{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"
"
]
},
{
"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 = \"0.5.0\")\n",
"# github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.5.0\", instantiate = true) # uncomment to force package installation"
]
},
{
"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 DataVoyager, 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": [
"commod price String Float64⍰ 4 rows × 2 columns
1 crude 4.2 2 gas 11.3 3 gold 12.1 4 silver missing
"
],
"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": [
"variable mean min median max nunique nmissing eltype Symbol Union… Any Union… Any Union… Union… Type 2 rows × 8 columns
1 commod crude silver 4 String 2 price 9.2 4.2 11.3 12.1 1 Union{Missing, Float64}
"
],
"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": [
"commod price String Float64⍰ 5 rows × 2 columns
1 crude 4.2 2 gas 11.3 3 gold 12.1 4 silver missing 5 nickel 5.1
"
],
"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": [
"t col1 Int64 Float64 2 rows × 2 columns
1 1 3.0 2 2 4.0
"
],
"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": [
"t col1 Int64 Float64⍰ 4 rows × 2 columns
1 1 3.0 2 2 4.0 3 3 missing 4 4 5.1
"
],
"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": [
"t col1 col2 Int64 Float64⍰ Float64 4 rows × 3 columns
1 1 3.0 9.0 2 2 4.0 16.0 3 3 0.0 0.0 4 4 5.1 26.01
"
],
"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": [
"id y Int64 Categorical… 4 rows × 2 columns
1 1 old 2 2 young 3 3 young 4 4 old
"
],
"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": [
"name children String Int64 1 rows × 2 columns
1 Kirk 2
"
],
"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": [
{
"data": {
"application/vnd.vegalite.v3+json": {
"data": {
"values": [
{
"PetalLength": 1.4,
"PetalWidth": 0.2,
"SepalLength": 5.1,
"SepalWidth": 3.5,
"Species": "setosa"
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"Species": "virginica"
},
{
"PetalLength": 5.5,
"PetalWidth": 1.8,
"SepalLength": 6.4,
"SepalWidth": 3.1,
"Species": "virginica"
},
{
"PetalLength": 4.8,
"PetalWidth": 1.8,
"SepalLength": 6.0,
"SepalWidth": 3.0,
"Species": "virginica"
},
{
"PetalLength": 5.4,
"PetalWidth": 2.1,
"SepalLength": 6.9,
"SepalWidth": 3.1,
"Species": "virginica"
},
{
"PetalLength": 5.6,
"PetalWidth": 2.4,
"SepalLength": 6.7,
"SepalWidth": 3.1,
"Species": "virginica"
},
{
"PetalLength": 5.1,
"PetalWidth": 2.3,
"SepalLength": 6.9,
"SepalWidth": 3.1,
"Species": "virginica"
},
{
"PetalLength": 5.1,
"PetalWidth": 1.9,
"SepalLength": 5.8,
"SepalWidth": 2.7,
"Species": "virginica"
},
{
"PetalLength": 5.9,
"PetalWidth": 2.3,
"SepalLength": 6.8,
"SepalWidth": 3.2,
"Species": "virginica"
},
{
"PetalLength": 5.7,
"PetalWidth": 2.5,
"SepalLength": 6.7,
"SepalWidth": 3.3,
"Species": "virginica"
},
{
"PetalLength": 5.2,
"PetalWidth": 2.3,
"SepalLength": 6.7,
"SepalWidth": 3.0,
"Species": "virginica"
},
{
"PetalLength": 5.0,
"PetalWidth": 1.9,
"SepalLength": 6.3,
"SepalWidth": 2.5,
"Species": "virginica"
},
{
"PetalLength": 5.2,
"PetalWidth": 2.0,
"SepalLength": 6.5,
"SepalWidth": 3.0,
"Species": "virginica"
},
{
"PetalLength": 5.4,
"PetalWidth": 2.3,
"SepalLength": 6.2,
"SepalWidth": 3.4,
"Species": "virginica"
},
{
"PetalLength": 5.1,
"PetalWidth": 1.8,
"SepalLength": 5.9,
"SepalWidth": 3.0,
"Species": "virginica"
}
]
},
"encoding": {
"color": {
"field": "Species",
"type": "nominal"
},
"x": {
"field": "PetalLength",
"type": "quantitative"
},
"y": {
"field": "PetalWidth",
"type": "quantitative"
}
},
"mark": "point"
},
"image/png": "",
"image/svg+xml": [
"setosa versicolor virginica Species 0 1 2 3 4 5 6 7 PetalLength 0.0 0.5 1.0 1.5 2.0 2.5 PetalWidth "
],
"text/plain": [
"VegaLite.VLSpec{:plot}"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"TypeError: Cannot read property 'getContext' of null\n",
" at resize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:3377:26)\n",
" at CanvasRenderer.prototype$6.resize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:3427:5)\n",
" at CanvasRenderer.prototype$4.initialize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:2989:17)\n",
" at CanvasRenderer.prototype$6.initialize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:3422:28)\n",
" at initializeRenderer (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-view/build/vega-view.js:630:8)\n",
" at renderHeadless (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-view/build/vega-view.js:736:12)\n",
" at processTicksAndRejections (internal/process/task_queues.js:93:5)\n",
" at async View.renderToCanvas [as toCanvas] (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-view/build/vega-view.js:771:15)\n"
]
}
],
"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": [
"Another useful tool for exploring tabular data is [DataVoyager.jl](https://github.com/queryverse/DataVoyager.jl)."
]
},
{
"cell_type": "markdown",
"metadata": {
"hide-output": false
},
"source": [
"```julia\n",
"using DataVoyager\n",
"iris |> Voyager()\n",
"```\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `Voyager()` function creates a separate window for analysis."
]
},
{
"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) 0.265947 0.0145253 18.3092 <1e-32 0.237122 0.294772\n",
"x 0.901144 0.0157633 57.1671 <1e-76 0.869862 0.932425\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) 0.266***\n",
" (0.015)\n",
"x 0.901***\n",
" (0.016)\n",
"----------------------\n",
"Estimator OLS\n",
"----------------------\n",
"N 100\n",
"R2 0.971\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 -81.575\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, @model(Sales ~ NDI, fe = StateCategorical + YearCategorical,\n",
" weights = Pop, vcov = cluster(StateCategorical)))\n",
"regtable(fixedeffectresults)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To explore data use the interactive DataVoyager and VegaLite."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"hide-output": false
},
"outputs": [
{
"data": {
"application/vnd.vegalite.v3+json": {
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}
]
},
"encoding": {
"color": {
"field": "Year",
"type": "quantitative"
},
"size": {
"field": "NDI",
"type": "quantitative"
},
"x": {
"field": "Price",
"type": "quantitative"
},
"y": {
"field": "Sales",
"type": "quantitative"
}
},
"mark": "point"
},
"image/png": "",
"image/svg+xml": [
"70 80 90 Year 5,000 10,000 15,000 20,000 NDI 0 50 100 150 200 Price 0 50 100 150 200 250 300 Sales "
],
"text/plain": [
"VegaLite.VLSpec{:plot}"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"TypeError: Cannot read property 'getContext' of null\n",
" at resize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:3377:26)\n",
" at CanvasRenderer.prototype$6.resize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:3427:5)\n",
" at CanvasRenderer.prototype$4.initialize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:2989:17)\n",
" at CanvasRenderer.prototype$6.initialize (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-scenegraph/build/vega-scenegraph.js:3422:28)\n",
" at initializeRenderer (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-view/build/vega-view.js:630:8)\n",
" at renderHeadless (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-view/build/vega-view.js:736:12)\n",
" at processTicksAndRejections (internal/process/task_queues.js:93:5)\n",
" at async View.renderToCanvas [as toCanvas] (/home/ubuntu/.julia/packages/VegaLite/sHyyT/deps/node_modules/vega-view/build/vega-view.js:771:15)\n"
]
}
],
"source": [
"cigar = dataset(\"plm\", \"Cigar\")\n",
"# cigar |> Voyager()\n",
"\n",
"cigar |> @vlplot(\n",
" :point,\n",
" x=:Price,\n",
" y=:Sales,\n",
" color=:Year,\n",
" size=:NDI\n",
")"
]
}
],
"metadata": {
"date": 1580349903.920809,
"download_nb": 1,
"download_nb_path": "https://julia.quantecon.org/",
"filename": "data_statistical_packages.rst",
"filename_with_path": "more_julia/data_statistical_packages",
"kernelspec": {
"display_name": "Julia 1.3.0",
"language": "julia",
"name": "julia-1.3"
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