more_julia/data_statistical_packages.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<a id='data-statistical-packages'></a>\n",
    "<div id=\"qe-notebook-header\" style=\"text-align:right;\">\n",
    "        <a href=\"https://quantecon.org/\" title=\"quantecon.org\">\n",
    "                <img style=\"width:250px;display:inline;\" src=\"https://assets.quantecon.org/img/qe-menubar-logo.svg\" alt=\"QuantEcon\">\n",
    "        </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data and Statistics Packages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "- [Data and Statistics Packages](#Data-and-Statistics-Packages)  \n",
    "  - [Overview](#Overview)  \n",
    "  - [DataFrames](#DataFrames)  \n",
    "  - [Statistics and Econometrics](#Statistics-and-Econometrics)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "This lecture explores some of the key packages for working with data and doing statistics in Julia.\n",
    "\n",
    "In particular, we will examine the `DataFrame` object in detail (i.e., construction, manipulation, querying, visualization, and nuances like missing data).\n",
    "\n",
    "While Julia is not an ideal language for pure cookie-cutter statistical analysis, it has many useful packages to provide those tools as part of a more general solution.\n",
    "\n",
    "This list is not exhaustive, and others can be found in organizations such as [JuliaStats](https://github.com/JuliaStats), [JuliaData](https://github.com/JuliaData/), and  [QueryVerse](https://github.com/queryverse)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hide-output": true
   },
   "outputs": [],
   "source": [
    "using InstantiateFromURL\n",
    "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.6.0\")\n",
    "# uncomment to force package installation and precompilation\n",
    "# github_project(\"QuantEcon/quantecon-notebooks-julia\", version=\"0.6.0\", instantiate=true, precompile = true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hide-output": true
   },
   "outputs": [],
   "source": [
    "using LinearAlgebra, Statistics\n",
    "using DataFrames, RDatasets, DataFramesMeta, CategoricalArrays, Query, VegaLite\n",
    "using GLM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DataFrames\n",
    "\n",
    "A useful package for working with data is [DataFrames.jl](https://github.com/JuliaStats/DataFrames.jl).\n",
    "\n",
    "The most important data type provided is a `DataFrame`, a two dimensional array for storing heterogeneous data.\n",
    "\n",
    "Although data can be heterogeneous within a `DataFrame`, the contents of the columns must be homogeneous\n",
    "(of the same type).\n",
    "\n",
    "This is analogous to a `data.frame` in R, a `DataFrame` in Pandas (Python) or, more loosely, a spreadsheet in Excel.\n",
    "\n",
    "There are a few different ways to create a DataFrame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing and Accessing a DataFrame\n",
    "\n",
    "The first is to set up columns and construct a dataframe by assigning names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>commod</th><th>price</th></tr><tr><th></th><th>String</th><th>Float64⍰</th></tr></thead><tbody><p>4 rows × 2 columns</p><tr><th>1</th><td>crude</td><td>4.2</td></tr><tr><th>2</th><td>gas</td><td>11.3</td></tr><tr><th>3</th><td>gold</td><td>12.1</td></tr><tr><th>4</th><td>silver</td><td>missing</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& commod & price\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & crude & 4.2 \\\\\n",
       "\t2 & gas & 11.3 \\\\\n",
       "\t3 & gold & 12.1 \\\\\n",
       "\t4 & silver &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×2 DataFrame\n",
       "│ Row │ commod │ price    │\n",
       "│     │ \u001b[90mString\u001b[39m │ \u001b[90mFloat64⍰\u001b[39m │\n",
       "├─────┼────────┼──────────┤\n",
       "│ 1   │ crude  │ 4.2      │\n",
       "│ 2   │ gas    │ 11.3     │\n",
       "│ 3   │ gold   │ 12.1     │\n",
       "│ 4   │ silver │ \u001b[90mmissing\u001b[39m  │"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DataFrames, RDatasets  # RDatasets provides good standard data examples from R\n",
    "\n",
    "# note use of missing\n",
    "commodities = [\"crude\", \"gas\", \"gold\", \"silver\"]\n",
    "last_price = [4.2, 11.3, 12.1, missing]\n",
    "df = DataFrame(commod = commodities, price = last_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Columns of the `DataFrame` can be accessed by name using `df.col`, as below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Union{Missing, Float64},1}:\n",
       "  4.2\n",
       " 11.3\n",
       " 12.1\n",
       "   missing"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the type of this array has values `Union{Missing, Float64}` since it was created with a `missing` value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{String,1}:\n",
       " \"crude\"\n",
       " \"gas\"\n",
       " \"gold\"\n",
       " \"silver\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.commod"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `DataFrames.jl` package provides a number of methods for acting on `DataFrame`’s, such as `describe`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nunique</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th>Symbol</th><th>Union…</th><th>Any</th><th>Union…</th><th>Any</th><th>Union…</th><th>Union…</th><th>Type</th></tr></thead><tbody><p>2 rows × 8 columns</p><tr><th>1</th><td>commod</td><td></td><td>crude</td><td></td><td>silver</td><td>4</td><td></td><td>String</td></tr><tr><th>2</th><td>price</td><td>9.2</td><td>4.2</td><td>11.3</td><td>12.1</td><td></td><td>1</td><td>Union{Missing, Float64}</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& variable & mean & min & median & max & nunique & nmissing & eltype\\\\\n",
       "\t\\hline\n",
       "\t& Symbol & Union… & Any & Union… & Any & Union… & Union… & Type\\\\\n",
       "\t\\hline\n",
       "\t1 & commod &  & crude &  & silver & 4 &  & String \\\\\n",
       "\t2 & price & 9.2 & 4.2 & 11.3 & 12.1 &  & 1 & Union\\{Missing, Float64\\} \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×8 DataFrame. Omitted printing of 1 columns\n",
       "│ Row │ variable │ mean   │ min   │ median │ max    │ nunique │ nmissing │\n",
       "│     │ \u001b[90mSymbol\u001b[39m   │ \u001b[90mUnion…\u001b[39m │ \u001b[90mAny\u001b[39m   │ \u001b[90mUnion…\u001b[39m │ \u001b[90mAny\u001b[39m    │ \u001b[90mUnion…\u001b[39m  │ \u001b[90mUnion…\u001b[39m   │\n",
       "├─────┼──────────┼────────┼───────┼────────┼────────┼─────────┼──────────┤\n",
       "│ 1   │ commod   │        │ crude │        │ silver │ 4       │          │\n",
       "│ 2   │ price    │ 9.2    │ 4.2   │ 11.3   │ 12.1   │         │ 1        │"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DataFrames.describe(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While often data will be generated all at once, or read from a file, you can add to a `DataFrame` by providing the key parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>commod</th><th>price</th></tr><tr><th></th><th>String</th><th>Float64⍰</th></tr></thead><tbody><p>5 rows × 2 columns</p><tr><th>1</th><td>crude</td><td>4.2</td></tr><tr><th>2</th><td>gas</td><td>11.3</td></tr><tr><th>3</th><td>gold</td><td>12.1</td></tr><tr><th>4</th><td>silver</td><td>missing</td></tr><tr><th>5</th><td>nickel</td><td>5.1</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& commod & price\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & crude & 4.2 \\\\\n",
       "\t2 & gas & 11.3 \\\\\n",
       "\t3 & gold & 12.1 \\\\\n",
       "\t4 & silver &  \\\\\n",
       "\t5 & nickel & 5.1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "5×2 DataFrame\n",
       "│ Row │ commod │ price    │\n",
       "│     │ \u001b[90mString\u001b[39m │ \u001b[90mFloat64⍰\u001b[39m │\n",
       "├─────┼────────┼──────────┤\n",
       "│ 1   │ crude  │ 4.2      │\n",
       "│ 2   │ gas    │ 11.3     │\n",
       "│ 3   │ gold   │ 12.1     │\n",
       "│ 4   │ silver │ \u001b[90mmissing\u001b[39m  │\n",
       "│ 5   │ nickel │ 5.1      │"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nt = (commod = \"nickel\", price= 5.1)\n",
    "push!(df, nt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Named tuples can also be used to construct a `DataFrame`, and have it properly deduce all types."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>t</th><th>col1</th></tr><tr><th></th><th>Int64</th><th>Float64</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>1</td><td>3.0</td></tr><tr><th>2</th><td>2</td><td>4.0</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& t & col1\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3.0 \\\\\n",
       "\t2 & 2 & 4.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ t     │ col1    │\n",
       "│     │ \u001b[90mInt64\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼───────┼─────────┤\n",
       "│ 1   │ 1     │ 3.0     │\n",
       "│ 2   │ 2     │ 4.0     │"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nt = (t = 1, col1 = 3.0)\n",
    "df2 = DataFrame([nt])\n",
    "push!(df2, (t=2, col1 = 4.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to modify a column, access the mutating version by the symbol `df[!, :col]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Union{Missing, Float64},1}:\n",
       "  4.2\n",
       " 11.3\n",
       " 12.1\n",
       "   missing\n",
       "  5.1"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[!, :price]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which allows modifications, like other mutating `!` functions in julia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Union{Missing, Float64},1}:\n",
       "  8.4\n",
       " 22.6\n",
       " 24.2\n",
       "   missing\n",
       " 10.2"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[!, :price] *= 2.0  # double prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As discussed in the next section, note that the [fundamental types](../getting_started_julia/fundamental_types.html#missing), is propagated, i.e. `missing * 2 === missing`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with Missing\n",
    "\n",
    "As we discussed in [fundamental types](../getting_started_julia/fundamental_types.html#missing), the semantics of `missing` are that mathematical operations will not silently ignore it.\n",
    "\n",
    "In order to allow `missing` in a column, you can create/load the `DataFrame`\n",
    "from a source with `missing`’s, or call `allowmissing!` on a column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>t</th><th>col1</th></tr><tr><th></th><th>Int64</th><th>Float64⍰</th></tr></thead><tbody><p>4 rows × 2 columns</p><tr><th>1</th><td>1</td><td>3.0</td></tr><tr><th>2</th><td>2</td><td>4.0</td></tr><tr><th>3</th><td>3</td><td>missing</td></tr><tr><th>4</th><td>4</td><td>5.1</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& t & col1\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64⍰\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3.0 \\\\\n",
       "\t2 & 2 & 4.0 \\\\\n",
       "\t3 & 3 &  \\\\\n",
       "\t4 & 4 & 5.1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×2 DataFrame\n",
       "│ Row │ t     │ col1     │\n",
       "│     │ \u001b[90mInt64\u001b[39m │ \u001b[90mFloat64⍰\u001b[39m │\n",
       "├─────┼───────┼──────────┤\n",
       "│ 1   │ 1     │ 3.0      │\n",
       "│ 2   │ 2     │ 4.0      │\n",
       "│ 3   │ 3     │ \u001b[90mmissing\u001b[39m  │\n",
       "│ 4   │ 4     │ 5.1      │"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allowmissing!(df2, :col1) # necessary to add in a for col1\n",
    "push!(df2, (t=3, col1 = missing))\n",
    "push!(df2, (t=4, col1 = 5.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the propagation of `missing` to caller functions, as well as a way to efficiently calculate with non-missing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean(df2.col1) = missing\n",
      "mean(skipmissing(df2.col1)) = 4.033333333333333\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4.033333333333333"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@show mean(df2.col1)\n",
    "@show mean(skipmissing(df2.col1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And to replace the `missing`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Union{Missing, Float64},1}:\n",
       " 3.0\n",
       " 4.0\n",
       " 0.0\n",
       " 5.1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.col1  .= coalesce.(df2.col1, 0.0) # replace all missing with 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manipulating and Transforming DataFrames\n",
    "\n",
    "One way to do an additional calculation with a `DataFrame` is to tuse the `@transform` macro from `DataFramesMeta.jl`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>t</th><th>col1</th><th>col2</th></tr><tr><th></th><th>Int64</th><th>Float64⍰</th><th>Float64</th></tr></thead><tbody><p>4 rows × 3 columns</p><tr><th>1</th><td>1</td><td>3.0</td><td>9.0</td></tr><tr><th>2</th><td>2</td><td>4.0</td><td>16.0</td></tr><tr><th>3</th><td>3</td><td>0.0</td><td>0.0</td></tr><tr><th>4</th><td>4</td><td>5.1</td><td>26.01</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& t & col1 & col2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64⍰ & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3.0 & 9.0 \\\\\n",
       "\t2 & 2 & 4.0 & 16.0 \\\\\n",
       "\t3 & 3 & 0.0 & 0.0 \\\\\n",
       "\t4 & 4 & 5.1 & 26.01 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×3 DataFrame\n",
       "│ Row │ t     │ col1     │ col2    │\n",
       "│     │ \u001b[90mInt64\u001b[39m │ \u001b[90mFloat64⍰\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼───────┼──────────┼─────────┤\n",
       "│ 1   │ 1     │ 3.0      │ 9.0     │\n",
       "│ 2   │ 2     │ 4.0      │ 16.0    │\n",
       "│ 3   │ 3     │ 0.0      │ 0.0     │\n",
       "│ 4   │ 4     │ 5.1      │ 26.01   │"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DataFramesMeta\n",
    "f(x) = x^2\n",
    "df2 = @transform(df2, col2 = f.(:col1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Categorical Data\n",
    "\n",
    "For data that is [categorical](https://juliadata.github.io/DataFrames.jl/stable/man/categorical/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>id</th><th>y</th></tr><tr><th></th><th>Int64</th><th>Categorical…</th></tr></thead><tbody><p>4 rows × 2 columns</p><tr><th>1</th><td>1</td><td>old</td></tr><tr><th>2</th><td>2</td><td>young</td></tr><tr><th>3</th><td>3</td><td>young</td></tr><tr><th>4</th><td>4</td><td>old</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & y\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Categorical…\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & old \\\\\n",
       "\t2 & 2 & young \\\\\n",
       "\t3 & 3 & young \\\\\n",
       "\t4 & 4 & old \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "4×2 DataFrame\n",
       "│ Row │ id    │ y            │\n",
       "│     │ \u001b[90mInt64\u001b[39m │ \u001b[90mCategorical…\u001b[39m │\n",
       "├─────┼───────┼──────────────┤\n",
       "│ 1   │ 1     │ old          │\n",
       "│ 2   │ 2     │ young        │\n",
       "│ 3   │ 3     │ young        │\n",
       "│ 4   │ 4     │ old          │"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using CategoricalArrays\n",
    "id = [1, 2, 3, 4]\n",
    "y = [\"old\", \"young\", \"young\", \"old\"]\n",
    "y = CategoricalArray(y)\n",
    "df = DataFrame(id=id, y=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{String,1}:\n",
       " \"old\"\n",
       " \"young\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "levels(df.y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualization, Querying, and Plots\n",
    "\n",
    "The `DataFrame` (and similar types that fulfill a standard generic interface) can fit into a variety of packages.\n",
    "\n",
    "One set of them is the [QueryVerse](https://github.com/queryverse).\n",
    "\n",
    "**Note:** The QueryVerse, in the same spirit as R’s tidyverse, makes heavy use of the pipeline syntax `|>`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g(f(x)) = 2.1972245773362196\n",
      "(x |> f) |> g = 2.1972245773362196\n"
     ]
    }
   ],
   "source": [
    "x = 3.0\n",
    "f(x) = x^2\n",
    "g(x) = log(x)\n",
    "\n",
    "@show g(f(x))\n",
    "@show x |> f |> g; # pipes nest function calls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To give an example directly from the source of the LINQ inspired [Query.jl](http://www.queryverse.org/Query.jl/stable/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>name</th><th>children</th></tr><tr><th></th><th>String</th><th>Int64</th></tr></thead><tbody><p>1 rows × 2 columns</p><tr><th>1</th><td>Kirk</td><td>2</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& name & children\\\\\n",
       "\t\\hline\n",
       "\t& String & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Kirk & 2 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "1×2 DataFrame\n",
       "│ Row │ name   │ children │\n",
       "│     │ \u001b[90mString\u001b[39m │ \u001b[90mInt64\u001b[39m    │\n",
       "├─────┼────────┼──────────┤\n",
       "│ 1   │ Kirk   │ 2        │"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Query\n",
    "\n",
    "df = DataFrame(name=[\"John\", \"Sally\", \"Kirk\"], age=[23., 42., 59.], children=[3,5,2])\n",
    "\n",
    "x = @from i in df begin\n",
    "    @where i.age>50\n",
    "    @select {i.name, i.children}\n",
    "    @collect DataFrame\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While it is possible to just use the `Plots.jl` library, there may be better options for displaying tabular data – such as [VegaLite.jl](https://github.com/queryverse/VegaLite.jl)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
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stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path><path transform=\"translate(162.85714285714286,7.692307692307709)\" d=\"M2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,-2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,2.7386127875258306,0\" style=\"fill: none; stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path><path transform=\"translate(148.57142857142858,23.076923076923105)\" d=\"M2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,-2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,2.7386127875258306,0\" style=\"fill: none; stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path><path transform=\"translate(142.85714285714286,53.846153846153854)\" d=\"M2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,-2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,2.7386127875258306,0\" style=\"fill: none; stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path><path transform=\"translate(148.57142857142858,46.15384615384617)\" d=\"M2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,-2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,2.7386127875258306,0\" style=\"fill: none; stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path><path transform=\"translate(154.2857142857143,23.076923076923105)\" d=\"M2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,-2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,2.7386127875258306,0\" style=\"fill: none; stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path><path transform=\"translate(145.7142857142857,61.53846153846154)\" d=\"M2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,-2.7386127875258306,0A2.7386127875258306,2.7386127875258306,0,1,1,2.7386127875258306,0\" style=\"fill: none; stroke: #e45756; stroke-width: 2; opacity: 0.7;\"></path></g><g class=\"mark-group role-legend\"><g transform=\"translate(218,0)\"><path class=\"background\" d=\"M0,0h65v61h-65Z\" style=\"pointer-events: none; fill: none;\"></path><g><g class=\"mark-group role-legend-entry\"><g transform=\"translate(0,16)\"><path class=\"background\" d=\"M0,0h0v0h0Z\" style=\"pointer-events: none; fill: none;\"></path><g><g class=\"mark-group role-scope\"><g transform=\"translate(0,0)\"><path class=\"background\" d=\"M0,0h65v12.5h-65Z\" style=\"pointer-events: none; fill: none; opacity: 1;\"></path><g><g class=\"mark-symbol role-legend-symbol\" style=\"pointer-events: none;\"><path transform=\"translate(6,6)\" d=\"M5,0A5,5,0,1,1,-5,0A5,5,0,1,1,5,0\" style=\"fill: none; stroke: #4c78a8; stroke-width: 1.5; opacity: 0.7;\"></path></g><g class=\"mark-text role-legend-label\" style=\"pointer-events: none;\"><text text-anchor=\"start\" transform=\"translate(16,9)\" style=\"font-family: sans-serif; font-size: 10px; fill: #000; opacity: 1;\">setosa</text></g></g><path class=\"foreground\" d=\"\" style=\"pointer-events: none; display: none; fill: none;\"></path></g><g transform=\"translate(0,16)\"><path class=\"background\" d=\"M0,0h65v12.5h-65Z\" style=\"pointer-events: none; fill: none; opacity: 1;\"></path><g><g class=\"mark-symbol role-legend-symbol\" style=\"pointer-events: none;\"><path transform=\"translate(6,6)\" d=\"M5,0A5,5,0,1,1,-5,0A5,5,0,1,1,5,0\" style=\"fill: none; stroke: #f58518; stroke-width: 1.5; opacity: 0.7;\"></path></g><g class=\"mark-text role-legend-label\" style=\"pointer-events: none;\"><text text-anchor=\"start\" transform=\"translate(16,9)\" style=\"font-family: sans-serif; font-size: 10px; fill: #000; opacity: 1;\">versicolor</text></g></g><path class=\"foreground\" d=\"\" style=\"pointer-events: none; display: none; fill: none;\"></path></g><g transform=\"translate(0,32)\"><path class=\"background\" d=\"M0,0h65v12.5h-65Z\" style=\"pointer-events: none; fill: none; opacity: 1;\"></path><g><g class=\"mark-symbol role-legend-symbol\" style=\"pointer-events: none;\"><path transform=\"translate(6,6)\" d=\"M5,0A5,5,0,1,1,-5,0A5,5,0,1,1,5,0\" style=\"fill: none; stroke: #e45756; stroke-width: 1.5; opacity: 0.7;\"></path></g><g class=\"mark-text role-legend-label\" style=\"pointer-events: none;\"><text text-anchor=\"start\" transform=\"translate(16,9)\" style=\"font-family: sans-serif; font-size: 10px; fill: #000; opacity: 1;\">virginica</text></g></g><path class=\"foreground\" d=\"\" style=\"pointer-events: none; display: none; fill: none;\"></path></g></g></g><path class=\"foreground\" d=\"\" style=\"pointer-events: none; display: none; fill: none;\"></path></g></g><g class=\"mark-text role-legend-title\" style=\"pointer-events: none;\"><text text-anchor=\"start\" transform=\"translate(0,9)\" style=\"font-family: sans-serif; font-size: 11px; font-weight: bold; fill: #000; opacity: 1;\">Species</text></g></g><path class=\"foreground\" d=\"\" style=\"pointer-events: none; display: none; fill: none;\"></path></g></g></g><path class=\"foreground\" d=\"\" style=\"display: none; fill: none;\"></path></g></g></g></svg>\n"
      ],
      "text/plain": [
       "@vlplot(\n",
       "    mark=\"point\",\n",
       "    encoding={\n",
       "        x={\n",
       "            field=\"PetalLength\"\n",
       "        },\n",
       "        y={\n",
       "            field=\"PetalWidth\"\n",
       "        },\n",
       "        color={\n",
       "            field=\"Species\"\n",
       "        }\n",
       "    },\n",
       "    data={\n",
       "        values=...\n",
       "    }\n",
       ")"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using RDatasets, VegaLite\n",
    "iris = dataset(\"datasets\", \"iris\")\n",
    "\n",
    "iris |> @vlplot(\n",
    "    :point,\n",
    "    x=:PetalLength,\n",
    "    y=:PetalWidth,\n",
    "    color=:Species\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics and Econometrics\n",
    "\n",
    "While Julia is not intended as a replacement for R, Stata, and similar specialty languages, it has a growing number of packages aimed at statistics and econometrics.\n",
    "\n",
    "Many of the packages live in the [JuliaStats organization](https://github.com/JuliaStats/).\n",
    "\n",
    "A few to point out\n",
    "\n",
    "- [StatsBase](https://github.com/JuliaStats/StatsBase.jl) has basic statistical functions such as geometric and harmonic means, auto-correlations, robust statistics, etc.  \n",
    "- [StatsFuns](https://github.com/JuliaStats/StatsFuns.jl) has a variety of mathematical functions and constants such as pdf and cdf of many distributions, softmax, etc.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### General Linear Models\n",
    "\n",
    "To run linear regressions and similar statistics, use the [GLM](http://juliastats.github.io/GLM.jl/latest/) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredChol{Float64,Cholesky{Float64,Array{Float64,2}}}},Array{Float64,2}}\n",
       "\n",
       "y ~ 1 + x\n",
       "\n",
       "Coefficients:\n",
       "──────────────────────────────────────────────────────────────────────────\n",
       "             Estimate  Std. Error  t value  Pr(>|t|)  Lower 95%  Upper 95%\n",
       "──────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)  0.280549   0.0140782  19.9279    <1e-35   0.252611   0.308486\n",
       "x            0.899161   0.0151784  59.2396    <1e-77   0.86904    0.929282\n",
       "──────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using GLM\n",
    "\n",
    "x = randn(100)\n",
    "y = 0.9 .* x + 0.5 * rand(100)\n",
    "df = DataFrame(x=x, y=y)\n",
    "ols = lm(@formula(y ~ x), df) # R-style notation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To display the results in a useful tables for LaTeX and the REPL, use\n",
    "[RegressionTables](https://github.com/jmboehm/RegressionTables.jl/) for output\n",
    "similar to the Stata package esttab and the R package stargazer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "----------------------\n",
      "                  y   \n",
      "              --------\n",
      "                   (1)\n",
      "----------------------\n",
      "(Intercept)   0.281***\n",
      "               (0.014)\n",
      "x             0.899***\n",
      "               (0.015)\n",
      "----------------------\n",
      "Estimator          OLS\n",
      "----------------------\n",
      "N                  100\n",
      "R2               0.973\n",
      "----------------------\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "using RegressionTables\n",
    "regtable(ols)\n",
    "# regtable(ols,  renderSettings = latexOutput()) # for LaTex output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixed Effects\n",
    "\n",
    "While Julia may be overkill for estimating a simple linear regression,\n",
    "fixed-effects estimation with dummies for multiple variables are much more computationally intensive.\n",
    "\n",
    "For a 2-way fixed-effect, taking the example directly from the documentation using [cigarette consumption data](https://github.com/johnmyleswhite/RDatasets.jl/blob/master/doc/plm/rst/Cigar.rst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "----------------------------\n",
      "                     Sales  \n",
      "                   ---------\n",
      "                         (1)\n",
      "----------------------------\n",
      "NDI                -0.005***\n",
      "                     (0.001)\n",
      "----------------------------\n",
      "StateCategorical         Yes\n",
      "YearCategorical          Yes\n",
      "----------------------------\n",
      "Estimator                OLS\n",
      "----------------------------\n",
      "N                      1,380\n",
      "R2                     0.803\n",
      "----------------------------\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "using FixedEffectModels\n",
    "cigar = dataset(\"plm\", \"Cigar\")\n",
    "cigar.StateCategorical =  categorical(cigar.State)\n",
    "cigar.YearCategorical =  categorical(cigar.Year)\n",
    "fixedeffectresults = reg(cigar, @formula(Sales ~ NDI + fe(StateCategorical) + fe(YearCategorical)),\n",
    "                            weights = :Pop, Vcov.cluster(:State))\n",
    "regtable(fixedeffectresults)"
   ]
  }
 ],
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  "download_nb_path": "https://julia.quantecon.org/",
  "filename": "data_statistical_packages.rst",
  "filename_with_path": "more_julia/data_statistical_packages",
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