modeling_tfr

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(lme4)\n",
    "library(plyr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data <- read.csv('/ihme/forecasting/data/fertility/inputs/asfr_ldi_edu.csv')\n",
    "data <- data[!(data$asfr==0),]\n",
    "mean.age <- read.csv('/ihme/forecasting/data/fertility/inputs/mean_fertile_age_by_asfr_ratio.csv')\n",
    "mean.age <- rename(mean.age,c('year' = 'year_id'))\n",
    "data <- merge.data.frame(x = data,y = mean.age,by = c('location_id','year_id'))\n",
    "data$sex <- NULL\n",
    "data$iso3 <- NULL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>location_id</th><th scope=col>year_id</th><th scope=col>age_group_id</th><th scope=col>asfr</th><th scope=col>ldi</th><th scope=col>edu</th><th scope=col>mean_fertile_age</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>101</td><td>1951</td><td>9</td><td>0.204566</td><td>9.36871</td><td>6.826699</td><td>27.82598</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>101</td><td>1951</td><td>13</td><td>0.03092</td><td>9.36871</td><td>6.414093</td><td>27.82598</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>101</td><td>1951</td><td>11</td><td>0.149179</td><td>9.36871</td><td>6.93765</td><td>27.82598</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>101</td><td>1951</td><td>10</td><td>0.2077373</td><td>9.36871</td><td>6.93765</td><td>27.82598</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>101</td><td>1951</td><td>14</td><td>0.0028385</td><td>9.36871</td><td>5.782532</td><td>27.82598</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>101</td><td>1951</td><td>12</td><td>0.0873706</td><td>9.36871</td><td>6.414093</td><td>27.82598</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllll}\n",
       "  & location_id & year_id & age_group_id & asfr & ldi & edu & mean_fertile_age\\\\\n",
       "\\hline\n",
       "\t1 & 101 & 1951 & 9 & 0.204566 & 9.36871 & 6.826699 & 27.82598\\\\\n",
       "\t2 & 101 & 1951 & 13 & 0.03092 & 9.36871 & 6.414093 & 27.82598\\\\\n",
       "\t3 & 101 & 1951 & 11 & 0.149179 & 9.36871 & 6.93765 & 27.82598\\\\\n",
       "\t4 & 101 & 1951 & 10 & 0.2077373 & 9.36871 & 6.93765 & 27.82598\\\\\n",
       "\t5 & 101 & 1951 & 14 & 0.0028385 & 9.36871 & 5.782532 & 27.82598\\\\\n",
       "\t6 & 101 & 1951 & 12 & 0.0873706 & 9.36871 & 6.414093 & 27.82598\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "  location_id year_id age_group_id      asfr     ldi      edu mean_fertile_age\n",
       "1         101    1951            9 0.2045660 9.36871 6.826699         27.82598\n",
       "2         101    1951           13 0.0309200 9.36871 6.414093         27.82598\n",
       "3         101    1951           11 0.1491790 9.36871 6.937650         27.82598\n",
       "4         101    1951           10 0.2077373 9.36871 6.937650         27.82598\n",
       "5         101    1951           14 0.0028385 9.36871 5.782532         27.82598\n",
       "6         101    1951           12 0.0873706 9.36871 6.414093         27.82598"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "head(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "regression <- function(formula) {\n",
    "    lm_lst <- list()\n",
    "    \n",
    "    for (age_group_id in 8:14) {\n",
    "        \n",
    "        train.data <- data[(data$age_group_id == age_group_id)&(data$year_id < 2000),]\n",
    "        lm_lst[[length(lm_lst) + 1]] <- formula(train.data)\n",
    "        \n",
    "    }\n",
    "    return(lm_lst)\n",
    "}    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "test.data.lst = list()\n",
    "for (age_group_id in 8:14){\n",
    "    test.data.lst[[length(test.data.lst)+1]] <- data[(data$age_group_id==age_group_id)&(data$year_id>=2000),]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "get.rmse <- function(fit.model){\n",
    "    rmse.lst <- list()\n",
    "    for (ix in 1:length(test.data.lst)){\n",
    "        predicted.data <- predict(fit.model[[ix]], newdata = test.data.lst[[ix]])\n",
    "        rmse <- sqrt(mean((test.data.lst[[ix]]$asfr - exp(predicted.data))^2))\n",
    "        rmse.lst[[ix]] <- rmse\n",
    "    }\n",
    "    names(rmse.lst) <- c('8','9','10','11','12','13','14')\n",
    "    return(rmse.lst)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$log(ASFR) = \\alpha + \\beta_1 LDI + \\beta_2 \\text{matern_edu}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ldi.edu.formula <- function(data) {\n",
    "    formula <- lm('log(asfr) ~ ldi + edu',data=data)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ldi.edu.lm <- regression(ldi.edu.formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = \"log(asfr) ~ ldi + edu\", data = data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-3.4750 -0.3378  0.1079  0.4378  1.2885 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -1.203754   0.055909  -21.53   <2e-16 ***\n",
       "ldi         -0.087355   0.007840  -11.14   <2e-16 ***\n",
       "edu         -0.153165   0.003068  -49.92   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.6423 on 9152 degrees of freedom\n",
       "Multiple R-squared:  0.4122,\tAdjusted R-squared:  0.4121 \n",
       "F-statistic:  3209 on 2 and 9152 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(ldi.edu.lm[[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "rmse.lst <- get.rmse(ldi.edu.lm)\n",
    "rmse.lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
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     "execution_count": 136,
     "metadata": {},
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   "source": [
    "mean(unlist(rmse.lst))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$log(ASFR) = \\alpha_0 + \\alpha_{country} + \\beta_1 LDI + \\beta_2 \\text{matern_edu}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ldi.edu.country.formula <- function(data) {\n",
    "    formula <- lmer('log(asfr) ~ 1 + ldi + edu + (1 | location_id)',data=data)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ldi.edu.country.lmer <- regression(ldi.edu.country.formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML ['lmerMod']\n",
       "Formula: log(asfr) ~ 1 + ldi + edu + (1 | location_id)\n",
       "   Data: data\n",
       "\n",
       "REML criterion at convergence: 2489.3\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-6.5343 -0.4474  0.0450  0.4691  4.3726 \n",
       "\n",
       "Random effects:\n",
       " Groups      Name        Variance Std.Dev.\n",
       " location_id (Intercept) 0.37708  0.6141  \n",
       " Residual                0.06836  0.2615  \n",
       "Number of obs: 9155, groups:  location_id, 188\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error t value\n",
       "(Intercept) -2.0777835  0.0941738  -22.06\n",
       "ldi          0.0000376  0.0110461    0.00\n",
       "edu         -0.1234294  0.0024559  -50.26\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "    (Intr) ldi   \n",
       "ldi -0.875       \n",
       "edu  0.592 -0.744"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(ldi.edu.country.lmer[[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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     "execution_count": 140,
     "metadata": {},
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   ],
   "source": [
    "rmse.lst <- get.rmse(ldi.edu.country.lmer)\n",
    "rmse.lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
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   "outputs": [
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   "source": [
    "mean(unlist(rmse.lst))"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$log(ASFR) = \\alpha + \\beta_1 LDI + \\beta_2 \\text{matern_edu} + \\beta_3 \\text{mean_fertile_age}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ldi.edu.mean.age.formula <- function(data) {\n",
    "    formula <- lm('log(asfr) ~ ldi + edu + mean_fertile_age',data=data)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ldi.edu.mean.age.lm <- regression(ldi.edu.mean.age.formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = \"log(asfr) ~ ldi + edu + mean_fertile_age\", data = data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-3.3834 -0.3331  0.0962  0.4193  1.2486 \n",
       "\n",
       "Coefficients:\n",
       "                  Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)       3.312478   0.157235   21.07   <2e-16 ***\n",
       "ldi              -0.112425   0.007514  -14.96   <2e-16 ***\n",
       "edu              -0.182474   0.003077  -59.31   <2e-16 ***\n",
       "mean_fertile_age -0.147378   0.004828  -30.53   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.612 on 9151 degrees of freedom\n",
       "Multiple R-squared:  0.4665,\tAdjusted R-squared:  0.4664 \n",
       "F-statistic:  2668 on 3 and 9151 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(ldi.edu.mean.age.lm[[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "$14\n",
       ":   0.0096530659545445\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`8`\n",
       "[1] 0.03158419\n",
       "\n",
       "$`9`\n",
       "[1] 0.04312499\n",
       "\n",
       "$`10`\n",
       "[1] 0.04734959\n",
       "\n",
       "$`11`\n",
       "[1] 0.04054672\n",
       "\n",
       "$`12`\n",
       "[1] 0.03615343\n",
       "\n",
       "$`13`\n",
       "[1] 0.02115178\n",
       "\n",
       "$`14`\n",
       "[1] 0.009653066\n"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse.lst <- get.rmse(ldi.edu.mean.age.lm)\n",
    "rmse.lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.032794823595509"
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      "text/latex": [
       "0.032794823595509"
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       "[1] 0.03279482"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(unlist(rmse.lst))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$log(ASFR) = \\alpha_0 + \\alpha_{country} + \\beta_1 LDI + \\beta_2 \\text{matern_edu} + \\beta_3 \\text{mean_fertile_age}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ldi.edu.country.mean.age.formula <- function(data) {\n",
    "    formula <- lmer('log(asfr) ~ 1 + ldi + edu + mean_fertile_age + (1 | location_id)',data=data)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ldi.edu.country.mean.age.lmer <- regression(ldi.edu.country.mean.age.formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML ['lmerMod']\n",
       "Formula: log(asfr) ~ 1 + ldi + edu + mean_fertile_age + (1 | location_id)\n",
       "   Data: data\n",
       "\n",
       "REML criterion at convergence: -862.2\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-5.3301 -0.5084  0.0482  0.5114  5.2038 \n",
       "\n",
       "Random effects:\n",
       " Groups      Name        Variance Std.Dev.\n",
       " location_id (Intercept) 0.38192  0.6180  \n",
       " Residual                0.04698  0.2167  \n",
       "Number of obs: 9155, groups:  location_id, 188\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error t value\n",
       "(Intercept)       4.639480   0.133966   34.63\n",
       "ldi              -0.057241   0.009274   -6.17\n",
       "edu              -0.146541   0.002074  -70.64\n",
       "mean_fertile_age -0.216972   0.003398  -63.86\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) ldi    edu   \n",
       "ldi         -0.590              \n",
       "edu          0.207 -0.713       \n",
       "mean_frtl_g -0.787  0.101  0.173"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(ldi.edu.country.mean.age.lmer[[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "\\begin{description}\n",
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       "$8\n",
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       "\n",
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       "$`8`\n",
       "[1] 0.01659732\n",
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     "execution_count": 150,
     "metadata": {},
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   ],
   "source": [
    "rmse.lst <- get.rmse(ldi.edu.country.mean.age.lmer)\n",
    "rmse.lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
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