUhtzKLjqX1p36plOdgG2kVip5EqOQLhrac2ZvHl\nrX8JIwUA2sWiU37VSCbu4ta91C75yyzeFYx0CtAuGqK1y29r65VoVr7Vs3iKK4x0CtDufMaG\nLIzy3ytx/x3aff8eonp0e6Hv0l8GlZ6hEJ9appxn0Y7/1eT3Menyi91FAtAuBsNAa2GQ/9qd\nA9WTkR7d55dcOjrpLp5qdt2fPH16LLJo36b9j/xSqJm0aAxHgHaRkI1fl/+fqN7DiU3/d22+\nx2f9azWkmO2bZnn1aS6LLMYv1eRjUvULgnKVCrSLhvEOoFr8fV9fk5H+ZMpP+3PEs67EQ81p\nSrnIom3NRvozLkdjOAC0i4m1I2B2jtQuXztuymHZMuUsi7VtwEikQLuo7DNSo/Q2wEjxgXZR\n2Wck1QQwUnygXVQM50iv7+ufzUj9daSP0lGwTDnLYlpZTQ4jEQPtoqLJ/1J77WSq36sc2dDU\nq+dIr+1eO/NyNIYDQLuo6PLLSzw366FdP9buquSyTDllMa2sJoeRiIF2UTHI/1BGNrTL13sl\nLuqlVDXlL4tpkZocRiIG2kWFl/y8okkLaBcVXvLziiYtoF1U9svv+XxUp+RoDPuBdlGBkXIB\n2kWFl/y8okkLaBcVXvLziiYtoF1UeMnPK5q0gHZR4SU/r2jSAtpFhZf8vKJJC2gXFV7y84om\nLaBdVHjJzyuatIB2UaGYr5KQ2HIkDLQDgAAYCQACYCQACICRACAARgKAABgJAAJgJAAIgJEA\nIABGAoAAGAkAAmAkAAiAkQAgAEYCgAAYCQACYCQACICRACAARgKAABgJAAJgJAAIgJEAIABG\nAoAAGAkAAmAkAAj4D7GyBFtKQHIjAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Omega\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o0<-psych::omega(en18dic[,mget(vars)], plot = T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La función omega del paquete `psych` tambien permite conocer cual sería la estructura factorial ideal dado los datos que se proponen. \n",
    "\n",
    "Cuando se encuentra que la estructura ideal presentada difiere a la estructura del índice propuesto por alguna otra metodología se puede pensar en replantear dicho índice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Buscar un mejor índice\n",
    "\n",
    "En base a los anteriores criterios de confiabilidad se propone un nuevo índice.\n",
    "\n",
    "Se quitarán variables con discriminación menor a 0.9, -3>severidad>3 y cambio de alpha al ser retirado muy pequeño."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:23.948094Z",
     "start_time": "2019-06-20T16:47:23.880Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.table: 12 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>raw_alpha</th><th scope=col>VarName</th><th scope=col>diff.a</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.7059350</td><td>dim1_ind1_h</td><td>-0.007267708</td></tr>\n",
       "\t<tr><td>0.7205153</td><td>dim1_ind2_h</td><td> 0.007312511</td></tr>\n",
       "\t<tr><td>0.6784367</td><td>dim1_ind3_h</td><td>-0.034766001</td></tr>\n",
       "\t<tr><td>0.7015845</td><td>dim2_ind1_h</td><td>-0.011618274</td></tr>\n",
       "\t<tr><td>0.6851860</td><td>dim2_ind2_h</td><td>-0.028016775</td></tr>\n",
       "\t<tr><td>0.7033710</td><td>dim2_ind3_h</td><td>-0.009831729</td></tr>\n",
       "\t<tr><td>0.7022749</td><td>dim3_ind1_h</td><td>-0.010927888</td></tr>\n",
       "\t<tr><td>0.6795186</td><td>dim3_ind2_h</td><td>-0.033684138</td></tr>\n",
       "\t<tr><td>0.6990778</td><td>dim4_ind1_h</td><td>-0.014124907</td></tr>\n",
       "\t<tr><td>0.6785415</td><td>dim4_ind2_h</td><td>-0.034661221</td></tr>\n",
       "\t<tr><td>0.6935830</td><td>dim4_ind3_h</td><td>-0.019619747</td></tr>\n",
       "\t<tr><td>0.6836468</td><td>dim4_ind4_h</td><td>-0.029555923</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.table: 12 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " raw\\_alpha & VarName & diff.a\\\\\n",
       " <dbl> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.7059350 & dim1\\_ind1\\_h & -0.007267708\\\\\n",
       "\t 0.7205153 & dim1\\_ind2\\_h &  0.007312511\\\\\n",
       "\t 0.6784367 & dim1\\_ind3\\_h & -0.034766001\\\\\n",
       "\t 0.7015845 & dim2\\_ind1\\_h & -0.011618274\\\\\n",
       "\t 0.6851860 & dim2\\_ind2\\_h & -0.028016775\\\\\n",
       "\t 0.7033710 & dim2\\_ind3\\_h & -0.009831729\\\\\n",
       "\t 0.7022749 & dim3\\_ind1\\_h & -0.010927888\\\\\n",
       "\t 0.6795186 & dim3\\_ind2\\_h & -0.033684138\\\\\n",
       "\t 0.6990778 & dim4\\_ind1\\_h & -0.014124907\\\\\n",
       "\t 0.6785415 & dim4\\_ind2\\_h & -0.034661221\\\\\n",
       "\t 0.6935830 & dim4\\_ind3\\_h & -0.019619747\\\\\n",
       "\t 0.6836468 & dim4\\_ind4\\_h & -0.029555923\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.table: 12 × 3\n",
       "\n",
       "| raw_alpha &lt;dbl&gt; | VarName &lt;chr&gt; | diff.a &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 0.7059350 | dim1_ind1_h | -0.007267708 |\n",
       "| 0.7205153 | dim1_ind2_h |  0.007312511 |\n",
       "| 0.6784367 | dim1_ind3_h | -0.034766001 |\n",
       "| 0.7015845 | dim2_ind1_h | -0.011618274 |\n",
       "| 0.6851860 | dim2_ind2_h | -0.028016775 |\n",
       "| 0.7033710 | dim2_ind3_h | -0.009831729 |\n",
       "| 0.7022749 | dim3_ind1_h | -0.010927888 |\n",
       "| 0.6795186 | dim3_ind2_h | -0.033684138 |\n",
       "| 0.6990778 | dim4_ind1_h | -0.014124907 |\n",
       "| 0.6785415 | dim4_ind2_h | -0.034661221 |\n",
       "| 0.6935830 | dim4_ind3_h | -0.019619747 |\n",
       "| 0.6836468 | dim4_ind4_h | -0.029555923 |\n",
       "\n"
      ],
      "text/plain": [
       "   raw_alpha VarName     diff.a      \n",
       "1  0.7059350 dim1_ind1_h -0.007267708\n",
       "2  0.7205153 dim1_ind2_h  0.007312511\n",
       "3  0.6784367 dim1_ind3_h -0.034766001\n",
       "4  0.7015845 dim2_ind1_h -0.011618274\n",
       "5  0.6851860 dim2_ind2_h -0.028016775\n",
       "6  0.7033710 dim2_ind3_h -0.009831729\n",
       "7  0.7022749 dim3_ind1_h -0.010927888\n",
       "8  0.6795186 dim3_ind2_h -0.033684138\n",
       "9  0.6990778 dim4_ind1_h -0.014124907\n",
       "10 0.6785415 dim4_ind2_h -0.034661221\n",
       "11 0.6935830 dim4_ind3_h -0.019619747\n",
       "12 0.6836468 dim4_ind4_h -0.029555923"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Discriminación\n",
    "out_vars = c()\n",
    "out_vars = c(out_vars, irtC[z1<0.9, VarName])\n",
    "#Severidad\n",
    "out_vars = c(out_vars, irtC[abs(Intercept)>3, VarName])\n",
    "#Alpha\n",
    "tmp1 = alpha1$alpha.drop  %>%  data.table\n",
    "tmp1[, VarName := vars]\n",
    "tmp1[, diff.a := raw_alpha - alpha1[[1]][[1]]]\n",
    "tmp1[, .(raw_alpha, VarName, diff.a)]\n",
    "out.a = tmp1[diff.a>=-0.01 & diff.a<0, VarName]\n",
    "out_vars = c(out_vars, out.a) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:34.424768Z",
     "start_time": "2019-06-20T16:47:34.376Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "5"
      ],
      "text/latex": [
       "5"
      ],
      "text/markdown": [
       "5"
      ],
      "text/plain": [
       "[1] 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "6"
      ],
      "text/latex": [
       "6"
      ],
      "text/markdown": [
       "6"
      ],
      "text/plain": [
       "[1] 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'dim1_ind2_h'</li>\n",
       "\t<li>'dim2_ind3_h'</li>\n",
       "\t<li>'dim2_ind1_h'</li>\n",
       "\t<li>'dim3_ind1_h'</li>\n",
       "\t<li>'dim1_ind1_h'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'dim1\\_ind2\\_h'\n",
       "\\item 'dim2\\_ind3\\_h'\n",
       "\\item 'dim2\\_ind1\\_h'\n",
       "\\item 'dim3\\_ind1\\_h'\n",
       "\\item 'dim1\\_ind1\\_h'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'dim1_ind2_h'\n",
       "2. 'dim2_ind3_h'\n",
       "3. 'dim2_ind1_h'\n",
       "4. 'dim3_ind1_h'\n",
       "5. 'dim1_ind1_h'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"dim1_ind2_h\" \"dim2_ind3_h\" \"dim2_ind1_h\" \"dim3_ind1_h\" \"dim1_ind1_h\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Total variables a reducirse\n",
    "out_vars  %>% unique  %>% length\n",
    "#se repiten por criterios?\n",
    "out_vars  %>% length\n",
    "#Quienes?\n",
    "out_vars = out_vars  %>% unique\n",
    "out_vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"Mejor\" conjunto de variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:39.965741Z",
     "start_time": "2019-06-20T16:47:39.935Z"
    }
   },
   "outputs": [],
   "source": [
    "vars2 = vars[vars %in% out_vars == F]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:43:46.164777Z",
     "start_time": "2019-06-20T16:43:46.131Z"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:47:41.397823Z",
     "start_time": "2019-06-20T16:47:41.159Z"
    }
   },
   "outputs": [
    {
     "data": {
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b35spHo8jWe2YBNu3yh3gf/3vKqho9o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\ngg==",
      "text/plain": [
       "Plot with title \"Omega\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o1<-psych::omega(en18dic[,mget(vars2)], plot = T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:50:28.173927Z",
     "start_time": "2019-06-20T16:50:28.126Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$`Omega Total`</dt>\n",
       "\t\t<dd>0.753475580177457</dd>\n",
       "\t<dt>$`Omega Jerárquico`</dt>\n",
       "\t\t<dd>0.42970449733992</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$`Omega Total`] 0.753475580177457\n",
       "\\item[\\$`Omega Jerárquico`] 0.42970449733992\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$`Omega Total`\n",
       ":   0.753475580177457\n",
       "$`Omega Jerárquico`\n",
       ":   0.42970449733992\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`Omega Total`\n",
       "[1] 0.7534756\n",
       "\n",
       "$`Omega Jerárquico`\n",
       "[1] 0.4297045\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$`Omega Total`</dt>\n",
       "\t\t<dd>0.74292259407707</dd>\n",
       "\t<dt>$`Omega Jerárquico`</dt>\n",
       "\t\t<dd>0.556817241895127</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$`Omega Total`] 0.74292259407707\n",
       "\\item[\\$`Omega Jerárquico`] 0.556817241895127\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$`Omega Total`\n",
       ":   0.74292259407707\n",
       "$`Omega Jerárquico`\n",
       ":   0.556817241895127\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`Omega Total`\n",
       "[1] 0.7429226\n",
       "\n",
       "$`Omega Jerárquico`\n",
       "[1] 0.5568172\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o1.i = list(\"Omega Total\" = o1$omega.tot, \"Omega Jerárquico\" = o1$omega_h)\n",
    "#anterior\n",
    "o0.i\n",
    "#Nuevo\n",
    "o1.i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T16:50:56.497113Z",
     "start_time": "2019-06-20T16:50:56.040Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 1 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>raw_alpha</th><th scope=col>std.alpha</th><th scope=col>G6(smc)</th><th scope=col>average_r</th><th scope=col>S/N</th><th scope=col>ase</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>median_r</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.7132027</td><td>0.7070646</td><td>0.715708</td><td>0.16746</td><td>2.413722</td><td>0.001668119</td><td>0.2869615</td><td>0.1912352</td><td>0.1571697</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       " raw\\_alpha & std.alpha & G6(smc) & average\\_r & S/N & ase & mean & sd & median\\_r\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.7132027 & 0.7070646 & 0.715708 & 0.16746 & 2.413722 & 0.001668119 & 0.2869615 & 0.1912352 & 0.1571697\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 9\n",
       "\n",
       "| raw_alpha &lt;dbl&gt; | std.alpha &lt;dbl&gt; | G6(smc) &lt;dbl&gt; | average_r &lt;dbl&gt; | S/N &lt;dbl&gt; | ase &lt;dbl&gt; | mean &lt;dbl&gt; | sd &lt;dbl&gt; | median_r &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 0.7132027 | 0.7070646 | 0.715708 | 0.16746 | 2.413722 | 0.001668119 | 0.2869615 | 0.1912352 | 0.1571697 |\n",
       "\n"
      ],
      "text/plain": [
       " raw_alpha std.alpha G6(smc)  average_r S/N      ase         mean     \n",
       " 0.7132027 0.7070646 0.715708 0.16746   2.413722 0.001668119 0.2869615\n",
       " sd        median_r \n",
       " 0.1912352 0.1571697"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 1 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>raw_alpha</th><th scope=col>std.alpha</th><th scope=col>G6(smc)</th><th scope=col>average_r</th><th scope=col>S/N</th><th scope=col>ase</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>median_r</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.6897498</td><td>0.6903572</td><td>0.6764703</td><td>0.2415646</td><td>2.229527</td><td>0.001912199</td><td>0.3498833</td><td>0.2546066</td><td>0.2339443</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       " raw\\_alpha & std.alpha & G6(smc) & average\\_r & S/N & ase & mean & sd & median\\_r\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.6897498 & 0.6903572 & 0.6764703 & 0.2415646 & 2.229527 & 0.001912199 & 0.3498833 & 0.2546066 & 0.2339443\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 9\n",
       "\n",
       "| raw_alpha &lt;dbl&gt; | std.alpha &lt;dbl&gt; | G6(smc) &lt;dbl&gt; | average_r &lt;dbl&gt; | S/N &lt;dbl&gt; | ase &lt;dbl&gt; | mean &lt;dbl&gt; | sd &lt;dbl&gt; | median_r &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 0.6897498 | 0.6903572 | 0.6764703 | 0.2415646 | 2.229527 | 0.001912199 | 0.3498833 | 0.2546066 | 0.2339443 |\n",
       "\n"
      ],
      "text/plain": [
       " raw_alpha std.alpha G6(smc)   average_r S/N      ase         mean     \n",
       " 0.6897498 0.6903572 0.6764703 0.2415646 2.229527 0.001912199 0.3498833\n",
       " sd        median_r \n",
       " 0.2546066 0.2339443"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha2<-psych::alpha(en18dic[,mget(vars2)])\n",
    "#Anterior\n",
    "alpha1$total\n",
    "#Nuevo\n",
    "alpha2$total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#En general se encuentra muy poca mejora"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Análisis confirmatorio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya que se encuentra poca mejoría con el nuevo índice propuesto, se hará análisis confirmatorio de los dos modelos propuestos por Omega"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Con todas las variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T17:19:38.658565Z",
     "start_time": "2019-06-20T17:19:38.627Z"
    }
   },
   "outputs": [],
   "source": [
    "#Función para extraer ecuación de omega óptimo\n",
    "opt.o.extract.eq = function(omega){\n",
    "    o0.s = omega$schmid$sl %>% data.table() \n",
    "\n",
    "    o0.s[,VarName := omega$schmid$sl  %>% rownames]\n",
    "\n",
    "    n0 = names(o0.s) \n",
    "    n0 = n0[names(o0.s)  %>% grepl(pattern = \"F\")]\n",
    "    n1 = substr(n0,1,(nchar(n0)-1))\n",
    "    o0.s = setnames(o0.s, old = n0, new=n1)\n",
    "\n",
    "    Fs = list()\n",
    "    h = c()\n",
    "    for (x in n1){\n",
    "        Fs[[x]] = o0.s[abs(get(x))>0.2, VarName]\n",
    "        Fs[[x]] = Fs[[x]] %>% paste(collapse = \" + \")\n",
    "        h = c(h, Fs[[x]])\n",
    "        Fs[[x]] = paste0(x,\" =~  + \" , Fs[[x]])\n",
    "    }\n",
    "    h = h %>% paste(collapse = \" + \")\n",
    "    h = paste0(\"h\",\" =~  + \" , h)\n",
    "    Fs = Fs  %>% unlist  %>% paste(collapse = \" \\n \")\n",
    "    opt.o.eq = paste0(h, \" \\n \", Fs) \n",
    "    return(opt.o.eq)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T17:20:48.730942Z",
     "start_time": "2019-06-20T17:20:48.690Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'h =~  + dim3_ind2_h + dim4_ind2_h + dim4_ind3_h + dim4_ind4_h + dim1_ind3_h + dim2_ind2_h + dim2_ind3_h + dim1_ind1_h + dim2_ind1_h + dim4_ind1_h \\n F1 =~  + dim3_ind2_h + dim4_ind2_h + dim4_ind3_h + dim4_ind4_h \\n F2 =~  + dim1_ind3_h + dim2_ind2_h + dim2_ind3_h \\n F3 =~  + dim1_ind1_h + dim2_ind1_h + dim4_ind1_h\\n                h  ~~ 0*F1 \\n                h  ~~ 0*F2 \\n                h  ~~ 0*F3 \\n                F1 ~~ 0*F2 \\n                F2 ~~ 0*F3 \\n                F1 ~~ 0*F3'</span>"
      ],
      "text/latex": [
       "'h =\\textasciitilde{}  + dim3\\_ind2\\_h + dim4\\_ind2\\_h + dim4\\_ind3\\_h + dim4\\_ind4\\_h + dim1\\_ind3\\_h + dim2\\_ind2\\_h + dim2\\_ind3\\_h + dim1\\_ind1\\_h + dim2\\_ind1\\_h + dim4\\_ind1\\_h \\textbackslash{}n F1 =\\textasciitilde{}  + dim3\\_ind2\\_h + dim4\\_ind2\\_h + dim4\\_ind3\\_h + dim4\\_ind4\\_h \\textbackslash{}n F2 =\\textasciitilde{}  + dim1\\_ind3\\_h + dim2\\_ind2\\_h + dim2\\_ind3\\_h \\textbackslash{}n F3 =\\textasciitilde{}  + dim1\\_ind1\\_h + dim2\\_ind1\\_h + dim4\\_ind1\\_h\\textbackslash{}n                h  \\textasciitilde{}\\textasciitilde{} 0*F1 \\textbackslash{}n                h  \\textasciitilde{}\\textasciitilde{} 0*F2 \\textbackslash{}n                h  \\textasciitilde{}\\textasciitilde{} 0*F3 \\textbackslash{}n                F1 \\textasciitilde{}\\textasciitilde{} 0*F2 \\textbackslash{}n                F2 \\textasciitilde{}\\textasciitilde{} 0*F3 \\textbackslash{}n                F1 \\textasciitilde{}\\textasciitilde{} 0*F3'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'h =~  + dim3_ind2_h + dim4_ind2_h + dim4_ind3_h + dim4_ind4_h + dim1_ind3_h + dim2_ind2_h + dim2_ind3_h + dim1_ind1_h + dim2_ind1_h + dim4_ind1_h \\n F1 =~  + dim3_ind2_h + dim4_ind2_h + dim4_ind3_h + dim4_ind4_h \\n F2 =~  + dim1_ind3_h + dim2_ind2_h + dim2_ind3_h \\n F3 =~  + dim1_ind1_h + dim2_ind1_h + dim4_ind1_h\\n                h  ~~ 0*F1 \\n                h  ~~ 0*F2 \\n                h  ~~ 0*F3 \\n                F1 ~~ 0*F2 \\n                F2 ~~ 0*F3 \\n                F1 ~~ 0*F3'</span>"
      ],
      "text/plain": [
       "[1] \"h =~  + dim3_ind2_h + dim4_ind2_h + dim4_ind3_h + dim4_ind4_h + dim1_ind3_h + dim2_ind2_h + dim2_ind3_h + dim1_ind1_h + dim2_ind1_h + dim4_ind1_h \\n F1 =~  + dim3_ind2_h + dim4_ind2_h + dim4_ind3_h + dim4_ind4_h \\n F2 =~  + dim1_ind3_h + dim2_ind2_h + dim2_ind3_h \\n F3 =~  + dim1_ind1_h + dim2_ind1_h + dim4_ind1_h\\n                h  ~~ 0*F1 \\n                h  ~~ 0*F2 \\n                h  ~~ 0*F3 \\n                F1 ~~ 0*F2 \\n                F2 ~~ 0*F3 \\n                F1 ~~ 0*F3\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Añado paths entre dimensiones\n",
    "opt.o.eq = paste0(opt.o.extract.eq(o0), \"\n",
    "                h  ~~ 0*F1 \n",
    "                h  ~~ 0*F2 \n",
    "                h  ~~ 0*F3 \n",
    "                F1 ~~ 0*F2 \n",
    "                F2 ~~ 0*F3 \n",
    "                F1 ~~ 0*F3\")\n",
    "opt.o.eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T17:23:55.513640Z",
     "start_time": "2019-06-20T17:23:47.544Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in lavaan::lavaan(model = opt.o.eq, data = en18dic, ordered = vars, :\n",
      "\"lavaan WARNING: the optimizer warns that a solution has NOT been found!\""
     ]
    }
   ],
   "source": [
    "fit <- lavaan::sem(opt.o.eq, data = en18dic,\n",
    "           ordered=vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T17:29:04.683654Z",
     "start_time": "2019-06-20T17:29:04.613Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 7 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>V1</th><th scope=col>V2</th><th scope=col>V3</th><th scope=col>V4</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1.0000000</td><td>1.0000000</td><td>0.0000000</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.9393270</td><td>0.7351558</td><td>0.0000000</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.8330115</td><td>0.0000000</td><td>1.0000000</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.6608722</td><td>0.0000000</td><td>0.5370961</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.6397349</td><td>0.0000000</td><td>0.0000000</td><td>1.0000000</td></tr>\n",
       "\t<tr><td>1.0031202</td><td>0.0000000</td><td>0.0000000</td><td>0.1890674</td></tr>\n",
       "\t<tr><td>0.8561810</td><td>0.0000000</td><td>0.0000000</td><td>0.1651309</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 7 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       " V1 & V2 & V3 & V4\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 1.0000000 & 1.0000000 & 0.0000000 & 0.0000000\\\\\n",
       "\t 0.9393270 & 0.7351558 & 0.0000000 & 0.0000000\\\\\n",
       "\t 0.8330115 & 0.0000000 & 1.0000000 & 0.0000000\\\\\n",
       "\t 0.6608722 & 0.0000000 & 0.5370961 & 0.0000000\\\\\n",
       "\t 0.6397349 & 0.0000000 & 0.0000000 & 1.0000000\\\\\n",
       "\t 1.0031202 & 0.0000000 & 0.0000000 & 0.1890674\\\\\n",
       "\t 0.8561810 & 0.0000000 & 0.0000000 & 0.1651309\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 7 × 4\n",
       "\n",
       "| V1 &lt;dbl&gt; | V2 &lt;dbl&gt; | V3 &lt;dbl&gt; | V4 &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1.0000000 | 1.0000000 | 0.0000000 | 0.0000000 |\n",
       "| 0.9393270 | 0.7351558 | 0.0000000 | 0.0000000 |\n",
       "| 0.8330115 | 0.0000000 | 1.0000000 | 0.0000000 |\n",
       "| 0.6608722 | 0.0000000 | 0.5370961 | 0.0000000 |\n",
       "| 0.6397349 | 0.0000000 | 0.0000000 | 1.0000000 |\n",
       "| 1.0031202 | 0.0000000 | 0.0000000 | 0.1890674 |\n",
       "| 0.8561810 | 0.0000000 | 0.0000000 | 0.1651309 |\n",
       "\n"
      ],
      "text/plain": [
       "  V1        V2        V3        V4       \n",
       "1 1.0000000 1.0000000 0.0000000 0.0000000\n",
       "2 0.9393270 0.7351558 0.0000000 0.0000000\n",
       "3 0.8330115 0.0000000 1.0000000 0.0000000\n",
       "4 0.6608722 0.0000000 0.5370961 0.0000000\n",
       "5 0.6397349 0.0000000 0.0000000 1.0000000\n",
       "6 1.0031202 0.0000000 0.0000000 0.1890674\n",
       "7 0.8561810 0.0000000 0.0000000 0.1651309"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "2.6010198092323"
      ],
      "text/latex": [
       "2.6010198092323"
      ],
      "text/markdown": [
       "2.6010198092323"
      ],
      "text/plain": [
       "[1] 2.60102"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>omega_h</dt>\n",
       "\t\t<dd>0.782037006188835</dd>\n",
       "\t<dt>omega_t</dt>\n",
       "\t\t<dd>0.942199371050265</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[omega\\textbackslash{}\\_h] 0.782037006188835\n",
       "\\item[omega\\textbackslash{}\\_t] 0.942199371050265\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "omega_h\n",
       ":   0.782037006188835omega_t\n",
       ":   0.942199371050265\n",
       "\n"
      ],
      "text/plain": [
       "  omega_h   omega_t \n",
       "0.7820370 0.9421994 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambdas<-as.data.frame(fit@Model@GLIST$lambda)\n",
    "error<-colSums(fit@Model@GLIST$theta)\n",
    "Slambda_2<-sum(lambdas[1])^2 + sum(lambdas[2])^2 + \n",
    "           sum(lambdas[3])^2 + sum(lambdas[4])^2\n",
    "error <- sum(error)\n",
    "\n",
    "omega_t <- Slambda_2 / (Slambda_2+error)\n",
    "omega_h <- sum(lambdas[1])^2 / (Slambda_2+error)\n",
    "omegamanual<-c(omega_h=omega_h,omega_t=omega_t)\n",
    "lambdas\n",
    "error\n",
    "omegamanual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El modelo propuesto con los datos no sirve. Se buscará algún otro subconjunto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subconjunto 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T17:28:20.665025Z",
     "start_time": "2019-06-20T17:28:20.621Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'h =~  + dim3_ind2_h + dim4_ind4_h + dim1_ind3_h + dim2_ind2_h + dim4_ind1_h + dim4_ind2_h + dim4_ind3_h \\n F1 =~  + dim3_ind2_h + dim4_ind4_h \\n F2 =~  + dim1_ind3_h + dim2_ind2_h \\n F3 =~  + dim4_ind1_h + dim4_ind2_h + dim4_ind3_h\\n                h  ~~ 0*F1 \\n                h  ~~ 0*F2 \\n                h  ~~ 0*F3 \\n                F1 ~~ 0*F2 \\n                F2 ~~ 0*F3 \\n                F1 ~~ 0*F3'</span>"
      ],
      "text/latex": [
       "'h =\\textasciitilde{}  + dim3\\_ind2\\_h + dim4\\_ind4\\_h + dim1\\_ind3\\_h + dim2\\_ind2\\_h + dim4\\_ind1\\_h + dim4\\_ind2\\_h + dim4\\_ind3\\_h \\textbackslash{}n F1 =\\textasciitilde{}  + dim3\\_ind2\\_h + dim4\\_ind4\\_h \\textbackslash{}n F2 =\\textasciitilde{}  + dim1\\_ind3\\_h + dim2\\_ind2\\_h \\textbackslash{}n F3 =\\textasciitilde{}  + dim4\\_ind1\\_h + dim4\\_ind2\\_h + dim4\\_ind3\\_h\\textbackslash{}n                h  \\textasciitilde{}\\textasciitilde{} 0*F1 \\textbackslash{}n                h  \\textasciitilde{}\\textasciitilde{} 0*F2 \\textbackslash{}n                h  \\textasciitilde{}\\textasciitilde{} 0*F3 \\textbackslash{}n                F1 \\textasciitilde{}\\textasciitilde{} 0*F2 \\textbackslash{}n                F2 \\textasciitilde{}\\textasciitilde{} 0*F3 \\textbackslash{}n                F1 \\textasciitilde{}\\textasciitilde{} 0*F3'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'h =~  + dim3_ind2_h + dim4_ind4_h + dim1_ind3_h + dim2_ind2_h + dim4_ind1_h + dim4_ind2_h + dim4_ind3_h \\n F1 =~  + dim3_ind2_h + dim4_ind4_h \\n F2 =~  + dim1_ind3_h + dim2_ind2_h \\n F3 =~  + dim4_ind1_h + dim4_ind2_h + dim4_ind3_h\\n                h  ~~ 0*F1 \\n                h  ~~ 0*F2 \\n                h  ~~ 0*F3 \\n                F1 ~~ 0*F2 \\n                F2 ~~ 0*F3 \\n                F1 ~~ 0*F3'</span>"
      ],
      "text/plain": [
       "[1] \"h =~  + dim3_ind2_h + dim4_ind4_h + dim1_ind3_h + dim2_ind2_h + dim4_ind1_h + dim4_ind2_h + dim4_ind3_h \\n F1 =~  + dim3_ind2_h + dim4_ind4_h \\n F2 =~  + dim1_ind3_h + dim2_ind2_h \\n F3 =~  + dim4_ind1_h + dim4_ind2_h + dim4_ind3_h\\n                h  ~~ 0*F1 \\n                h  ~~ 0*F2 \\n                h  ~~ 0*F3 \\n                F1 ~~ 0*F2 \\n                F2 ~~ 0*F3 \\n                F1 ~~ 0*F3\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Añado paths entre dimensiones\n",
    "opt.o.eq = paste0(opt.o.extract.eq(o1), \"\n",
    "                h  ~~ 0*F1 \n",
    "                h  ~~ 0*F2 \n",
    "                h  ~~ 0*F3 \n",
    "                F1 ~~ 0*F2 \n",
    "                F2 ~~ 0*F3 \n",
    "                F1 ~~ 0*F3\")\n",
    "opt.o.eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-20T17:28:46.975857Z",
     "start_time": "2019-06-20T17:28:43.479Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :\n",
      "\"lavaan WARNING:\n",
      "    Could not compute standard errors! The information matrix could\n",
      "    not be inverted. This may be a symptom that the model is not\n",
      "    identified.\"Warning message in lav_test_satorra_bentler(lavobject = NULL, lavsamplestats = lavsamplestats, :\n",
      "\"lavaan WARNING: could not invert information matrix\n",
      "\""
     ]
    }
   ],
   "source": [
    "fit <- lavaan::sem(opt.o.eq, data = en18dic,\n",
    "           ordered=vars2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
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    "ExecuteTime": {
     "end_time": "2019-06-20T17:29:11.294278Z",
     "start_time": "2019-06-20T17:29:11.184Z"
    }
   },
   "outputs": [
    {
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       "<table>\n",
       "<caption>A data.frame: 7 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>V1</th><th scope=col>V2</th><th scope=col>V3</th><th scope=col>V4</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1.0000000</td><td>1.0000000</td><td>0.0000000</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.9393270</td><td>0.7351558</td><td>0.0000000</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.8330115</td><td>0.0000000</td><td>1.0000000</td><td>0.0000000</td></tr>\n",
       "\t<tr><td>0.6608722</td><td>0.0000000</td><td>0.5370961</td><td>0.0000000</td></tr>\n",
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       "\t<tr><td>1.0031202</td><td>0.0000000</td><td>0.0000000</td><td>0.1890674</td></tr>\n",
       "\t<tr><td>0.8561810</td><td>0.0000000</td><td>0.0000000</td><td>0.1651309</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
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      "text/latex": [
       "A data.frame: 7 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       " V1 & V2 & V3 & V4\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 1.0000000 & 1.0000000 & 0.0000000 & 0.0000000\\\\\n",
       "\t 0.9393270 & 0.7351558 & 0.0000000 & 0.0000000\\\\\n",
       "\t 0.8330115 & 0.0000000 & 1.0000000 & 0.0000000\\\\\n",
       "\t 0.6608722 & 0.0000000 & 0.5370961 & 0.0000000\\\\\n",
       "\t 0.6397349 & 0.0000000 & 0.0000000 & 1.0000000\\\\\n",
       "\t 1.0031202 & 0.0000000 & 0.0000000 & 0.1890674\\\\\n",
       "\t 0.8561810 & 0.0000000 & 0.0000000 & 0.1651309\\\\\n",
       "\\end{tabular}\n"
      ],
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       "\n",
       "A data.frame: 7 × 4\n",
       "\n",
       "| V1 &lt;dbl&gt; | V2 &lt;dbl&gt; | V3 &lt;dbl&gt; | V4 &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1.0000000 | 1.0000000 | 0.0000000 | 0.0000000 |\n",
       "| 0.9393270 | 0.7351558 | 0.0000000 | 0.0000000 |\n",
       "| 0.8330115 | 0.0000000 | 1.0000000 | 0.0000000 |\n",
       "| 0.6608722 | 0.0000000 | 0.5370961 | 0.0000000 |\n",
       "| 0.6397349 | 0.0000000 | 0.0000000 | 1.0000000 |\n",
       "| 1.0031202 | 0.0000000 | 0.0000000 | 0.1890674 |\n",
       "| 0.8561810 | 0.0000000 | 0.0000000 | 0.1651309 |\n",
       "\n"
      ],
      "text/plain": [
       "  V1        V2        V3        V4       \n",
       "1 1.0000000 1.0000000 0.0000000 0.0000000\n",
       "2 0.9393270 0.7351558 0.0000000 0.0000000\n",
       "3 0.8330115 0.0000000 1.0000000 0.0000000\n",
       "4 0.6608722 0.0000000 0.5370961 0.0000000\n",
       "5 0.6397349 0.0000000 0.0000000 1.0000000\n",
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      "text/plain": [
       "[1] 2.60102"
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    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>omega_h</dt>\n",
       "\t\t<dd>0.782037006188835</dd>\n",
       "\t<dt>omega_t</dt>\n",
       "\t\t<dd>0.942199371050265</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[omega\\textbackslash{}\\_h] 0.782037006188835\n",
       "\\item[omega\\textbackslash{}\\_t] 0.942199371050265\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "omega_h\n",
       ":   0.782037006188835omega_t\n",
       ":   0.942199371050265\n",
       "\n"
      ],
      "text/plain": [
       "  omega_h   omega_t \n",
       "0.7820370 0.9421994 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambdas<-as.data.frame(fit@Model@GLIST$lambda)\n",
    "error<-colSums(fit@Model@GLIST$theta)\n",
    "Slambda_2<-sum(lambdas[1])^2 + sum(lambdas[2])^2 + \n",
    "           sum(lambdas[3])^2 + sum(lambdas[4])^2\n",
    "error <- sum(error)\n",
    "\n",
    "omega_t <- Slambda_2 / (Slambda_2+error)\n",
    "omega_h <- sum(lambdas[1])^2 / (Slambda_2+error)\n",
    "omegamanual<-c(omega_h=omega_h,omega_t=omega_t)\n",
    "lambdas\n",
    "error\n",
    "omegamanual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los omegas están decentes, al menos el total, las cargas factoriales deberían ser mayores a 0.5. Habrá que hacer más investigación."
   ]
  }
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