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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Input modeling\n",
      "=============="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the simualtions so far, we've been generating training data by sampling from Ramscar et al.'s counts as if they were a multinomial distribution.  That is, each number between 1 and 15 is selected with a probability proportional to the number of times Ramscar et al. found that number name mentioned in their corpus survey (e.g., they counted 455 mentions of *one* out of 998 total mentions of numbers between 1 and 15, so each training instance in our sample has a cardinality 1 with a probability of 455/998=0.456."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This isn't great, for lots of reasons.  A big problem is that we never get sets with cardinality greater than 15.  In real life, presumably, small counts are much more frequent than large counts, but even so, there are lots of possible large counts.  Thus, the total probability mass of counts >15 could be pretty large, which in turn means we may be really skewing things. Also, since we're just using Ramscar et al.'s empirical distribution, it's hard to manipulate that in the ways the Jeremy was recommending."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We also don't know whether the distribution of mentions of number is anything like the distribution of numbers.  That is, there may be no relation between the frequency with which a language user encounters a set of three objects and the frequency with which language users say the word *three*.  Yet we're using the latter as an estimate for the former.  Is that justfied?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, to move forward, it'll be helpful to have a theoretically justifiable model for the distribution of set cardinalities.  They're counts, so the obvious choice is a Poisson distribution.  But, there's a problem: because of the nature of the data, we've got no zero counts.  The empty set never comes up in training. We could try a variant, though.  The **zero-truncated Poisson** (ZTP) is like a Poisson distribition, but with no zero counts.  Fitting a ZTP distribution in R is pretty easy.  First get the data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(ndl)\n",
      "data(numbers)\n",
      "numbers$Outcomes <- type.convert(numbers$Outcomes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "This is ndl version 0.2.16. \n",
        "For an overview of the package, type 'help(\"ndl.package\")'.\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If the counts really are distributed following the ZTP distribution, then the mean should be equal to the variance.  As a first step, we can check to see if that relationshop holds:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R mean(rep(numbers$Outcomes,numbers$Frequency))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "array([ 2.67635271])"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R var(rep(numbers$Outcomes,numbers$Frequency))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([ 6.14489661])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Nope.  The variance is much too high.  This isn't too surprising.  Given how many different kinds of contexts are represented in the corpora that Ramscar looked at, it's reasonable to expect the counts to be overdispersed.  This suggests that the ZTP distribution won't be a good fit, but let's try it anyway:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "library(VGAM)\n",
      "m1 <- vglm(Outcomes~1,family=\"pospoisson\",weights=Frequency,data=numbers)\n",
      "summary(m1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Loading required package: splines\n",
        "Loading required package: stats4\n",
        "\n",
        "Attaching package: \u2018VGAM\u2019\n",
        "\n",
        "The following object is masked from \u2018package:stats4\u2019:\n",
        "\n",
        "    coef\n",
        "\n",
        "The following objects are masked from \u2018package:splines\u2019:\n",
        "\n",
        "    bs, ns\n",
        "\n",
        "The following objects are masked from \u2018package:stats\u2019:\n",
        "\n",
        "    case.names, coef, coefficients, df.residual, dfbeta, fitted,\n",
        "    fitted.values, formula, hatvalues, poly, residuals, variable.names,\n",
        "    weights\n",
        "\n",
        "The following objects are masked from \u2018package:base\u2019:\n",
        "\n",
        "    identity, scale.default\n",
        "\n",
        "\n",
        "Call:\n",
        "vglm(formula = Outcomes ~ 1, family = \"pospoisson\", data = numbers, \n",
        "    weights = Frequency)\n",
        "\n",
        "Pearson residuals:\n",
        "                Min     1Q Median     3Q    Max\n",
        "log(lambda) -24.944 8.6047 11.462 14.908 20.436\n",
        "\n",
        "Coefficients:\n",
        "            Estimate Std. Error z value\n",
        "(Intercept)  0.89364   0.022083  40.468\n",
        "\n",
        "Number of linear predictors:  1 \n",
        "\n",
        "Name of linear predictor: log(lambda) \n",
        "\n",
        "Dispersion Parameter for pospoisson family:   1\n",
        "\n",
        "Log-likelihood: -2101.056 on 14 degrees of freedom\n",
        "\n",
        "Number of iterations: 5 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A [hanging rootogram](http://www.datavis.ca/gallery/bright-ideas.php) is a diagnostic plot for comparing empirical counts with a theoretical distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "library(vcd)\n",
      "rootogram(numbers$Frequency,dpospois(1:15,exp(0.89364))*998)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Loading required package: grid\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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f9NevX48bb7wRV155pc/2MRs2oKHPlotXTqjzwq8/9zyOFY3zfChtcd111+HJJ5/0bOMb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\nTkSuQmCC\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not good at all.  As an alternative, we can try the **Zero-Truncated Negative Binomial** distribution (the negative binomial is a generalization of the Poisson with an additional parameter to allow for overdispersion):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "m2 <- vglm(Outcomes~1,family=\"posnegbinomial\",weights=Frequency,data=numbers)\n",
      "summary(m2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "vglm(formula = Outcomes ~ 1, family = \"posnegbinomial\", data = numbers, \n",
        "    weights = Frequency)\n",
        "\n",
        "Pearson residuals:\n",
        "              Min      1Q  Median     3Q    Max\n",
        "log(munb) -20.836  3.0551  6.5328 7.6187 9.3196\n",
        "log(size) -10.147 -6.3514 -4.5322 1.2671 9.2883\n",
        "\n",
        "Coefficients:\n",
        "              Estimate Std. Error z value\n",
        "(Intercept):1 -0.53464    0.38655 -1.3831\n",
        "(Intercept):2 -1.82627    0.48355 -3.7768\n",
        "\n",
        "Number of linear predictors:  2 \n",
        "\n",
        "Names of linear predictors: log(munb), log(size)\n",
        "\n",
        "Dispersion Parameter for posnegbinomial family:   1\n",
        "\n",
        "Log-likelihood: -1740.027 on 28 degrees of freedom\n",
        "\n",
        "Number of iterations: 6 \n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "rootogram(numbers$Frequency,dposnegbin(1:15,size=exp(-1.82625),munb=exp(-0.53464))*998)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h5ptvNs6GW7ZsiQkTJiA+Pj4GGSPjkLVbb4b+5VfQ+Zx2ZDQYa0kBCkS1QEC9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\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Much better!  This distribution is theoretically justifiable and is a good fit to the observed counts, so instead of re-sampling training data from the corpus counts, we can generate (hypothetical, simulated) training data be generating random ZTNB variates.  We can also see what the probably of getting a set with more than 15 elements in it is:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "1-pposnegbin(15,munb=exp(-0.53481),size=exp(-1.82653))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 0.004958314\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "The choice of distribution for modeling the inputs seems solid.  But what about the parameters?  We've been using the data from the ndl package in R, which is allegedly from an unpublished paper by Ramscar et al. The numbers they report in the [PNAS paper](http://www.plosone.org/article/info:doi/10.1371/journal.pone.0022501) are slightly different.  How well do those fit?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First we'll check the Spanish data from [Table 1](http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0022501.t001&representation=PNG_M):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "num <- 1:7\n",
      "spanish <- c(1079,928,469,249,234,155,86)\n",
      "ms <- vglm(num~1,weights=spanish,family=posnegbinomial())\n",
      "summary(ms)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "vglm(formula = num ~ 1, family = posnegbinomial(), weights = spanish)\n",
        "\n",
        "Pearson residuals:\n",
        "              Min        1Q  Median     3Q    Max\n",
        "log(munb) -32.885   0.66876 15.4914 22.884 24.817\n",
        "log(size) -25.524 -14.86999  1.6291 14.003 20.377\n",
        "\n",
        "Coefficients:\n",
        "              Estimate Std. Error z value\n",
        "(Intercept):1  0.67067   0.022924  29.256\n",
        "(Intercept):2  1.10129   0.107875  10.209\n",
        "\n",
        "Number of linear predictors:  2 \n",
        "\n",
        "Names of linear predictors: log(munb), log(size)\n",
        "\n",
        "Dispersion Parameter for posnegbinomial family:   1\n",
        "\n",
        "Log-likelihood: -5351.886 on 12 degrees of freedom\n",
        "\n",
        "Number of iterations: 6 \n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R rootogram(spanish,dposnegbin(1:7,size=exp(1.10129),munb=exp(0.67067))*sum(spanish))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VIAEXKC8bRyBvAlaRIorc716QtXWrnBGPkoTzxsfaCARKgAQcqO4i2EQQsNwL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\n"
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not too bad.  Ramscar et al. describe this as an 'inverse power relation'.  If that were really what's going on, we'd expect to see a straight line on a plot of rank vs. frequency, which we don't:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R plot(1:7,spanish,log='xy',type='l')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OuB8QESDgsAAJ2GFwikMAgb8EKlSoYM6Ehw8f/tdK3iEQEAEScEAammoiYKuA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\ngAACCDgk8P8AFhJDJrK/BIgAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's check the English counts:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "english <- c(856,707,368,224,204,156,87)\n",
      "me <- vglm(num~1,weights=english,family=posnegbinomial())\n",
      "summary(me)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "vglm(formula = num ~ 1, family = posnegbinomial(), weights = english)\n",
        "\n",
        "Pearson residuals:\n",
        "              Min       1Q  Median     3Q    Max\n",
        "log(munb) -29.007 -0.54148 12.7489 19.550 21.972\n",
        "log(size) -25.120 -7.43579  5.7971 11.691 16.939\n",
        "\n",
        "Coefficients:\n",
        "              Estimate Std. Error z value\n",
        "(Intercept):1  0.72634   0.025027 29.0222\n",
        "(Intercept):2  1.02552   0.103180  9.9392\n",
        "\n",
        "Number of linear predictors:  2 \n",
        "\n",
        "Names of linear predictors: log(munb), log(size)\n",
        "\n",
        "Dispersion Parameter for posnegbinomial family:   1\n",
        "\n",
        "Log-likelihood: -4500.582 on 12 degrees of freedom\n",
        "\n",
        "Number of iterations: 5 \n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R rootogram(english,dposnegbin(1:7,size=exp(1.02552),munb=exp(0.72634))*sum(english))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tTB1jTsCqU0ehCY/ImTJV9rtzYq78FBgBBHIXIADnbsQWCPgiYNWsqdBE937w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\nPXacHN6JHqg2JAAHqjkoDAIIIFCAAu7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      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, not too bad.  But not perfect, either.  It's suspicious that the model overestimates the frequencies for 3 and 4 and underestimates 5, 6, and 7 in both Spanish and English.  I have a feeling the model isn't such a perfect fit after all (once again, reality trumps statistics!).  But it's still pretty good, with very similar results for the two languages.  And, very different results (at least in terms of the parameter estimates) from the ndl dataset we've been using."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}