2c:["$","title",null,{"children":"Decomposing Metrics, Part 1 - Dimensions | Martin Daniel | Observable"}] 31:T436,html `

Let's focus on the United States as an example. Between 1990s and 2000s, the US increased it's carbon emissions from ${d3.format('.3s')(region_decade_map['United States'][1990])} to ${d3.format('.3s')(region_decade_map['United States'][2000])}, hence an absolute ${d3.format('.3s')((region_decade_map['United States'][2000]) - region_decade_map['United States'][1990])} tons of Co2. If we compare that number to the global 1990s value, that is ${d3.format('.3s')((region_decade_map['United States'][2000]) - region_decade_map['United States'][1990])} / ${d3.format('.3s')(world_decade_map[1990])} = ${d3.format('.3f')((region_decade_map['United States'][2000] - region_decade_map['United States'][1990]) / world_decade_map[1990])} That number is called volume change. Think of it as how much the US grew in 2000s compared with the world 1990s baseline. More generally, we can say that the volume change of a dimension x between two dates t1 and t2 for a total value of y, is equal to: `32:T60d,view = { const total_decade = Array.from(d3a.rollup(region_data, v => d3.sum(v, d => d.carbon_emissions), d => Math.floor(d.date.getFullYear() / 10) * 10), ([decade, total_emissions]) => ({decade, total_emissions})) return vl.data(region_data) .title({'text': "Decadal Volume of Co2 Emissions", 'anchor': 'start', 'subtitle': 'US, World - Data from Our World in Data'}) .transform( vl.calculate('floor(year(datum.date) / 10) * 10').as('decade'), vl.filter("datum.region == 'United States'"), vl.groupby('decade').aggregate(vl.sum('carbon_emissions').as('carbon_emissions')), vl.lookup('decade').from(vl.data(total_decade).key('decade').fields('total_emissions')) ) .encode( vl.x().fieldO("decade"), ) .layer([ vl.markBar({'height': 5}) .encode(vl.y().fieldQ("total_emissions").axis({'format':'s', 'title': 'Tons of Co2'})), vl.markBar({'color': 'green'}) .encode(vl.y().fieldQ("carbon_emissions"), vl.tooltip('carbon_emissions').format('.3s')), vl.markText({'dy': -10}) .encode(vl.y().fieldQ("carbon_emissions"), vl.text().field('carbon_emissions').format('.2s')), vl.markText({'dy': -10}) .encode(vl.y().fieldQ("total_emissions"), vl.text().field('total_emissions').format('.2s')), ]) .render() }33:T7b7,volume_change_bis = { const volume_change_80_90 = volume_change(region_decade_map, world_decade_map, 'United States', 1980, 1990) const volume_change_90_20 = volume_change(region_decade_map, world_decade_map, 'United States', 1990, 2000) const vc_data = [{'metric': '1980s to 1990s', 'value': volume_change_80_90}, {'metric': '1990s to 2000s', 'value': volume_change_90_20}] const chart_left = vl.data(region_data) .transform( vl.calculate('floor(year(datum.date) / 10) * 10').as('decade'), vl.filter("datum.region == 'United States'"), vl.groupby('decade').aggregate(vl.sum('carbon_emissions').as('carbon_emissions')), vl.lookup('decade').from(vl.data(world_decade_array).key('decade').fields('carbon_emissions')).as('total_emissions') ) .encode( vl.x().fieldO("decade"), ) .layer([ vl.markBar({'height': 5}) .encode(vl.y().fieldQ("total_emissions").axis({'title': 'Tons Co2', 'format': 's'}), vl.tooltip('total_emissions')), vl.markBar({'color': 'green'}) .encode(vl.y().fieldQ("carbon_emissions"), vl.tooltip('carbon_emissions').format('.3s')), vl.markText({'dy': -10}) .encode(vl.y().fieldQ("carbon_emissions"), vl.text().field('carbon_emissions').format('.2s')), vl.markText({'dy': -10}) .encode(vl.y().fieldQ("total_emissions"), vl.text().field('total_emissions').format('.2s')), ]) const chart_right = vl.markBar() .data(vc_data) .encode(vl.y().fieldO('metric').axis({'title': 'Period'}), vl.x().fieldQ('value').axis({'title': 'Volume Change'}) ) return vl.concat(chart_left, chart_right) .title({'text': "Volume change for United States Co2 Emissions", 'anchor': 'start', 'subtitle': 'Data from Our World in Data'}).render() }34:T616,ctg_toy = { const total_map = d3.nest() .key(d => d.time) .rollup(d => d[0].value) .object(data_ctg.filter(d => d.variable == 'Y')); const dim_map = d3.nest() .key(d => d.variable) .key(d => d.time) .rollup(d => d[0].value) .object(data_ctg); const ctg_x = contribution_to_growth(dim_map, total_map, 'x', 1980, 1990, 10) const ctg_z = contribution_to_growth(dim_map, total_map, 'v', 1980, 1990, 10) const volume_change_z = ((data_ctg[5].value - data_ctg[4].value) / data_ctg[0].value).toString(); console.log(ctg_x); const vc = vl.markBar() .data([ // {'variable': 'y', 'metric': 'Y Growth Rate 1980','value': total_map[1980] / total_map[1970]}, // {'variable': 'y', 'metric': 'Y Growth Rate 1990','value': total_map[1990] / total_map[1980]}, {'variable': 'Y', 'metric': 'Y Growth Rate acceleration','value': (total_map[1990] / total_map[1980]) - (total_map[1980] / total_map[1970])}, {'variable': 'x', 'metric': 'x Contribution to Growth','value': ctg_x}, {'variable': 'v', 'metric': 'v Contribution to Growth','value': ctg_z}] ) .encode( vl.y().fieldO('metric'), vl.x().fieldQ('value'), vl.color().fieldN('variable') ) const gr = vl .data(data_ctg) .encode( vl.x().fieldO('time'), vl.y().fieldQ('value'), ) .layer([ vl.markRect({'height': 5}).encode(vl.color().fieldN('variable')), vl.markText({'dy': -10}).encode(vl.text().field('variable'))] ) return vl.concat(gr, vc).title("Growth Rate and Contribution to Growth") .render() }35:T601,function plot_waterfall(dimension_map, total_map, dimension_name, t1, t2, step) { const data = prepare_waterfall_data(dimension_map, total_map, dimension_name, t1, t2, step); return vl.data(data) .title({'text': 'Contribution to Co2 Growth by ' +dimension_name, 'subtitle': 'Bewteen ' + t1 + ' and ' + t2, 'anchor': 'start', }) .transform( vl.window(vl.first_value(vl.fieldQ('ctg')).as('first_value'), vl.sum(vl.fieldQ('ctg')).as('cum_ctg') ), vl.calculate("datum.dimension === 'end' ? datum.ctg : datum.cum_ctg").as('end'), vl.calculate("datum.dimension === 'end' ? 0 : datum.cum_ctg - datum.ctg").as('start'), vl.calculate("(datum.dimension === 'end' || datum.dimension === 'start') ? 'growth_rate' : 'ctg'").as('color_cat') ) .encode( vl.y().fieldO('dimension').sort(data).axis({'title': ''}), vl.x().fieldQ('start').axis({'title': ''}), vl.tooltip('ctg').format('2f'), vl.x2().fieldQ('end'), ) .layer( [vl.markBar().encode( vl.color({"condition":[ { "test": "datum.color_cat === 'ctg' & datum.ctg > 0", "value": "#93c4aa" }, { "test": "datum.color_cat === 'ctg' & datum.ctg < 0", "value": "#f78a64"} ], "value": "#f7e0b6" })), vl.markText({'dx':15}).encode(vl.text('ctg').format('.2f'))] ).render() }36:[{"id":"c6a17d32961adc5013b4f5b48b03e9627505ed43e7be7eafcfb2d5cb5fb513e715e7fd6ee4ffb08da96aaa06eb554a0ac8b555f36cd81bcb882d80c104374c7f","href":"https://static.observableusercontent.com/files/c6a17d32961adc5013b4f5b48b03e9627505ed43e7be7eafcfb2d5cb5fb513e715e7fd6ee4ffb08da96aaa06eb554a0ac8b555f36cd81bcb882d80c104374c7f","name":"country_sector_emissions.csv","type":"text/csv","lastModified":1598134269885.552,"size":2176429},{"id":"49776ff4f19d0d43840731a2fa7ac09f94dbe69b3430d2a25a150743bb4bcba7a724dded3b435c4fd892188088d70e61e9131bde2e2db097031a5872769d297a","href":"https://static.observableusercontent.com/files/49776ff4f19d0d43840731a2fa7ac09f94dbe69b3430d2a25a150743bb4bcba7a724dded3b435c4fd892188088d70e61e9131bde2e2db097031a5872769d297a","name":"region_emissions@2.csv","type":"text/csv","lastModified":1598121203411.136,"size":53683}] 2f:{"id":"28ed9dd491f09be4","slug":"decomposing-metrics","title":"Decomposing Metrics, Part 1 - Dimensions","thumbnail":"204ac0677e16bd7aeb073625348ed15bec09e56c26affb0700f51ca8d6116507","access_level":"public","create_time":"$D2020-08-16T13:52:21.213Z","update_time":"$D2022-10-02T15:52:46.027Z","view_time":null,"first_public_time":"$D2020-08-23T14:05:27.407Z","fork":false,"stars":6,"starred":false,"owner":{"type":"team","id":"1285cbe9780022a7","login":"martinda","name":"Martin Daniel","avatar_url":"https://avatars-next.observableusercontent.com/7411c7430fecc4cf8a463a3afae4aa11d972a1cd4a5b5c58860bb0f333e069d2","tier":"starter_2024"},"version":2844,"publish_version":2844,"role":null,"authored":false,"authors":[{"type":"individual","id":"efc81dc346b02bf8","login":"martinda","name":"Martin Daniel","avatar_url":"https://avatars-next.observableusercontent.com/7411c7430fecc4cf8a463a3afae4aa11d972a1cd4a5b5c58860bb0f333e069d2","tier":null}],"members":[{"type":"individual","id":"efc81dc346b02bf8","login":"martinda","name":"Martin Daniel","avatar_url":"https://avatars-next.observableusercontent.com/7411c7430fecc4cf8a463a3afae4aa11d972a1cd4a5b5c58860bb0f333e069d2","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Decomposing Metrics, Part 1 - Dimensions","cells":[{"id":6,"value":"md`# Decomposing Metrics, Part 1 - Dimensions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":0,"value":"md`_Analysis_ comes from the greek world [_analúō_](https://en.wiktionary.org/wiki/%E1%BC%80%CE%BD%CE%AC%CE%BB%CF%85%CF%83%CE%B9%CF%82#grc), which means _dissolving a whole into its parts_. Nothing new under the sun since Aristotle: the modern field of _Analytics_ tries to untangle the components that explain the variation of a phenomemon of interest. \n\nIn this _decomposing metric_ series, I want to show you a couple of frameworks that I found incredibly helpful to understand the variations of metrics. Nothing fancy, just simple arithmetic and intuition to describe and explain the world around us, by _breaking it down into smaller parts_. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1753,"value":"md `### Growth Rates`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"md `Let's start with a problem (and a big one): how can we understand the variations of global Co2 emissions? \n\nWe will use data compiled by [Our World in Data](https://ourworldindata.org/grapher/annual-co-emissions-by-region) that can easily be downloaded from [that link](https://ourworldindata.org/grapher/annual-co-emissions-by-region). That dataset retrieves yearly tons of Co2 emitted by different regions of the world since 1750. For simplicity we will use data from 1900 onwards:`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":185,"value":"vl.markBar()\n .title({'text': 'Yearly Evolution of Global Co2 emissions',\n 'subtitle': 'Data from Our World in Data',\n 'anchor': 'start'})\n .data(world_year_array)\n .encode(\n vl.x().fieldT('date'),\n vl.y().fieldQ('carbon_emissions').axis({'title': 'Tons of Co2', 'format': \"s\"}),\n vl.tooltip('carbon_emissions').format('.3s')\n )\n .render()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1767,"value":"html `

In 1900, the world emitted ${d3.format(\".3s\")(world_year_map[1900])} tons of Co2 in the athmosphere. That number grew to ${d3.format(\".3s\")(world_year_map[2018])} in 2018. \n

To simplify things, we will sum up Co2 emissions by decade. In the 1900s the World emitted ${d3.format(\".4s\")(world_decade_map[1900])} tons of Co2 and that number grew to ${d3.format(\".4s\")(world_decade_map[2000])} in the 2000s. Note that we do not have full data for the 2010 decade as our dataset ends in 2018.

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1261,"value":"html ``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":502,"value":"vl.markBar()\n .title({'text': 'Decadal Volume of Global Co2 Emissions',\n 'anchor': 'start',\n 'subtitle': 'Data from Our World in Data'})\n .data(world_year_array)\n .transform(\n vl.calculate('floor(year(datum.date) / 10) * 10').as('decade'),\n vl.groupby('decade')\n .aggregate(vl.sum('carbon_emissions').as('carbon_emissions'))\n )\n .encode(\n vl.x().fieldO('decade').axis({'title': 'Decade'}),\n vl.y().fieldQ('carbon_emissions').axis({'title': 'Tons of Co2', 'format': \"s\"}),\n vl.tooltip('carbon_emissions').format('s')\n )\n .render()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1264,"value":"html `To compute a decadal growth rate , we simply divide the value of emissions on a given decade by the previous one. For instance, in 2000s, carbon emissions grew by ${d3.format('.2f')(world_decade_map[2000] / world_decade_map[1990])} versus the 1990s value. \n\nYou can use any baseline for your growth rate: day, week, month, year etc.. Analysts will often use year over year to compare with a similar period last year (which can be handy when you have seasonality to smooth out).\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"vl.data(world_year_array)\n .title({'text': 'Decadal Volume and Growth Rate of Global Co2 Emissions',\n 'anchor': 'start',\n 'subtitle': 'Data from Our World in Data'})\n .transform(\n vl.calculate('floor(year(datum.date) / 10) * 10').as('decade'),\n vl.groupby('decade')\n .aggregate(vl.sum('carbon_emissions').as('carbon_emissions')),\n vl.window({\"op\": \"lag\", \n \"field\": \"carbon_emissions\",\n \"as\": \"last_decade\"})\n .sort(vl.field('decade').order('ascending')),\n vl.calculate('datum.carbon_emissions / datum.last_decade').as('growth_rate')\n )\n .encode(\n vl.x().fieldO('decade').axis({'title': 'Decade'}),\n vl.y().fieldQ('carbon_emissions').axis({'title': 'Tons of Co2', 'format': \"s\"}),\n )\n .layer(\n vl.markBar()\n .encode(vl.tooltip('carbon_emissions').format('.3s')),\n vl.markText({'dy': -5})\n .encode(vl.text('growth_rate').format('.2f'))\n )\n .render();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"html `So between the 1990s and 2000s, carbon emissions have increased from ${d3.format('.2f')(world_decade_map[1990] / world_decade_map[1980])} to ${d3.format('.2f')(world_decade_map[2000] / world_decade_map[1990])}. The difference is then ${d3.format('.3f')((world_decade_map[2000] / world_decade_map[1990]) - (world_decade_map[1990] / world_decade_map[1980]))}x. How can we explain that acceleration?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":538,"value":"md `Let's split the same graph per region of the world. Here each color represents the total emissions for a given region. You can mouse over the graph to get the exact value.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"vl.markBar()\n .title({'text': 'Decadal Volume of Regional Co2 Emissions',\n 'subtitle': 'Data from Our World in Data',\n 'anchor': 'start'})\n .data(region_data)\n .transform(\n vl.calculate('floor(year(datum.date) / 10) * 10').as('decade'),\n vl.groupby(['decade', 'region'])\n .aggregate(vl.sum('carbon_emissions').as('carbon_emissions')),\n vl.window({\"op\": \"lag\", \n \"field\": \"carbon_emissions\",\n \"as\": \"last_decade\"})\n .sort(vl.field('decade').order('ascending'),\n vl.field('region').order('descending'),),\n vl.calculate('datum.carbon_emissions / datum.last_decade').as('growth_rate')\n )\n .encode(\n vl.facet(vl.fieldO('region'), {'columns': 4}),\n vl.x().fieldT(\"decade\").type('ordinal'),\n vl.y().fieldQ(\"carbon_emissions\")\n .axis({'format': \"s\",\n 'title': 'Tons of Co2'}),\n vl.tooltip(['region', 'decade', 'carbon_emissions']),\n vl.color().fieldN(\"region\")\n )\n .render()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2569,"value":"md `Similar to the graph above, we can compute the decadal growth rate of Co2 emissions for each region of the world: `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1881,"value":"vl.markBar()\n .title({'text': 'Decadal Growth Rate of Regional Co2 Emissions',\n 'subtitle': 'Data from Our World in Data',\n 'anchor': 'start'})\n .data(region_data)\n .transform(\n vl.calculate('floor(year(datum.date) / 10) * 10').as('decade'),\n vl.groupby(['decade', 'region'])\n .aggregate(vl.sum('carbon_emissions').as('carbon_emissions')),\n vl.window({\"op\": \"lag\", \n \"field\": \"carbon_emissions\",\n \"as\": \"last_decade\"})\n .groupby(vl.field('region'))\n .sort(vl.field('region').order('ascending'),\n vl.field('decade').order('ascending')),\n vl.calculate('datum.carbon_emissions / datum.last_decade').as('growth_rate')\n )\n .encode(\n vl.facet(vl.fieldO('region'), {'columns': 4}),\n vl.x().fieldT(\"decade\").type('ordinal'),\n vl.y().fieldQ(\"growth_rate\")\n .axis({'format': \"s\",\n 'title': 'Metrics Tons of Co2'}),\n vl.color(vl.fieldN('region')),\n vl.tooltip('growth_rate').format('.3s'),\n )\n .render()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1272,"value":"md `## Volume Change`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":631,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2209,"value":"md `## ${tex `v = {\\frac{x(t1) - x(t2)}{y(t1)}}`}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1493,"value":"function volume_change(dimension_map, total_map, dimension, t1, t2){\n return (dimension_map[dimension][t2] - dimension_map[dimension][t1]) / total_map[t1]\n};","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":669,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1224,"value":"md `Below is an illustration of volume change for a toy dataset. You can play with the parameter to measure the volume change. Notice that when x_t1 = 0 and x_t2 = Y_t2, we have 100% volume change. That makes sense, it essentially means that the dimension x \"explains\" 100% of the variation.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1154,"value":"data_test = [{'variable':'y', 'value': 50, 'time': 1980},\n {'variable':'y', 'value': 100, 'time': 1990},\n {'variable':'x', 'value': range_x[0], 'time': 1980},\n {'variable':'x', 'value': range_x[1], 'time': 1990}];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1196,"value":"viewof range_x = {\n const form = html``;\n form.oninput = () => form.value = [\n form.xt1.valueAsNumber, \n form.xt2.valueAsNumber, \n ];\n form.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":862,"value":"v = {\n \nconst volume_change = ((data_test[3].value - data_test[2].value) / data_test[0].value).toString();\nconst growth_rate = (data_test[1].value / data_test[0].value)\n\nconst vc = vl.markBar()\n .data([{'variable': 'x', 'metric': 'X volume change','value': volume_change},\n {'variable': 'y', 'metric': 'Y Growth Rate','value': growth_rate}]\n )\n .encode(\n vl.y().fieldO('metric'),\n vl.x().fieldQ('value'),\n vl.color().fieldO('variable')\n )\n\nconst gr = vl\n .data(data_test)\n .encode(\n vl.x().fieldO('time'),\n vl.y().fieldQ('value'),\n )\n .layer([\n vl.markRect({'height': 5}).encode(vl.color().fieldO('variable')),\n vl.markText({'dy': -10}).encode(vl.text().field('variable'))]\n )\n\nreturn vl.concat(gr, vc).title(\"Growth Rate and Volume Change\")\n .render()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":869,"value":"md `Since we want to understand the difference between two growth rates, we need to repeat the same process for the difference between the 1990s and 2000s. Below we compute the two volume changes for the US.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2730,"value":"html `

In the 1990s, the US explained ${d3.format('.3f')(volume_change(region_decade_map, world_decade_map, 'United States', 1980, 1990))} of global Co2 growth rate and in the 2000s, that number dropped to ${d3.format('.3f')(volume_change(region_decade_map, world_decade_map, 'United States', 1990, 2000))}. The difference between those two numbers (${d3.format('.3f')(volume_change(region_decade_map, world_decade_map, 'United States', 1990, 2000) - volume_change(region_decade_map, world_decade_map, 'United States', 1980, 1990))}) is called Contribution to Growth.

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1337,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1374,"value":"md `## Contribution To Growth`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1367,"value":"md `Contribution to Growth is then defined as : \n\n> Contribution to Growth (t1, t2) = Volume Change (t2) - Volume Change (t1)\n\nBelow is another toy example displaying the contribution to growth of two variable (v,x) in the acceleration of a variable y. You can play with the values of x at 3 different times: 1970, 1980 and 1990. Notice the following pattern: the sum of (v,x) contribution to growth is always equal to the growth rate acceleration of our variable Y.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2393,"value":"data_ctg = [ {'variable':'Y', 'value': 50, 'time': 1970},\n {'variable':'Y', 'value': 55, 'time': 1980},\n {'variable':'Y', 'value': 100, 'time': 1990},\n {'variable':'x', 'value': range_ctg[0], 'time': 1970},\n {'variable':'x', 'value': range_ctg[1], 'time': 1980},\n {'variable':'x', 'value': range_ctg[2], 'time': 1990},\n {'variable':'v', 'value': 50 - range_ctg[0], 'time': 1970},\n {'variable':'v', 'value': 55 - range_ctg[1], 'time': 1980},\n {'variable':'v', 'value': 100 - range_ctg[2], 'time': 1990}];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2399,"value":"viewof range_ctg = {\n const form = html``;\n form.oninput = () => form.value = [\n form.xt1.valueAsNumber,\n form.xt2.valueAsNumber, \n form.xt3.valueAsNumber, \n ];\n form.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2404,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2578,"value":"html `

Going back to our Co2 example, we find that between 1990s and 2000s, the US contributed ${d3.format('.3f')(contribution_to_growth(region_decade_map, world_decade_map, 'United States', 1990, 2000, 10))} to the global ${d3.format('.3f')((world_decade_map[2000] / world_decade_map[1990]) - world_decade_map[1990] / world_decade_map[1980])} acceleration. Intuitively, that means that the US contributed more to the 1990s than it did in the 2000s. So which other regions contributed positively to our global acceleration? Let's take a look at China:

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1515,"value":"function contribution_to_growth(dimension_map, total_map, dimension, t1, t2, step){\n const volume_change_1 = volume_change(dimension_map, total_map, dimension, (t1 - step), t1)\n const volume_change_2 = volume_change(dimension_map, total_map, dimension, (t2 - step), t2)\n return volume_change_2 - volume_change_1\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2301,"value":"contribution_to_growth(region_decade_map, world_decade_map, 'China', 1990, 2000, 10)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2309,"value":"html `Interesting! China contributed +${d3.format('.3f')(contribution_to_growth(region_decade_map, world_decade_map, 'China', 1990, 2000, 10))}x to our 1990s > 2000s Co2 acceleration. Since we wanted to explain ${d3.format('.3f')((world_decade_map[2000] / world_decade_map[1990]) - (world_decade_map[1990] / world_decade_map[1980]))}x, that's ~2/3 of our acceleration! \n\nWe can visualize each region contribution in the Waterfall graph below. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1716,"value":"plot_waterfall(region_decade_map, world_decade_map, 'region', 1990, 2000, 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2347,"value":"html `Let's try with another period. Between the 1960s and 1970s, Co2 emissions have increased from ${d3.format('.2f')(world_decade_map[1960] / world_decade_map[1950])} to ${d3.format('.2f')(world_decade_map[1970] / world_decade_map[1960])}. The difference is then ${d3.format('.2f')((world_decade_map[1970] / world_decade_map[1960]) - d3.format('.2f')(world_decade_map[1960] / world_decade_map[1950]))}x, here is the breakdown: `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2356,"value":"plot_waterfall(region_decade_map, world_decade_map, 'region', 1960, 1970, 10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2388,"value":"md `Quite a different story isn't it? Here we find that western countries like Europe (excl. EU-28) and the US are the main culprit.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2501,"value":"md `## Multiple Dimensions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2669,"value":"md `Since we can decompose a metric in mutually exclusive segments, we can combine multiple segments in our contribution to growth. To illustrate that idea, I have added another dataset from [Our World in Data](https://ourworldindata.org/emissions-by-sector#annual-co2-emissions-by-sector) that splits yearly Co2 emissions by **country** and **sector** of the economy. Given data is not available prior 1990, I have decided to aggregate that data on a 5 years window. Below is a volume graph of Co2 emissions with a 5-year step:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2446,"value":"vl.markBar()\n .title({'text': '5-years Volume of Global Co2 by Sector',\n 'subtitle': 'Data from Our World in Data',\n 'anchor': 'start'})\n .data(sector_data)\n .transform(\n vl.calculate('floor(year(datum.date) / 5) * 5').as('date'),\n vl.groupby(['date', 'sector'])\n .aggregate(vl.sum('carbon_emissions').as('carbon_emissions')),\n )\n .encode(\n vl.facet(vl.fieldO('sector'), {'columns': 4}),\n vl.x().fieldO(\"date\"),\n vl.y().fieldQ(\"carbon_emissions\").axis({'format': 's'}),\n vl.tooltip(['sector', 'carbon_emissions']),\n vl.color().fieldN(\"sector\")\n )\n .render()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2689,"value":"md `Similar to previous decomposition, we can decompose Co2 emissions growth rate acceleration between 2000 and 2005:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2520,"value":"plot_waterfall(sector_5years_map, world_5years_map, 'sector', 2000, 2005, 5)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2692,"value":"md `Running that same decomposisition by country and sector reveals other trends. Between 2000 and 2005, acceleration was mainly driven by China _Manufacturing & Construction_ sector as well as _Electricity & Heat_.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2635,"value":"plot_waterfall(sector_country_5years_map, world_5years_map, 'Country, Sector', 2000, 2005, 5)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2696,"value":"md `## That's it! What's next? \n\nCongrats 🎉. You made it to the end of Part 1 of metrics decomposition serie. You have learned how to compute _volume change_ and _contribution to growth_ to decompose growth rate acceleration by mutually exclusive segments. \n\nIn the next posts, we will explore how to decompose a metric via multiplicative equations. Here is a [little teaser](https://en.wikipedia.org/wiki/Kaya_identity).\n\nI hope you found that write up useful. Feel free to share your thoughts on [Twitter](https://twitter.com/martindaniel4)!\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"import {vl} from '@vega/vega-lite-api'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"import {printTable} from '@uwdata/data-utilities'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1923,"value":"region_data = d3.csvParse(await FileAttachment(\"region_emissions@2.csv\").text(), d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2179,"value":"region_year_map = d3.nest()\n .key(function(d) { return d.region; })\n .key(function(d) { return d.date.getFullYear(); })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(region_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2046,"value":"world_year_map = d3.nest()\n .key(function(d) { return d.date.getFullYear(); })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(region_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2185,"value":"region_decade_map = d3.nest()\n .key(function(d) { return d.region;})\n .key(function(d) { return Math.floor(d.date.getFullYear() / 10) * 10; })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(region_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2253,"value":"world_decade_array = Array.from(\n d3.nest()\n .key(function(d) { return Math.floor(d.date.getFullYear() / 10) * 10})\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .entries(region_data),\n d => ({'decade': +d['key'], 'carbon_emissions': d['value']}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2007,"value":"world_year_array = Array.from(\n d3.nest()\n .key(function(d) { return d.date})\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .entries(region_data),\n d => ({'date': d['key'], 'carbon_emissions': d['value']}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2083,"value":"world_decade_map = d3.nest()\n .key(function(d) { return Math.floor(d.date.getFullYear() / 10) * 10; })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(region_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2513,"value":"world_5years_map = d3.nest()\n .key(function(d) { return Math.floor(d.date.getFullYear() / 5) * 5; })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(sector_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2442,"value":"sector_data = d3.csvParse(await FileAttachment(\"country_sector_emissions.csv\").text(), d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2515,"value":"sector_5years_map = d3.nest()\n .key(function(d) { return d.sector; })\n .key(function(d) { return Math.floor(d.date.getFullYear() / 5) * 5; })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(sector_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2631,"value":"sector_country_5years_map = d3.nest()\n .key(function(d) { return d.region + ', ' +d.sector; })\n .key(function(d) { return Math.floor(d.date.getFullYear() / 5) * 5; })\n .rollup(function(v) { return d3.sum(v, function(d) { return d.carbon_emissions; }); })\n .object(sector_data);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1659,"value":"function prepare_waterfall_data(dimension_map, total_map, dimension, t1, t2, step) {\n \n const ctg = Object.keys(dimension_map).map(d => { \n const o = {}\n o['dimension'] = d;\n o['ctg'] = contribution_to_growth(dimension_map, total_map, d, t1, t2, step);\n return o;\n });\n \n const growth_rate_t1 = total_map[t1] / total_map[t1-step];\n const growth_rate_t2 = total_map[t2] / total_map[t2-step];\n const top_n = 7;\n \n // Filter top_n dimensions and filter the rest in Other\n ctg.sort((a,b) => Math.abs(b.ctg) - Math.abs(a.ctg))\n const top_10 = ctg.slice(0, top_n);\n const ctg_other = d3.sum(ctg.slice(top_n, ctg.length), d => d.ctg);\n top_10.push({'dimension': 'Other', 'ctg': ctg_other}) \n \n // Add start and end\n top_10.sort((a,b) => {return b.ctg - a.ctg})\n top_10.unshift({'dimension': 'start', 'ctg': growth_rate_t1})\n top_10.push({'dimension': 'end', 'ctg': growth_rate_t2})\n \n return top_10\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1555,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":643,"value":"d3a = require(\"d3-array@^2.2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 30:"$2f:body" 2b:E{"digest":"NEXT_REDIRECT;replace;/@martinda/decomposing-metrics;307;"}