Linked visuals for data exploration 🔍🎯

Here’s a type of visualization I haven’t gotten excited to share in a while:

A visualization on entirely static data!

Below are 8,155 policy data points in a scatterplot along with distributions for key features.

All visuals are interactive and linked (‘coordinated’); you can:

• drag to filter intervals on the scatterplot or the distributions above it
• toggle the features below it

Visuals, summary stats and the table all update like ⚡ thanks to a neat coming-together of technology described below.

Duration is very significant here, so I map it to the color scale; sum assured likewise and I map it to the plot x axis.

There are still variances that can be explored using interactions on other features. Outlier details can be picked up using the table.

Linked interaction is also helpful for higher-level exploration:

• How many policies are ‘profitable’ versus ‘unprofitable’ (roughly)? What are corresponding values?
• Are new policies (low duration in force) ‘profitable’? Are all of them?

“value of future cashflows” & duration

The value is of calculated future cashflows for life term assurance policies; more information linked under ‘data origin & actuarial model’.

The policies are ‘in force’: duration in force indicating how long ago they started.

There are no reserve cashflows or other accounting smoothing included¹, so the value profile is heavily dependant on duration:

• at later durations policy holders are older, and are usually loss-making due to higher death/claim probabilities
• whereas at early durations they are generally profit-making for the insurance company

🖌️🕹️

viewof x = {
  await vg.coordinator().exec(
    vg.sql`CREATE TABLE IF NOT EXISTS policy_data AS
    SELECT *, pv_net_cf/policy_count as pv_net_cf_pp,
    (age_at_entry-20)*4 as age_at_entry_color
     FROM 'https://calcwithdec.dev/posts/linked-visuals/policy-results-SE-noNB.parquet'
    --FROM 'http://127.0.0.1:8080/posts/mosaic-cashflow-aggregates/policy-results-SE-noNB.parquet'
    WHERE (duration_mth != policy_term*12)
    `
  );

  // policy_data2 workaround for query needed for selection total
  // (see summary below)
  await vg.coordinator().exec(vg.sql`CREATE TABLE IF NOT EXISTS policy_data2 AS SELECT * from policy_data`);

  // can't param the color domain, so I remap age values in age_at_entry_color above
  const $color_field = vg.Param.value("duration_mth");
  const color_scheme = "turbo";

  const $filter = vg.Selection.crossfilter(); // for everything
  const $highlight = vg.Selection.intersect(); // for term
  const $highlight2 = vg.Selection.intersect(); // for sex

  const dots = vg.plot(
    vg.frame({ fill: "#fff9fd" }),
    vg.dot(vg.from("policy_data", { filterBy: $filter }), {
      x: "sum_assured",
      y: "pv_net_cf_pp",
      fill: vg.sql`if(${$color_field}='duration_mth',duration_mth, age_at_entry_color)`,
      symbol: "sex",
      minWidth: 600,
      // tip: true, // too much noise and doesn't show p; table better atm
      r: 2
    }),
    vg.colorScheme(color_scheme),
    vg.aspectRatio(0.8),
    //vg.grid(true), // doesn't work with frame
    vg.xLabelAnchor("center"),
    vg.xLabelOffset(30),
    vg.xLabel("sum assured"),
    vg.yLabel(
      "value future cashflows (premiums - claims - expenses incl. commissions)"
    ),
    vg.yLabelOffset(-20),

    vg.name("dots"),
    vg.intervalXY({ as: $filter }),
    vg.xDomain([0, 1e6]),
    vg.yDomain([-12.6e3, 22.8e3]), // -12.3k to 22.2k
    vg.width(550),
    //vg.minWidth(450),
    vg.height(400 - 100),
    vg.colorDomain(vg.Fixed),
    vg.axisY({
      ticks: 3,
      tickFormat: d3.format(".1s")
    }),
    vg.axisX({
      // if axiX/Y of these appears earlier interactions break!
      tickFormat: d3.format(".1s")
    }),
    // vg.symbolDomain(vg.Fixed) not possible
    vg.margins({ left: 35, top: 20, bottom: 30, right: 20 })
  );

  // now mostly a lot of repetition:

  const terms = vg.plot(
    vg.barY(vg.from("policy_data", { filterBy: $filter }), {
      x: "policy_term",
      y: vg.count(),
      fill: "green"
    }),
    vg.yAxis(null),
    vg.toggleX({ as: $filter }),
    vg.toggleX({ as: $highlight }),
    vg.highlight({ by: $highlight }),
    vg.xDomain(vg.Fixed),
    vg.axisX({ label: "policy term", labelAnchor: "center" }),
    vg.axisY({
      label: "#",
      labelAnchor: "center",
      ticks: 2,
      tickFormat: d3.format(".1s")
    }),
    vg.width((450 * 5) / 8 - 100),
    vg.height(80)
  );

  const ages = vg.plot(
    vg.rectY(vg.from("policy_data", { filterBy: $filter }), {
      x: vg.bin("age_at_entry"), // must be binned for intervalX
      y: vg.count(),
      fill: "steelblue", // how to condition on $color_field ?
      inset: 0.5
    }),
    vg.xAxis("top"),
    vg.xLabel("age at entry"),
    vg.xLabelAnchor("center"),
    vg.yAxis(null),
    vg.xTicks([]),
    vg.xDomain(vg.Fixed),
    vg.intervalX({ as: $filter }), // create an interval selection brush
    vg.xDomain(vg.Fixed), // don't change the x-axis domain across updates
    vg.axisY({
      label: "#",
      labelAnchor: "center",
      ticks: 2,
      tickFormat: d3.format(".1s")
    }),
    vg.axisX({
      label: "",
      ticks: [20, 40, 60]
    }),
    vg.width(400),
    vg.height(80)
  );

  const durs = vg.plot(
    vg.rectY(vg.from("policy_data", { filterBy: $filter }), {
      x: vg.bin("duration_mth"),
      y: vg.count(),
      fill: vg.bin("duration_mth"),
      inset: 0.5
    }),
    vg.colorDomain(vg.Fixed),
    vg.colorScheme(color_scheme),
    vg.xAxis("top"),
    vg.xLabel("duration in force (yrs)"),
    vg.xLabelAnchor("center"),
    vg.yAxis(null),
    vg.xTicks([]),
    vg.xDomain(vg.Fixed),
    vg.intervalX({ as: $filter }), // create an interval selection brush
    vg.xDomain(vg.Fixed), // don't change the x-axis domain across updates
    vg.axisX({
      label: "",
      tickFormat: (d) => d / 12,
      ticks: [0, 120, 180, 240]
    }),
    vg.axisY({
      label: "#",
      labelAnchor: "center",
      ticks: 2,
      tickFormat: d3.format(".1s")
    }),
    vg.width(400),
    vg.height(80)
  );

  const sex = vg.plot(
    vg.barY(vg.from("policy_data", { filterBy: $filter }), {
      x: "sex",
      y: vg.count(),
      fill: "purple"
    }),
    vg.toggleX({ as: $filter }),
    vg.toggleX({ as: $highlight2 }),
    vg.highlight({ by: $highlight2 }),
    vg.xDomain(vg.Fixed),
    vg.axisX({ label: "sex", labelAnchor: "center" }),
    vg.axisY({
      label: "#",
      labelAnchor: "center",
      ticks: 2,
      tickFormat: d3.format(".1s")
    }),
    vg.width((450 * 3) / 8 - 50),
    vg.height(80)
  );

  const summary_count = vg.plot(
    vg.text(vg.from("policy_data2", { filterBy: $filter }), {
      x: 0.1, //vg.sum(0),
      y: 0, //vg.sum(1),
      text: vg.sql`count(*)`, //vg.sum(vg.sql`pv_net_cf_pp`)
      fontSize: 20,
      //fontFamily: "monospace",
      anchor: "right",
      fill: vg.sql`if(sum("pv_net_cf_pp") > 0, 3, 2)` // -> colorDomain -> category10 scheme
    }),
    vg.yDomain([0, 1]),
    vg.xDomain([0, 1]),
    vg.colorDomain([1, 2, 3, 4]),
    vg.colorScheme("category10"),
    vg.xAxis(null),
    vg.yAxis(null),
    vg.axisY({
      label: "# selected policies ..",
      labelAnchor: "top",
      ticks: []
    }),
    vg.height(50)
  );

  const summary_value = vg.plot(
    vg.text(vg.from("policy_data2", { filterBy: $filter }), {
      x: 0.1, //vg.sum(0),
      y: 0, //vg.sum(1),
      text: vg.sql`sum("pv_net_cf_pp")`, //vg.sum(vg.sql`pv_net_cf_pp`)
      fontSize: 15,
      fontFamily: "monospace",
      anchor: "right",
      fill: vg.sql`if(sum("pv_net_cf_pp") > 0, 3, 2)` // -> colorDomain -> category10 scheme
    }),
    vg.yDomain([0, 1]),
    vg.xDomain([0, 1]),
    vg.colorDomain([1, 2, 3, 4]),
    vg.colorScheme("category10"),
    vg.xAxis(null),
    vg.yAxis(null),
    vg.axisY({
      label: "selected total value ..",
      labelAnchor: "top",
      ticks: []
    }),
    vg.height(50)
  );

  const table = vg.table({
    from: "policy_data",
    height: 150,
    width: 150,
    filterBy: $filter,
    format: { p: (d) => d },
    columns: ["p", "pv_net_cf_pp"], // comment this for complete data
    width: { p: 50 }
  });

  return vg.hconcat(
    vg.vconcat(
      ages,
      vg.vspace(10),
      durs,
      vg.vspace(10),
      dots,
      vg.hconcat(terms, sex),

      // 🚧
      vg.menu({
        label: "🚧 color field ⚠️ ",
        as: $color_field,
        options: ["age_at_entry", "duration_mth"]
      })
    ),
    vg.hspace(10),
    vg.vconcat(vg.vspace(90), vg.vconcat(summary_count,summary_value), table, vg.vspace(100))
  );
}

data origin & actuarial model

Data comes from running lifelib: “an open-source Python package featuring practical actuarial models, tools, and examples”, specifically the Basic Term SE model and in it’s default configuration.

These default model points were randomly generated; but I removed some future new business and reversed a modelled effect of scaling by policy_count: so that now each mark above represents the value of one policy (pv_net_cf_pp).

My data manipulation carried out in Python is in this notebook 📓.

Other adjustments are included with the visualization code².

interaction technology

I made this because I was excited to try Mosaic: a visualization framework from UW Interactive Data Lab and CMU Data Interaction Group: the same people who develop Vega, Vega Lite³ along with other cutting-edge visualization/interaction work and research.

There’s more cool stuff behind-the-scenes. Mosaic is fast like ⚡ by pushing processing to a database, and DuckDB-Wasm is a database that makes this possible in your browser: without the complexity of a remote database, although that’s also an option.

The code is ~250 lines but is a lot of repetition, and I have the flexibility of SQL in there - besides an elegant visualization API that’s also facilated by Observable Plot.

Obligatory

If ~8k data points doesn’t impress you, try 10 million or else 7.6 million !

lifelib & Python

lifelib & Python are other awesome things I was glad to use here; I’ll post more on both in future.

// import vgplot and configure Mosaic to use DuckDB-WASM
vg = {
  const vg = await import('https://cdn.jsdelivr.net/npm/@uwdata/vgplot@0.7.1/+esm');
  vg.coordinator().databaseConnector(vg.wasmConnector());
  return vg;
}

Footnotes

1. Reserves and accounting rules are very important in insurance! More on this in a future post

2. View Source linked at the bottom of this page

3. I use Vega/Vega Lite in most of my published visualization/interaction work