ch7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: rstan\n",
      "Loading required package: ggplot2\n",
      "rstan (Version 2.9.0, packaged: 2016-01-05 16:17:47 UTC, GitRev: 05c3d0058b6a)\n",
      "For execution on a local, multicore CPU with excess RAM we recommend calling\n",
      "rstan_options(auto_write = TRUE)\n",
      "options(mc.cores = parallel::detectCores())\n",
      "Loading required package: parallel\n",
      "rethinking (Version 1.58)\n"
     ]
    }
   ],
   "source": [
    "## R code 7.1\n",
    "library(rethinking)\n",
    "data(rugged)\n",
    "d <- rugged\n",
    "\n",
    "# make log version of outcome\n",
    "d$log_gdp <- log( d$rgdppc_2000 )\n",
    "\n",
    "# extract countries with GDP data\n",
    "dd <- d[ complete.cases(d$rgdppc_2000) , ]\n",
    "\n",
    "# split countries into Africa and not-Africa\n",
    "d.A1 <- dd[ dd$cont_africa==1 , ] # Africa\n",
    "d.A0 <- dd[ dd$cont_africa==0 , ] # not Africa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.2\n",
    "# African nations\n",
    "m7.1 <- map(\n",
    "    alist(\n",
    "        log_gdp ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bR*rugged ,\n",
    "        a ~ dnorm( 8 , 100 ) ,\n",
    "        bR ~ dnorm( 0 , 1 ) ,\n",
    "        sigma ~ dunif( 0 , 10 )\n",
    "    ) ,\n",
    "    data=d.A1 )\n",
    "\n",
    "# non-African nations\n",
    "m7.2 <- map(\n",
    "    alist(\n",
    "        log_gdp ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bR*rugged ,\n",
    "        a ~ dnorm( 8 , 100 ) ,\n",
    "        bR ~ dnorm( 0 , 1 ) ,\n",
    "        sigma ~ dunif( 0 , 10 )\n",
    "    ) ,\n",
    "    data=d.A0 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.3\n",
    "m7.3 <- map(\n",
    "    alist(\n",
    "        log_gdp ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bR*rugged ,\n",
    "        a ~ dnorm( 8 , 100 ) ,\n",
    "        bR ~ dnorm( 0 , 1 ) ,\n",
    "        sigma ~ dunif( 0 , 10 )\n",
    "    ) ,\n",
    "    data=dd )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.4\n",
    "m7.4 <- map(\n",
    "    alist(\n",
    "        log_gdp ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bR*rugged + bA*cont_africa ,\n",
    "        a ~ dnorm( 8 , 100 ) ,\n",
    "        bR ~ dnorm( 0 , 1 ) ,\n",
    "        bA ~ dnorm( 0 , 1 ) ,\n",
    "        sigma ~ dunif( 0 , 10 )\n",
    "    ) ,\n",
    "    data=dd )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      WAIC pWAIC dWAIC weight    SE   dSE\n",
       "m7.4 476.4   4.4   0.0      1 15.29    NA\n",
       "m7.3 539.4   2.6  62.9      0 13.24 15.05"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.5\n",
    "compare( m7.3 , m7.4 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1000 / 1000 ]\n",
      "[ 1000 / 1000 ]\n"
     ]
    }
   ],
   "source": [
    "## R code 7.6\n",
    "rugged.seq <- seq(from=-1,to=8,by=0.25)\n",
    "\n",
    "# compute mu over samples, fixing cont_africa=0\n",
    "mu.NotAfrica <- link( m7.4 , data=data.frame(cont_africa=0,rugged=rugged.seq) )\n",
    "\n",
    "# compute mu over samples, fixing cont_africa=1\n",
    "mu.Africa <- link( m7.4 , data=data.frame(cont_africa=1,rugged=rugged.seq) )\n",
    "\n",
    "# summarize to means and intervals\n",
    "mu.NotAfrica.mean <- apply( mu.NotAfrica , 2 , mean )\n",
    "mu.NotAfrica.PI <- apply( mu.NotAfrica , 2 , PI , prob=0.97 )\n",
    "mu.Africa.mean <- apply( mu.Africa , 2 , mean )\n",
    "mu.Africa.PI <- apply( mu.Africa , 2 , PI , prob=0.97 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.7\n",
    "m7.5 <- map(\n",
    "    alist(\n",
    "        log_gdp ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + gamma*rugged + bA*cont_africa ,\n",
    "        gamma <- bR + bAR*cont_africa ,\n",
    "        a ~ dnorm( 8 , 100 ) ,\n",
    "        bA ~ dnorm( 0 , 1 ) ,\n",
    "        bR ~ dnorm( 0 , 1 ) ,\n",
    "        bAR ~ dnorm( 0 , 1 ) ,\n",
    "        sigma ~ dunif( 0 , 10 )\n",
    "    ) ,\n",
    "    data=dd )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      WAIC pWAIC dWAIC weight    SE   dSE\n",
       "m7.5 469.3   5.2   0.0   0.97 15.08    NA\n",
       "m7.4 476.2   4.3   6.9   0.03 15.39  6.16\n",
       "m7.3 539.6   2.7  70.3   0.00 13.24 15.10"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.8\n",
    "compare( m7.3 , m7.4 , m7.5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.9\n",
    "m7.5b <- map(\n",
    "    alist(\n",
    "        log_gdp ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bR*rugged + bAR*rugged*cont_africa + bA*cont_africa,\n",
    "        a ~ dnorm( 8 , 100 ) ,\n",
    "        bA ~ dnorm( 0 , 1 ) ,\n",
    "        bR ~ dnorm( 0 , 1 ) ,\n",
    "        bAR ~ dnorm( 0 , 1 ) ,\n",
    "        sigma ~ dunif( 0 , 10 )\n",
    "    ) ,\n",
    "    data=dd )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1000 / 1000 ]\n",
      "[ 1000 / 1000 ]\n"
     ]
    }
   ],
   "source": [
    "## R code 7.10\n",
    "rugged.seq <- seq(from=-1,to=8,by=0.25)\n",
    "\n",
    "mu.Africa <- link( m7.5 , data=data.frame(cont_africa=1,rugged=rugged.seq) )\n",
    "mu.Africa.mean <- apply( mu.Africa , 2 , mean )\n",
    "mu.Africa.PI <- apply( mu.Africa , 2 , PI , prob=0.97 )\n",
    "\n",
    "mu.NotAfrica <- link( m7.5 , data=data.frame(cont_africa=0,rugged=rugged.seq) )\n",
    "mu.NotAfrica.mean <- apply( mu.NotAfrica , 2 , mean )\n",
    "mu.NotAfrica.PI <- apply( mu.NotAfrica , 2 , PI , prob=0.97 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<path style=\"fill:none;stroke-width:0.75;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 1.703125 201.304688 L 19.824219 204.925781 L 37.941406 208.546875 L 56.0625 212.167969 L 74.183594 215.792969 L 92.300781 219.414062 L 146.664062 230.277344 L 164.78125 233.898438 L 201.023438 241.140625 L 219.144531 244.765625 L 237.261719 248.386719 L 291.625 259.25 L 309.742188 262.871094 L 345.984375 270.113281 L 364.101562 273.738281 L 418.464844 284.601562 L 436.582031 288.222656 L 490.945312 299.085938 L 504 301.695312 \"/>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip2)\" clip-rule=\"nonzero\">\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## R code 7.11\n",
    "# plot African nations with regression\n",
    "d.A1 <- dd[dd$cont_africa==1,]\n",
    "plot( log(rgdppc_2000) ~ rugged , data=d.A1 ,\n",
    "    col=rangi2 , ylab=\"log GDP year 2000\" ,\n",
    "    xlab=\"Terrain Ruggedness Index\" )\n",
    "mtext( \"African nations\" , 3 )\n",
    "lines( rugged.seq , mu.Africa.mean , col=rangi2 )\n",
    "shade( mu.Africa.PI , rugged.seq , col=col.alpha(rangi2,0.3) )\n",
    "\n",
    "# plot non-African nations with regression\n",
    "d.A0 <- dd[dd$cont_africa==0,]\n",
    "plot( log(rgdppc_2000) ~ rugged , data=d.A0 ,\n",
    "    col=\"black\" , ylab=\"log GDP year 2000\" ,\n",
    "    xlab=\"Terrain Ruggedness Index\" )\n",
    "mtext( \"Non-African nations\" , 3 )\n",
    "lines( rugged.seq , mu.NotAfrica.mean )\n",
    "shade( mu.NotAfrica.PI , rugged.seq )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Mean StdDev  5.5% 94.5%\n",
       "a      9.18   0.14  8.97  9.40\n",
       "bA    -1.85   0.22 -2.20 -1.50\n",
       "bR    -0.18   0.08 -0.31 -0.06\n",
       "bAR    0.35   0.13  0.14  0.55\n",
       "sigma  0.93   0.05  0.85  1.01"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.12\n",
    "precis(m7.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.13\n",
    "post <- extract.samples( m7.5 )\n",
    "gamma.Africa <- post$bR + post$bAR*1\n",
    "gamma.notAfrica <- post$bR + post$bAR*0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.165301124886182"
      ],
      "text/latex": [
       "0.165301124886182"
      ],
      "text/markdown": [
       "0.165301124886182"
      ],
      "text/plain": [
       "[1] 0.1653011"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "-0.183390641995646"
      ],
      "text/latex": [
       "-0.183390641995646"
      ],
      "text/markdown": [
       "-0.183390641995646"
      ],
      "text/plain": [
       "[1] -0.1833906"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.14\n",
    "mean( gamma.Africa)\n",
    "mean( gamma.notAfrica )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## R code 7.15\n",
    "dens( gamma.Africa , xlim=c(-0.5,0.6) , ylim=c(0,5.5) ,\n",
    "    xlab=\"gamma\" , col=rangi2 )\n",
    "dens( gamma.notAfrica , add=TRUE )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0031"
      ],
      "text/latex": [
       "0.0031"
      ],
      "text/markdown": [
       "0.0031"
      ],
      "text/plain": [
       "[1] 0.0031"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.16\n",
    "diff <- gamma.Africa - gamma.notAfrica\n",
    "sum( diff < 0 ) / length( diff )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1000 / 1000 ]\n",
      "[ 1000 / 1000 ]\n"
     ]
    },
    {
     "data": {
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       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## R code 7.17\n",
    "# get minimum and maximum rugged values\n",
    "q.rugged <- range(dd$rugged)\n",
    "\n",
    "# compute lines and confidence intervals\n",
    "mu.ruggedlo <- link( m7.5 ,\n",
    "    data=data.frame(rugged=q.rugged[1],cont_africa=0:1) )\n",
    "mu.ruggedlo.mean <- apply( mu.ruggedlo , 2 , mean )\n",
    "mu.ruggedlo.PI <- apply( mu.ruggedlo , 2 , PI )\n",
    "\n",
    "mu.ruggedhi <- link( m7.5 ,\n",
    "    data=data.frame(rugged=q.rugged[2],cont_africa=0:1) )\n",
    "mu.ruggedhi.mean <- apply( mu.ruggedhi , 2 , mean )\n",
    "mu.ruggedhi.PI <- apply( mu.ruggedhi , 2 , PI )\n",
    "\n",
    "# plot it all, splitting points at median\n",
    "med.r <- median(dd$rugged)\n",
    "ox <- ifelse( dd$rugged > med.r , 0.05 , -0.05 )\n",
    "plot( dd$cont_africa + ox , log(dd$rgdppc_2000) ,\n",
    "    col=ifelse(dd$rugged>med.r,rangi2,\"black\") ,\n",
    "    xlim=c(-0.25,1.25) , xaxt=\"n\" , ylab=\"log GDP year 2000\" ,\n",
    "    xlab=\"Continent\" )\n",
    "axis( 1 , at=c(0,1) , labels=c(\"other\",\"Africa\") )\n",
    "lines( 0:1 , mu.ruggedlo.mean , lty=2 )\n",
    "shade( mu.ruggedlo.PI , 0:1 )\n",
    "lines( 0:1 , mu.ruggedhi.mean , col=rangi2 )\n",
    "shade( mu.ruggedhi.PI , 0:1 , col=col.alpha(rangi2,0.25) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t27 obs. of  4 variables:\n",
      " $ bed   : Factor w/ 3 levels \"a\",\"b\",\"c\": 1 1 1 1 1 1 1 1 1 2 ...\n",
      " $ water : int  1 1 1 2 2 2 3 3 3 1 ...\n",
      " $ shade : int  1 2 3 1 2 3 1 2 3 1 ...\n",
      " $ blooms: num  0 0 111 183.5 59.2 ...\n"
     ]
    }
   ],
   "source": [
    "## R code 7.18\n",
    "library(rethinking)\n",
    "data(tulips)\n",
    "d <- tulips\n",
    "str(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Caution, model may not have converged.\n",
      "Code 1: Maximum iterations reached.\n"
     ]
    }
   ],
   "source": [
    "## R code 7.19\n",
    "m7.6 <- map(\n",
    "    alist(\n",
    "        blooms ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bW*water + bS*shade ,\n",
    "        a ~ dnorm( 0 , 100 ) ,\n",
    "        bW ~ dnorm( 0 , 100 ) ,\n",
    "        bS ~ dnorm( 0 , 100 ) ,\n",
    "        sigma ~ dunif( 0 , 100 )\n",
    "    ) ,\n",
    "    data=d )\n",
    "m7.7 <- map(\n",
    "    alist(\n",
    "        blooms ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bW*water + bS*shade + bWS*water*shade ,\n",
    "        a ~ dnorm( 0 , 100 ) ,\n",
    "        bW ~ dnorm( 0 , 100 ) ,\n",
    "        bS ~ dnorm( 0 , 100 ) ,\n",
    "        bWS ~ dnorm( 0 , 100 ) ,\n",
    "        sigma ~ dunif( 0 , 100 )\n",
    "    ) ,\n",
    "    data=d )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.20\n",
    "m7.6 <- map(\n",
    "    alist(\n",
    "        blooms ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bW*water + bS*shade ,\n",
    "        a ~ dnorm( 0 , 100 ) ,\n",
    "        bW ~ dnorm( 0 , 100 ) ,\n",
    "        bS ~ dnorm( 0 , 100 ) ,\n",
    "        sigma ~ dunif( 0 , 100 )\n",
    "    ) ,\n",
    "    data=d ,\n",
    "    method=\"Nelder-Mead\" ,\n",
    "    control=list(maxit=1e4) )\n",
    "m7.7 <- map(\n",
    "    alist(\n",
    "        blooms ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bW*water + bS*shade + bWS*water*shade ,\n",
    "        a ~ dnorm( 0 , 100 ) ,\n",
    "        bW ~ dnorm( 0 , 100 ) ,\n",
    "        bS ~ dnorm( 0 , 100 ) ,\n",
    "        bWS ~ dnorm( 0 , 100 ) ,\n",
    "        sigma ~ dunif( 0 , 100 )\n",
    "    ) ,\n",
    "    data=d ,\n",
    "    method=\"Nelder-Mead\" ,\n",
    "    control=list(maxit=1e4) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In sqrt(diag(vcov(model))): NaNs produced"
     ]
    },
    {
     "data": {
      "text/plain": [
       "      m7.6    m7.7   \n",
       "a       53.47 -156.84\n",
       "bW      76.37  184.59\n",
       "bS     -38.93   51.27\n",
       "sigma   57.38   96.78\n",
       "bWS        NA  -48.16\n",
       "nobs       27      27"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.21\n",
    "coeftab(m7.6,m7.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in mvrnorm(n = n, mu = mu, Sigma = vcov(object)): 'Sigma' is not positive definite\n",
     "output_type": "error",
     "traceback": [
      "Error in mvrnorm(n = n, mu = mu, Sigma = vcov(object)): 'Sigma' is not positive definite\n"
     ]
    }
   ],
   "source": [
    "## R code 7.22\n",
    "compare( m7.6 , m7.7 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 7.23\n",
    "d$shade.c <- d$shade - mean(d$shade)\n",
    "d$water.c <- d$water - mean(d$water)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      m7.8    m7.9   \n",
       "a      129.00  129.01\n",
       "bW      74.22   74.96\n",
       "bS     -40.74  -41.14\n",
       "sigma   57.35   45.22\n",
       "bWS        NA  -51.87\n",
       "nobs       27      27"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.24\n",
    "m7.8 <- map(\n",
    "    alist(\n",
    "        blooms ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bW*water.c + bS*shade.c ,\n",
    "        a ~ dnorm( 130 , 100 ) ,\n",
    "        bW ~ dnorm( 0 , 100 ) ,\n",
    "        bS ~ dnorm( 0 , 100 ) ,\n",
    "        sigma ~ dunif( 0 , 100 )\n",
    "    ) ,\n",
    "    data=d ,\n",
    "    start=list(a=mean(d$blooms),bW=0,bS=0,sigma=sd(d$blooms)) )\n",
    "m7.9 <- map(\n",
    "    alist(\n",
    "        blooms ~ dnorm( mu , sigma ) ,\n",
    "        mu <- a + bW*water.c + bS*shade.c + bWS*water.c*shade.c ,\n",
    "        a ~ dnorm( 130 , 100 ) ,\n",
    "        bW ~ dnorm( 0 , 100 ) ,\n",
    "        bS ~ dnorm( 0 , 100 ) ,\n",
    "        bWS ~ dnorm( 0 , 100 ) ,\n",
    "        sigma ~ dunif( 0 , 100 )\n",
    "    ) ,\n",
    "    data=d ,\n",
    "    start=list(a=mean(d$blooms),bW=0,bS=0,bWS=0,sigma=sd(d$blooms)) )\n",
    "coeftab(m7.8,m7.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>a:</strong> 122.22494796705"
      ],
      "text/latex": [
       "\\textbf{a:} 122.22494796705"
      ],
      "text/markdown": [
       "**a:** 122.22494796705"
      ],
      "text/plain": [
       "       a \n",
       "122.2249 "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.25\n",
    "k <- coef(m7.7)\n",
    "k[1] + k[2]*2 + k[3]*2 + k[4]*2*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>a:</strong> 129.007971929144"
      ],
      "text/latex": [
       "\\textbf{a:} 129.007971929144"
      ],
      "text/markdown": [
       "**a:** 129.007971929144"
      ],
      "text/plain": [
       "      a \n",
       "129.008 "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.26\n",
    "k <- coef(m7.9)\n",
    "k[1] + k[2]*0 + k[3]*0 + k[4]*0*0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "        Mean StdDev   5.5%  94.5%\n",
       "a     129.01   8.67 115.15 142.87\n",
       "bW     74.96  10.60  58.02  91.90\n",
       "bS    -41.14  10.60 -58.08 -24.20\n",
       "bWS   -51.87  12.95 -72.57 -31.18\n",
       "sigma  45.22   6.15  35.39  55.06"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.27\n",
    "precis(m7.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1000 / 1000 ]\n",
      "[ 1000 / 1000 ]\n",
      "[ 1000 / 1000 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “water.c = 1”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## R code 7.28\n",
    "# make a plot window with three panels in a single row\n",
    "par(mfrow=c(1,3)) # 1 row, 3 columns\n",
    "\n",
    "# loop over values of water.c and plot predictions\n",
    "shade.seq <- -1:1\n",
    "for ( w in -1:1 ) {\n",
    "    dt <- d[d$water.c==w,]\n",
    "    plot( blooms ~ shade.c , data=dt , col=rangi2 ,\n",
    "        main=paste(\"water.c =\",w) , xaxp=c(-1,1,2) , ylim=c(0,362) ,\n",
    "        xlab=\"shade (centered)\" )\n",
    "    mu <- link( m7.9 , data=data.frame(water.c=w,shade.c=shade.seq) )\n",
    "    mu.mean <- apply( mu , 2 , mean )\n",
    "    mu.PI <- apply( mu , 2 , PI , prob=0.97 )\n",
    "    lines( shade.seq , mu.mean )\n",
    "    lines( shade.seq , mu.PI[1,] , lty=2 )\n",
    "    lines( shade.seq , mu.PI[2,] , lty=2 )\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): object 'y' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): object 'y' not found\n"
     ]
    }
   ],
   "source": [
    "## R code 7.29\n",
    "m7.x <- lm( y ~ x + z + x*z , data=d )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): object 'y' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): object 'y' not found\n"
     ]
    }
   ],
   "source": [
    "## R code 7.30\n",
    "m7.x <- lm( y ~ x*z , data=d )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): object 'y' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): object 'y' not found\n"
     ]
    }
   ],
   "source": [
    "## R code 7.31\n",
    "m7.x <- lm( y ~ x + x*z - z , data=d )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): object 'y' not found\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): object 'y' not found\n"
     ]
    }
   ],
   "source": [
    "## R code 7.32\n",
    "m7.x <- lm( y ~ x*z*w , data=d )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'(Intercept)'</li>\n",
       "\t<li>'x'</li>\n",
       "\t<li>'z'</li>\n",
       "\t<li>'w'</li>\n",
       "\t<li>'x:z'</li>\n",
       "\t<li>'x:w'</li>\n",
       "\t<li>'z:w'</li>\n",
       "\t<li>'x:z:w'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item '(Intercept)'\n",
       "\\item 'x'\n",
       "\\item 'z'\n",
       "\\item 'w'\n",
       "\\item 'x:z'\n",
       "\\item 'x:w'\n",
       "\\item 'z:w'\n",
       "\\item 'x:z:w'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. '(Intercept)'\n",
       "2. 'x'\n",
       "3. 'z'\n",
       "4. 'w'\n",
       "5. 'x:z'\n",
       "6. 'x:w'\n",
       "7. 'z:w'\n",
       "8. 'x:z:w'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"(Intercept)\" \"x\"           \"z\"           \"w\"           \"x:z\"        \n",
       "[6] \"x:w\"         \"z:w\"         \"x:z:w\"      "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 7.33\n",
    "x <- z <- w <- 1\n",
    "colnames( model.matrix(~x*z*w) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in `$<-.data.frame`(`*tmp*`, \"lang.per.cap\", value = numeric(0)): replacement has 0 rows, data has 27\n",
     "output_type": "error",
     "traceback": [
      "Error in `$<-.data.frame`(`*tmp*`, \"lang.per.cap\", value = numeric(0)): replacement has 0 rows, data has 27\n"
     ]
    }
   ],
   "source": [
    "## R code 7.34\n",
    "d$lang.per.cap <- d$num.lang / d$k.pop"
   ]
  }
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